ADVANCED OPTION PRICE MOVEMENTS

ADVANCED OPTION PRICE MOVEMENTS




The concepts outlined in this chapter form the basis for the option strategies in Part Two. These concepts expand on the basics in Chapter 3. They are not necessary for most traders who are mainly looking at option strategies to hold to expiration. The first topic in this chapter will be a quick introduction to option pricing models, particularly the Black-Scholes Model. Also discussed will be the greeks and how they affect the price of an option; probability distributions and how they affect options; option pricing models and their advantages, disadvantages, and foibles and using them. The final major topic will be the concept of delta neutral.


which is a key concept for many of the advanced strategies in this book. Which option should you buy? What if you are looking for the price of Widget futures to move from 50 to 60 over the next four months? Do you buy the option that expires in three months and roll it over near expiration? Or do you buy the six-month option and liquidate it in four months? The answer to these questions is whichever option maximizes profit for a given level of risk.


To decide on an option, you need to find the fair value and characteristics of the various options available for your preferred strategy. You need to find out which option provides the best value, which requires an ability to determine the fair value of an option and to monitor the changes in that fair value. You must be able to determine the likely future price of that option, given changes in such critical components of options prices as time, volatility, and the change in the price of the underlying instrument (UI)


OPTION PRICING MODELS




Option pricing models help you answer key questions:
* What is a particular option worth?

* Is the option over- or undervalued?
* What will the option price be under different scenarios?


Option pricing models provide guidance, not certainty. The output of an option pricing model is based on the accuracy of the model itself as well as the accuracy and timeliness of the inputs. Option pricing models provide a compass to aid in evaluating an option or an option strategy. However, no option model has yet been designed that truly takes into account the totality of reality. Corners are cut, so only an approximation of reality is represented in the models. The model is not reality but only a guide to reality. Thus, the compass is slightly faulty, but having it is better than wandering blindly in the forest. Option pricing models allow the trader to deal with the complexity of options rather than be overwhelmed. 


Option pricing models provide a framework for analysis of specific options and option strategies. They give the strategist an opportunity to try out “what if” scenarios. Although option pricing models are not 100 percent accurate, they provide more than enough accuracy for nearly all option trading styles. The inability to account for the last tick in the price of an option is essentially irrelevant for nearly all traders. On the other hand, arbitrageurs, who are looking to make very small profits from a large number of trades, need to be keenly aware of the drawbacks and inaccuracies of option pricing models. They must look at every factor through a microscope. 


 One early book that was related to options pricing was Beat the Market by Sheen Kassouf and Ed Thorp. This book sold very well and outlined a method of evaluating warrants on stocks, which are essentially long-term options on stocks. However, these models that came before the Black-Scholes Model are rarely mentioned today mainly because of two factors: (1) they were not arbitrage models; and (2) options were not popular, so few traders or academics were paying attention to options pricing problems.

Arbitrage Models


An arbitrage model is a pricing model in which all the components of the model are related to each other in such a way that if you know all of the components of the model but one, you can solve for the unknown component. This applies to all of the components. It ties up all the factors relating to the pricing of an option in one tidy package. Furthermore, an arbitrage model is a model that prices the option, given certain inputs, at a price where the buyer or seller would be ambivalent between the UI and the option. 

 
For example, a thoroughly rational bettor would be ambivalent between being given $1 or putting up $1 with another bettor and flipping a coin to see who wins the $2. The expected return from both of these deals is $1. An arbitrage model attempts to do the same thing. The expected return from, say, owning 100 shares of Widget mania at $50 should be exactly the same as owning an option to buy the same shares. There are many different option pricing models. The most popular is the Black-Scholes Model. Other models for pricing options are:


* Cox-Ross-Rubenstein (or Binomial) Model
* Garman-Kohlhagen Model
 
* Jump Diffusion Model
* Whalley Model
 
* Value Line Model


Each model takes a look at evaluating options from a different perspective. Usually the goal of the model is to better estimate the fair value of an option. Sometimes the goal is to speed up computation of the fair value.

Black-Scholes Model



The first arbitrage model is the most famous and most popular option pricing model—the Black-Scholes Model. Professors Stanley Black and Myron Scholes were fortunate that they published their revolutionary model just as the Chicago Board Options Exchange (CBOE) was founded. The opening of the CBOE shifted the trading of options from a small over- the-counter backwater of the financial community to a huge and growing market and created a demand for greater information about options pricing. The Black-Scholes was deservedly at the right place at the right time. The initial version of the Black-Scholes Model was for European options that did not pay dividends. 


They added the dividend component soon after. Mr. Black made modifications to the model so that it could be used for options on futures. This model is often called the Black Model. Mark Garman and Steven Kohlhagen then created the Garman-Kohlhagen Model by modifying the Black-Scholes Model so that it gave more accurate pricing of options on foreign exchange. All of these versions of the Black-Scholes Model are similar enough that they are often simply described generically as the Black-Scholes Model. Another popular model is the Cox-Ross-Rubenstein, or Binomial, Model. 


This model takes a different approach to the pricing of options. However, many option traders feel that it is generally more accurate than the Black-Scholes Models. The main drawback, however, is that it is computationally more time consuming. The Black-Scholes Model is used only for pricing European options. Yet most options traded in the world are American options, which allow for early exercise. It has been found, however, that the increase in accuracy from using a true American-pricing model is usually not worth the greater cost in computational time and energy. 




This is particularly true with options on futures. Arbitrageurs will sometimes shift to an American pricing model when a stock option gets near expiration or becomes deep in-the-money. These are the circumstances when the chances of early exercise become more likely and the greater accuracy of a model that prices American-style options becomes more important. Another apparent oddity is that the Black-Scholes Model does not price put options, only calls. However, the price of a put can be found by using the model to price a call and using the put-call parity principle.


The Black-Scholes Model assumes that two positions can be con- structed that have essentially the same risk and return. The assumption is that, for a very small move in either of the two positions, the price of the other position will move in essentially the same direction and magnitude. This was called the riskless hedge and the relationship between the two positions was known as the hedge ratio. Generally speaking, the hedge ratio describes the number of the underlying instrument for each option. 


For example, a hedge ratio of 0.50 means that one half of the value of one option is needed to hedge the option. In the case of a stock option, a hedge ratio of 0.50 would mean that 50 shares of the underlying stock are needed to hedge one option. In the case of an option on a futures contract, a hedge ratio of 0.50 would mean that one half of a futures contract is needed to hedge the option. Clearly, one can-not hold only one half of a futures contract, but that is how many would be needed to theoretically hedge the option on that futures contract. 


The Black-Scholes Model assumes that the two sides of the position are equal and that an investor would be indifferent as to which one he or she wished to own. You would not care whether you owned a call or the UI if the call were theoretically correctly priced. In the same way, a put would be a substitute for a short position in the UI. This was a major intellectual breakthrough. Previously, option pricing models were based more on observing the past rather than strictly and mathematically looking at the relationship of the option to the UI. An arbitrage model relies heavily on the inputs into the model for its accuracy. Designing a model using gibberish for inputs will lead to a model that outputs gibberish. The Black-Scholes Model takes these factors into account:


* Current price of the UI
 
* Strike price of the option
 
* Current interest rates
 
* Expected volatility of the UI until expiration
 
* The possible distribution of future prices
 
* The number of days to expiration
 
* Dividends (for options on stocks and stock indexes)


Given this information, the model can be used to find the fair price of the option. But suppose the current price of the option was known, and what was wanted was the expected volatility that was implied in the price of the option. No problem. The Black-Scholes Model could be used to solve for the expected volatility. The model can be used to solve for any of the listed factors, given that the other factors are known. This is a powerful flexibility. A further advantage of the model is that the calculations are easy. The various factors in the model lend themselves to easy calculation using a sophisticated calculator or a simple computer. 


The calculations with other models, which might give better results, take so long that they have limited use. Option traders are usually willing to give up a little accuracy to obtain an answer before the option expires! The Black-Scholes Model is the standard pricing model for options. It has stood the test of time. All of the examples in this book, and virtually all other books, are derived using the Black-Scholes Model. However, the model has some drawbacks. As a result, the model is no longer the standard for options on bonds, foreign exchange, and futures, though the standard models for these three items are modifications of the original.


Assumptions of the Black-Scholes Model



Examining the assumptions of the Black-Scholes Model is not done to criticize the model but to identify its strengths and weaknesses so that the strategist does not make a wrong move based on a false assumption.

Current Price of the UI


The current price of the UI is usually known with some certainty for most option traders. They can look on the screen or call their broker and get a price for the UI. It usually does not matter if the price quote is a little wrong. However, arbitrageurs often have a problem determining exactly what the price of the UI is. They ask: How wide is the bid/ask spread? Is the last trade on the bid, in the middle, or on the ask? Has the bid/ask spread moved since the last trade? Are prices extremely volatile, and will I have a hard time executing a trade at the current bid or ask because the bids and offers are moving so much .


The Strike Price of the Option


Fortunately, this one factor is stable and does not change significantly. Strike prices for stock options do change whenever there is a stock split or a stock dividend.
 

Interest Rates


The Black-Scholes Model assumes that setting up the right relationship between the UI and the option will lead to a neutral preference by the investor. The value of the UI and the value of the option will be balanced because the Black-Scholes Model is an arbitrage model. The model assumes that the so-called risk-free rate is the proper rate. Traditionally, the risk-free rate is considered the rate paid on U.S. government securities, specifically, Treasury bills, notes, and bonds. To make the model work, it is assumed that interest is being paid or received on balances. It is assumed that all positions are financed, an assumption that is reasonable because there is always an opportunity cost even if the position is not financed. 


The Black-Scholes Model assumes that you would invest your money in Treasury bills if you did not invest it in an option. The term of the interest rate used in the model should be the term to expiration of the option. For example, if you are pricing an option that matures in 76 days, then you should theoretically use the interest rate corresponding to a Treasury bill that matures in 76 days. In the real world, of course, you would simply select a Treasury bill that matures close to that perfect number of days. 


The problem is that the model assumes that you both invest your money and borrow money at the risk-free rate. It is quite reasonable to assume that you will invest your money in Treasury bills in the real world. However, only the U.S. government can borrow at the Treasury-bill rate. All other borrowers must pay more, sometimes much more. As a result, some options traders assume that they invest at the Treasury-bill yield but that they borrow at the Eurodollar yield or at the prime rate. In general, the rate assumed in the model will have little effect on the price of the option. The level of interest rates mainly affects the price of multi year options.



Probability Distribution

 
The probability distribution is the expected future possible distribution of prices, that is, the probability that any price will occur in the future. The model basically assumes that prices are randomly distributed around the current price in roughly a bell shaped curve.


Expected or Implied Volatility


Expected volatility is the volatility of the price of the UI expected in the future by the investor or the market. Expected volatility is the width of the bell curve mentioned in the preceding paragraph.

Days to Expiration


Fortunately, the number of days to expiration of the option does not change.

Taxes


The Black-Scholes Model does not take into account the effect o taxes on the pricing of options. In fact, no major model does. This is not a major problem, but it might affect some arbitrageurs. For example, it was shown that the model assumes the risk-free or T-bill rate as the interest rate, but that is not usually the case in the real world: The investor might be receiving T-bill interest, which is exempt from state and local taxes, but paying the equivalent of Eurodollar rates or even the prime rate. The investor might or might not be able to deduct the cost of the borrowing from the proceeds of the trade. Some traders will be taxed differently on the interest or dividend in- come than on the gain or loss from the option. Interest and dividend in- come are usually ordinary income, whereas gains and losses from options are capital gains and losses. Taxes are an important subject but beyond the scope of this book. Variations in taxes could have an impact on the fair price of an option for a particular trader.


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Share:

THE GREEKS OF OPTION

THE GREEKS OF OPTION





Purchasing a stock has an obvious risk/reward profile. If the stock goes up, you make money: If it goes down, you lose money. The reverse is true if you sell a stock short. We refer to this loss exposure as directional risk (refer to Graph ) . Furthermore, the amount of the profit or loss is easy to anticipate. If you purchase 100 shares of XYZ, for each $1 increase in price the position increases in value by $100, and for each $1 reduction in price, the position loses $100 in value. If you sell 100 shares of stock short, for each $1 decrease in price you will make $100, and you will lose $100 for each $1 increase in price. By contrast, determining the risk/reward profile of an option position is much more complicated. As we have seen, an option's value can be affected by a change in anyone of these five variables :


* Stock price

* Time until expiration

* Volatility

* Interest rate

* Amount and timing of dividends


When two or more of these inputs changes, the changes can either act to offset each other in whole or in part or can work in concert to magnify either the increase or decrease in price. The situation is further complicated when options are used in combination.



Fortunately; there are analytical tools available to simplify the analysis of option positions. These tools are commonly referred to collectively as the Greeks and individually as delta, theta, gamma, rho, vega, and omega. Individually; they each measure some aspect of an option position's market risk/reward profile. This statement is true whether the position is a simple one involving one or perhaps a few different options or an extremely complicated position (such as a professional floor trader who has scores of different option contracts-some of which are long and some of which are short-and who may have a long or short position in the underlying asset).


Collectively; the Greeks provide the practiced trader with a comprehensive assessment of a position's risk/reward profile. Not only will the trader have an accurate picture of which market conditions will enhance the value of the position and which will subject it to a loss of value, but the trader will be in a position to determine what adjustments are appropriate in order to reflect the trader's current expectations concerning the stock. The trader can also reduce exposure to one or more aspects of market risk.

The Greeks

The various Greeks, the variables with which they are associated, and a short introductory definition of each are summarized in . This chapter not only explores how the Greeks affect option pricing individually but also describes how they affect option pricing in combination. With the availability of option-analytical software, it is neither



necessary nor particularly useful for you to learn the mathematical formulas involved. What is important, however, is that you grasp conceptually the insight that these tools provide. This knowledge will help you identify your risks and respond to them appropriately: Let's start our inquiry by examining the impact of price movement of  the underlying asset on an option's theoretical value. We will isolate the impact of change in price of the underlying asset by keeping the other inputs constant while varying the price of the stock. Consider Stock ABC
that has a volatility of 50. Using an interest rate of 5 percent, assume that the company does not issue a dividend. A table of the theoretical values of the 60-level calls and puts with 30 days to go until their expiration is shown in  This table highlights two important aspects of the relationship between the price of an option and the price of the underlying stock:




1.  As the price of ABC increases, the price of the 60-level call also increases-while the price of the corresponding put decreases. With the stock at $50, the theoretical values of the call and put are $.41 and $10.25, respectively: By the time the price of the stock reaches $55, for example, the theoretical value of the call has risen to $1.46.  The put's theoretical value has declined to $6.23.



2.  As the price of ABC increases, the price of the call increases while the price of the put decreases. With the stock at $50, a $1 increase in the stock theoretically produces a $.14 increase in the price of the 60- level call and a $.87 decrease in the price of the corresponding put. The call increases in price by $.29 when the stock increases from $54 to $55 and by $.80 when the stock increases from $66 to $67. Correspondingly, the put declines by $.72 when the stock goes from $54 ton $55 but only by $.21 as the stock increases from $66 to $67.


The relationship between the change in the price of a stock and the corresponding change in the price of an option is referred to as the option's delta.

Delta


The delta is the most widely known of the Greeks and is an extremely important gauge of any option strategy. Delta measures how sensitive an option's price is to change in the value of the underlying stock. There are two particularly useful ways to look at delta: the measure of how much the option's price will change compared to a change in the price of the underlying asset, and the approximate probability that the option will finish ITM. We will explore both of these perspectives in some detail.

Related Change


An option's delta is the ratio of the change in its the or etical value to a small change in the price of the underlying stock. More commonly (but marginally less precise), delta is defined as how much an option's price changes for every $1 change in the price of the stock. A positive delta means that an option's price moves in the same direction as price movement in the underlying asset. An option that has a positive delta will increase in value as the underlying asset increases in value and will decrease in value as the price of the underlying asset decreases.


Conversely; a negative delta reflects the fact that an option's price moves in the opposite direction from the price movement in the underlying asset.
An option that has a negative delta will decrease in value as the underlying asset increases and will increase in value as the underlying asset decreases. Because a long call and short put increase in value as the underlying asset increases (in other words, their value rises and falls along with the underlying asset), they have a positive delta. Conversely, both a long put and a short call have negative deltas, because their values decrease as the underlying asset increases in price and increase when the


stock price declines. Going back to the table presented earlier in this chapter, with ABC stock trading at $50, the fact that the 60-level call's price would theoretically increase by $.13 when the stock price increased $1 to reach $51 indicates a delta of .13. In comparison, the delta of the 60- level put with the stock trading at $50 would be - .87. Because one equity option contract generally represents options on 100 shares of the underlying asset, the delta is most commonly expressed as the aggregate change in price of the option contract for a $1 change in the underlying asset. In other words, the delta for one option is multiplied by 100 (the number of shares represented by one contract). Under this approach, the 60-level call with ABC trading at $50 would have a delta of 13, not .13. From now on, we will refer to option deltas by using this aggregate designation.


Many option strategies and positions include holdings in the underlying asset, which can be long or short. When you are determining the delta for a complicated position that includes a combination of options and/or positions in the underlying asset, the aggregate delta of the entire position is most relevant. Using the same ratio definition of the delta as for options, the delta of one share of long stock is + 1, while the delta of one share of short stock is -1. Therefore, if a position included 1,000 shares of stock, this stock would contribute 1,000 deltas to the aggregate position delta. On the other hand, if the position included a short of 1,000 shares, this short position would contribute -1,000 deltas to the aggregate position delta.






If the holding is:                                It will contribute the following:


Long underlying security                                 Positive delta

Short underlying security                                Negative delta                                                                                                                         
Long call                                                          Positive delta

Short call                                                         Negative delta

Long put                                                          Negative delta

Short put                                                         Positive delta



Although you can calculate an option's delta precisely by using an option-pricing model, many experienced option traders approximate option deltas by using the following rules of thumb:


* An ATM option typically has a delta of about +50 for calls and -50 for puts.

* With the stock trading at or near a strike price, give the nearest ITM options a delta of 75 and the next-closest ITM options a delta of 90. Then, estimate the deltas of all other ITM options to be 100.

* With the stock trading at or near a strike price, give the nearest OTM options a delta of 25 and the next-closest OTM options a delta of 10. All other OTM options should receive a zero delta.


Determining Options Deltas


 Option Strike Price           Call Delta          Put Delta
            45                             +100                   0
            50                             +90                   -10
            55                             +75                   -25
            60                             +50                   -50
            65                             +25                   -75
            70                             +10                   -90
            75                                0                     -100



For example, if XYZ were trading at $60, we would approximate option deltas as shown in Table.


As you learned in the previous chapter, being long a call and short a put with the same strike and expiration is the equivalent of being long 100 shares of the underlying asset (synthetic long stock). Because long 100 shares always represent an aggregate 100 deltas, combining the deltas of the long call and the short put with the same strike price and expiration date must also always equal 100. Similarly; the aggregate delta of a short call, long put position with the same strike price and expiration date will be -100, the equivalent of being short 100 shares of the underlying asset. This example highlights an important relationship between the deltas of puts and calls with the same strike price and expiration date. If you know one, you can easily determine the other. For example, if the March 60 call has a delta of +38, the delta of the March 60 put is -62.

Probability of an ITM Finish upon Expiration

An easy way to think of delta is as the probability that the option will finish ITM upon expiration. The ATM calls and puts each have a 50-50 (or 50 percent) chance of finishing ITM upon expiration and both carry an approximate delta of 50. The ITM calls and puts have a much greater chance of finishing ITM upon expiration than their ATM counterparts with a deeper ITM call or put having a higher likelihood of finishing ITM than one that is less ITM. Their deltas reflect those respective probabilities. The OTM options have the least percentage chance of finishing ITM and not surprisingly; their small deltas reflect this decreased probability.


Delta and Time

The time until expiration impacts an option's delta. Considering delta as the probability of finishing ITM makes it easier to understand this effect. This thought leads to the following relationship:


* The delta for an ITM option will move towards 100 as time expiration decreases. The likelihood of the option staying ITM increases as

* the time until expiration decreases. The delta of an ATM option will remain at 50, because it still has a 50-50 chance of finishing ITM.

* The delta of an OTM option will move towards zero as expiration approaches, because the likelihood of the option finishing ITM decreases as the time until expiration decreases.


examples of delta and time until expiration. As we can see from these examples, strike prices at differing expiration dates have different deltas. Hence, as the time until expiration increases, the probability that the underlying asset will move towards.


Share:

TYPES OF BUY SELL IN OPTION

TYPES OF BUY SELL IN OPTION 


 


Having reviewed the basics of option characteristics, we are now aware that we have a number of investment choices: stock, calls on the stock, and puts on the stock. For each of these, we can initiate a position either by purchase (referred to as a long position) or by sale (referred to as a short position), thus giving us six different initiating strategies :



* Long stock

* Short stock
 
* Long call
 
* Short call
 
* Long put
 
* Short put

These tools are what we can use to construct all option-based strategies. By combining these building blocks, the individual investor can create strategies ranging from basic to complex. Mastery of each of the individual building blocks is essential for understanding how they work in combination. Therefore, we will now look at each of these six alternatives in some detail. Retail investors are already familiar with one of these building blocks: long stock. With an understanding of the other five building blocks, the investor will have the ability to create positions that are best suited to capitalize off any market outlook. The only limit to creating positions is the investor's creativity. Once you master the six building blocks, the possibilities are endless.


Long Stock


Long stock is the most common position among investors. After analyzing the fundamentals of a company and deducing that the company's product, its revenue model, and current market conditions reflect the likelihood of positive growth, the retail investor purchases the stock as an investment in that company: Over a period of time, if the investor's analysis proves correct, the stock value increases-rendering a profit. In this case, the investor who purchases stock with his or her own capital is said to be long stock.
 

Here is an example. An investor who has no position in XYZ purchases 100 shares of XYZ at $50 per share. The investor is now long 100 shares of XYZ.  shows the profit and loss associated with the outright ownership of stock.



The profit in this case is unlimited. This position will profit as the stock increases in value. Each $1 increase in the market price of the stock will result in $100 worth of profit. The loss in this example is limited. This position will generate a loss as the stock declines in price. The risk is limited only because the stock can only decrease to zero. Each $1 decrease in the market price of the stock will result in $100 worth of loss. The outlook on this stock is bullish.


Short Stock


Being long stock is a bullish strategy, meaning that you believe there will be a rise in the market price. What if the stock is not performing positively; however? What if it is declining in price? Or, what if the investor believes that the stock is highly overvalued and is ready for a significant price pullback? Is the investor simply out of luck? Stock that is in a downward trend (decreasing in value) is referred to as behaving bearishly. Similarly, an investor who has a pessimistic out-look on a stock is referred to as being bearish.


The bearish trader can take advantage of an anticipated declining market by selling a stock short. In other words, he or she will sell a stock that he or she does not currently own. In this case, the brokerage firm lends the investor a certain number of stock shares at a particular price under the condition that the investor has capital in his or her account in order to cover the cost of the stock.



being borrowed. With the stock in hand, the investor now has the ability to capitalize off what he or she is speculating to be a downward move in the stock. The investor sells the borrowed stock in the marketplace at its existing price and waits until the price decreases. Once the stock price declines, the investor buys the stock back in the open market at the lower price. He or she is then able to return the stock to the brokerage firm while capturing the profit. To be sure, by selling stock short, a retail iIlvestor can take advantage of a declining market. There is always a risk that the stock that has been sold short will increase in price, however. This situation could force the investor to purchase the stock back at a higher price, resulting in a loss. If the investor is correct, however, the stock will decrease in price and he or she can buy the stock back from the open market in order to capture profit. 


 Here is an example. An investor who has no position in XYZ borrows 100 shares from his broker and sells it for $50 per share.  the profits and losses associated with the short sale of a security. In this case, the profit is limited to the amount collected for the stock and risk is unlimited. The profit in this situation is limited. This position will profit as the stock declines in value. Each $1 decrease in the market price of the stock will result in $100 worth of profit. The loss in this case is unlimited. This position will lose money as the stock rises in value. Each $1 increase in the market price of the stock will result in $100 worth of loss. There is also the risk of stock being demanded back by the brokerage firm. The outlook on this stock is bearish.


Long Call

The buyer (holder) of a call has as much profit potential as the owner of the underlying stock but has significantly limited the risk of loss. Because of the limited capital used in controlling a large interest, the long call position is a leveraged position. The risk involved is the total amount paid for the call. A long call position is used when the trader is bullish on the underlying security and is an alternative to long stock.
 



Here is an example. XYZ stock is trading at $50 per share, and the XYZ July 50 call is trading at $2. An investor purchases one XYZ July 50 call for $200. Figure 3-3 shows the profits and losses associated with ownership of a call option. The profit potential to the upside is similar to that of long stock, whereas the risk is limited to the purchase price of the option. The profit in this case is unlimited. When measured upon expiration of the option, each $1 increase in the price of the stock higher than $52 ($50 strike price of the option plus $2 paid for the option) results in $100 worth of profit.


 The profit from a long call will always be less than the profit from the same amount of long stock as represented by the option because of the time premium paid for the option. In this case, the profit from long stock would be $200 higher than the profit derived from the option. The loss in this situation is limited to the amount paid to purchase the option. When measured upon expiration of the option, if the stock is trading at $50 or lower, the option will expire worthless-and the entire. investment in the option will be lost. There will be a partial loss if the stock is trading between $50 and $52 upon expiration of the option. The outlook on this stock is bullish.


Short Call



The seller (writer) of a short call has as much loss potential as the short seller of stock but faces much less potential for gain. The retail investor will need to meet capital requirements in order to transact this position. He or she will also need to have cash in the account in order to cover the short call position or to own the underlying security. The short call is frequently combined with long stock. This strategy is called a covered call or a buy-write and is covered in detail in  "Trading Strategies." Here is an example. XYZ is trading at $50 per share, and the XYZ July 50 call is trading at $2. One XYZ July 50 call is sold for $200. Figure 3-4 illustrates the risks and losses associated with the sale of a call option. The profit potential is limited to the amount collected for the sale of the option and the risk is unlimited. 


The profit in this situation is limited. The total profit to the option seller is the $2, or $2 X 100 = $200. When measured upon expiration of the option, if the stock is trading at $50 or lower, the option will expire worthless and the entire premium received is retained. There will be a lesser gain if the stock is trading between $50 and $52 upon expiration of the option. The loss here is unlimited. When measured upon expiration of the option, each $1 increase in the price of the stock higher than $52 ($50 strike price of the option plus the $2 received for the option) will result in $100 worth of loss. The outlook on this stock is neutral/bearish.


Long Put



A long put position is used when the trader is bearish on the underlying security. The buyer/holder of a put carries the profit potential of a short stock position but has a significantly limited risk of loss. There are no margin requirements for a long put position, and the risk is the total amount purchased for the put. Also, for those who do not trade on margin, selling stock short is not an available option. Therefore, a long put is the exclusive vehicle for speculating on a decline in the price of the underlying stock.
 

Here is an example. XYZ is trading at $50 per share, and the XYZ July 50 put is trading at $2. One XYZ July 50 put is purchased for $200. The profit and loss associated with the purchase of a put is illustrated in . The profit potential is considered to be unlimited, although the underlying can only go to zero, and the loss is limited to the purchase price of the option. The profit in this instance is limited. The profit potential of the long put is limited only because the value of the underlying stock can only decline to zero. When measured upon expiration of the option, each $1 decrease in the price of the stock lower than $48 ($50 strike price of the option minus the $2 paid for the option) will result in $100 worth of profit.
 

The profit from a long put will always be less than the profit that would have been earned by selling the same amount of stock short, covered by the option contract due to the time premium paid for the long put. The loss here is limited to the amount paid in order to purchase the option. When measured upon expiration of the option, if the stock is trading at $50 or higher, the option will expire worthless-and the entire investment in the option will be lost. There will be a smaller loss if the stock is trading between $48 and $50 upon expiration of the option. The outlook on this stock is bearish. The buyer (holder) of a put has much of the profit potential of a short stock position but has significantly limited the risk of loss. No margin is required for this position. The risk is the total amount purchased for the put.


Short Put



The seller (writer) of a put has as much of the same loss potential as a long stock position but has much less potential for gain. The retail trader or investor is required to meet capital requirements for this transaction (in other words, he or she will need to have cash in the account as security against the short put). This requirement is referred to as a cash-covered put, which is similar to a covered call (discussed in the strategy section of this book). Cash in the account covers the short put.
 

Here is an example. XYZ is trading at $50 per share, and the XYZ July 50 put is trading at $2. One XYZ July 50 put is sold for $200. Figure 3-6 illustrates the profits and losses associated with the sale of a put. As with the outright sale of any option, the profit potential is limited to the amount collected for the sale of the option and the risk is unlimited, or in this case limited as the underlying can only go to zero. The profit here is limited to the amount received upon sale of the
option. 


When measured upon expiration of the option, if the stock is trading at $50 or higher, the option will expire worthless and the entire premium received will be retained. There will be a lesser gain if the stock is trading between $48 and $50 upon expiration of the option. The loss here is unlimited. When measured upon expiration of the option, each $1 decrease in the price of the stock lower than $48 ($50 strike price of the option minus the $2 received for the option) will result  in $100 worth of loss. There will be a smaller loss if the stock is trading between $48 and $50 upon expiration of the option. The outlook on this stock is neutrall bullish.



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INTRODUCTION TO OPTIONS


INTRODUCTION TO OPTIONS

 



An option is a contract written by a seller that conveys to the buyer the right — but not the obligation — to buy (in the case of a call option) or to sell (in the case of a put option) a particular asset, at a particular price (Strike price / Exercise price) in future. In return for granting the option, the seller collects a payment (the premium) from the buyer. Exchange- traded options form an important class of options which have standardized contract features and trade on public exchanges, facilitating trading among large number of investors. They provide settlement guarantee by the Clearing Corporation thereby reducing counter party risk. Options can be used for hedging, taking a view on the future direction of the market, for arbitrage or for implementing strategies which can help in generating income for investors under various market conditions


OPTION TERMINOLOGY

 

• Index options: 

These options have the index as the underlying. In India, they have a European style settlement. Eg. Nifty options, Mini Nifty options etc.

• Stock options:

 Stock options are options on individual stocks. A stock option contract gives the holder the right to buy or sell the underlying shares at the specified price. They have an American style settlement.

• Buyer of an option:

 The buyer of an option is the one who by paying the option premium buys the right but not the obligation to exercise his option on the seller/writer.

• Writer / seller of an option: 

The writer / seller of a call/put option is the one who receives the option premium and is thereby obliged to sell/buy the asset if the buyer exercises on him.

• Call option: 

A call option gives the holder the right but not the obligation to buy an asset by a certain date for a certain price.



• Put option: 

A put option gives the holder the right but not the obligation to sell an asset by a certain date for a certain price.

• Option price/premium: 

Option price is the price which the option buyer pays to the option seller. It is also referred to as the option premium.

• Expiration date: 

The date specified in the options contract is known as the expiration date, the exercise date, the strike date or the maturity.

• Strike price: 

The price specified in the options contract is known as the strike price or the exercise price.

• American options: 

American options are options that can be exercised at any time upto the expiration date.


• European options:

 European options are options that can be exercised only on the expiration date itself.

• In-the-money option: 

An in-the-money (ITM) option is an option that would lead to a positive cash flow to the holder if it were exercised immediately. A call option on the index is said to be in-the-money when the current index stands at a level higher than the strike
price (i.e. spot price > strike price). If the index is much higher than the strike price, the call is said to be deep ITM. In the case of a put, the put is ITM if the index is below the strike price.

• At-the-money option: 


An at-the-money (ATM) option is an option that would lead to zero cashflow if it were exercised immediately. An option on the index is at-the-money when the
current index equals the strike price (i.e. spot price = strike price).

• Out-of-the-money option: 


An out-of-the-money (OTM) option is an option that would lead to a negative cash flow if it were exercised immediately. A call option on the index is out-of-the-money when the current index stands at a level which is less than the strike
price (i.e. spot price < strike price). If the index is much lower than the strike price, the call is said to be deep OTM. In the case of a put, the put is OTM if the index is above the strike price.

• Intrinsic value of an option: 

The option premium can be broken down into two components - intrinsic value and time value. The intrinsic value of a call is the amount the option is ITM, if it is ITM. If the call is OTM, its intrinsic value is zero. Putting it another way, the intrinsic value of a call is Max[0, (S t — K)] which means the intrinsicvalue of a call is the greater of 0 or (S t — K). Similarly, the intrinsic value of a put is Max[0, K — S t ],i.e. the greater of 0 or (K — S t ). K is the strike price and S t is the spot price.


• Time value of an option:

The time value of an option is the difference between its premium and its intrinsic value. Both calls and puts have time value. An option that is OTM or ATM has only time value. Usually, the maximum time value exists when the option is ATM. The longer the time to expiration, the greater is an option's time value, all else equal. bAt expiration, an option should have no time value.


OPTIONS PAYOFFS


The optionality characteristic of options results in a non-linear payoff for options. In simple words, it means that the losses for the buyer of an option are limited, however the profits are potentially unlimited. For a writer (seller), the payoff is exactly the opposite. His profits are limited to the option premium, however his losses are potentially unlimited. These non-linear payoffs are fascinating as they lend themselves to be used to generate various payoffs by using combinations of options and the underlying. We look here at the six basic
payoffs (pay close attention to these pay-offs, since all the strategies in the book are derived out of these basic payoffs).

Payoff profile of buyer of asset: Long asset

 Payoff for investor who went Long ABC Ltd. at Rs. 2220


In this basic position, an investor buys the underlying asset, ABC Ltd. shares for instance, for Rs. 2220, and sells it at a future date at an unknown price, S t . Once it is purchased, the investor is said to be "long" the asset.  shows the payoff for a long position on ABC Ltd.The figure shows the profits/losses from a long position on ABC Ltd.. The investor bought ABC Ltd. at Rs. 2220. If the share price goes up, he profits. If the share price falls he loses.


Payoff profile for seller of asset: Short asset



Payoff for investor who went Short ABC Ltd. at Rs. 2220


In this basic position, an investor shorts the underlying asset, ABC Ltd. shares for instance, for Rs. 2220, and buys it back at a future date at an unknown price, S t . Once it is sold, the investor is said to be "short" the asset.  shows the payoff for a short position on ABC Ltd.The figure shows the profits/losses from a short position on ABC Ltd.. The investor sold ABC Ltd. at Rs. 2220. If the share price falls, he profits. If the share price rises, he loses.

Payoff profile for buyer of call options: Long call


A call option gives the buyer the right to buy the underlying asset at the strike price specified in the option. The profit/loss that the buyer makes on the option depends on the spot price of the underlying. If upon expiration, the spot price exceeds the strike price, he makes a profit. Higher the spot price, more is the profit he makes. If the spot price of the underlying is less than the strike price, he lets his option expire un-exercised. His loss in this case is the premium he paid for buying the option.  gives the payoff for the buyer of a three month call option (often referred to as long call) with a strike of 2250 bought at a premium of 86.60.


Payoff for buyer of call option


The figure shows the profits/losses for the buyer of a three-month Nifty 2250 call option. As can be seen, as the spot Nifty rises, the call option is in-the-money. If upon expiration, Nifty closes above the strike of 2250, the buyer would exercise his option and profit to the extent of the difference between the Nifty-close and the strike price. The profits possible on this option are potentially unlimited. However if Nifty falls below the strike of 2250, he lets the option expire. His losses are limited to the extent of the premium he paid for buying the option.

Payoff profile for writer (seller) of call options: Short call


A call option gives the buyer the right to buy the underlying asset at the strike price specified in the option. For selling the option, the writer of the option charges a premium. The profit/loss that the buyer makes on the option depends on the spot price of the underlying. Whatever is the buyer's profit is the seller's loss. If upon expiration, the spot price exceeds the strike price, the buyer will exercise the option on the writer. Hence as the spot price increases the writer of the option starts making losses. Higher the spot price, more is the loss he makes. If upon expiration the spot price of the underlying is less than the strike price, the buyer lets his option expire un-exercised and the writer gets to keep the premium.gives the payoff for the writer of a three month call option (often referred to as short call) with a strike of 2250 sold at a premium of 86.60.


Payoff for writer of call option


The figure shows the profits/losses for the seller of a three-month Nifty 2250 call option. As the spot Nifty rises, the call option is in-the-money and the writer starts making losses. If upon expiration, Nifty closes above the strike of 2250, the buyer would exercise his option on the writer who would suffer a loss to the extent of the difference between the Nifty-close and the strike price. The loss that can be incurred by the writer of the option is potentially unlimited, whereas the maximum profit is limited to the extent of the up-front option premium of Rs.86.60 charged by him.

 Payoff profile for buyer of put options: Long put


A put option gives the buyer the right to sell the underlying asset at the strike price specified in the option. The profit/loss that the buyer makes on the option depends on the spot price of the underlying. If upon expiration, the spot price is below the strike price, he makes a profit. Lower the spot price, more is the profit he makes. If the spot price of the underlying is higher than the strike price, he lets his option expire un-exercised. His loss in this case is the premium he paid for buying the option. gives the payoff for the buyer of a three month put option (often referred to as long put) with a strike of 2250 bought at a premium of 61.70.


Payoff for buyer of put option


The figure shows the profits/losses for the buyer of a three-month Nifty 2250 put option. As can be seen, as the spot Nifty falls, the put option is in-the-money. If upon expiration, Nifty closes below the strike of 2250, the buyer would exercise his option and profit to the extent of the difference between the strike price and Nifty-close. The profits possible on this option can be as high as the strike price. However if Nifty rises above the strike of 2250, he lets the option expire. His losses are limited to the extent of the premium he paid for buying the option.


Payoff profile for writer (seller) of put options: Short put


A put option gives the buyer the right to sell the underlying asset at the strike price specified in the option. For selling the option, the writer of the option charges a premium. The profit/loss that the buyer makes on the option depends on the spot price of the underlying. Whatever is the buyer's profit is the seller's loss. If upon expiration, the spot price happens to be below the strike price, the buyer will exercise the option on the writer. If upon expiration the spot price of the underlying is more than the strike price, the buyer lets his option un-exercised and the writer gets to keep the premium. Figure 1.6 gives the payoff for the writer of a three month put option (often referred to as short put) with a strike of 2250 sold at a premium of 61.70



Payoff for writer of put option


The figure shows the profits/losses for the seller of a three-month Nifty 2250 put option. As the spot Nifty falls, the put option is in-the-money and the writer starts making losses. If upon expiration, Nifty closes below the strike of 2250, the buyer would exercise his option on the writer who would suffer a loss to the extent of the difference between the strike price and Nifty- close. The loss that can be incurred by the writer of the option is a maximum extent of the strike price (Since the worst that can happen is that the asset price can fall to zero) whereas the maximum profit is limited to the extent of the up-front option premium of Rs.61.70 charged by him.


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LACK OF DICIPLINE IN TRADERS

LACK OF DISCIPLINE IN TRADERS



Let’s say you are new to futures trading. Or let’s say you have traded futures in the past without much success and have decided to start fresh with a new approach and a clean slate. And you’ve done it all and followed every step. You have:
• Determined how much money you can truly afford to risk
• Opened a brokerage account with that amount of cash
• Settled on a diversified portfolio of markets
• Developed a trading system in which you have complete confidence
• Developed specific, unambiguous entry and exit criteria
• Back-tested your system and have generated good hypothetical results
•Walked your system forward, paper traded it over new data and have generated good results
• Sized your account so that you reasonably expect no more than a 25% draw down

• Built in risk controls including stop-loss orders to minimize your risk

You’re as ready as you can be. With high hopes and great anticipation you place an order to enter your first trade. So what happens next? Well, if you are like many traders the first three trades you make will be losses. After the first loss, you’ll say “no big deal; it’s part of trading.” After the second loss you’ll think “I wonder if I’m doing something wrong.” After the third loss you’ll tell yourself
“some thing’s wrong, and I need to regroup.” You will have no idea why your system has suddenly fallen apart.

So you decide to go flat and skip the next signal, a buy signal. Two days later the market that you should be long explodes to the upside leaving you in the dust. You tell yourself “it’s too late to jump on board now, so I’ll just wait for the next trade,” relieved at least that your confidence in your system has been restored. So you wait for the next signal from your system. And you wait and you wait and you wait. And in the meantime that market continues to tack on gains virtually every day. Your system is doing great, but you on the other hand are not doing
so well. You start mentally adding the money that you should have made on this trade to your account and say “I should have this much in my account now.” But every day your account balance remains the same, while that market just keeps rising higher and higher. By the time you enter the next trade you have a missed a $5,000 winner. And the next trade is another loser.


If you are one of the lucky ones, at this point your loss is relatively small, you conclude that you are in over your head, and you decide that enough is enough. You close your account and walk away, joining that fateful 90%. For the rest of your life whenever the topic of futures trading comes up you step forward like a  eteran with a purple heart and tell your “war story:” “yeah, I traded futures, listen to me kid.......” Or maybe you don’t quit so easily. If you are one of the unlucky ones, you keep trading, suffer more indignities at the hands of the futures markets, and lose even more money before your account is finally laid to rest. And so it goes for 90% of the people who enter the exciting world of commodities speculation. 


Given all of the potential pitfalls that we have discussed so far it is easy to understand why the person who decides to “take a shot” and is completely unprepared fails at futures trading. But what about the trader in this example? He was completely prepared both financially and emotionally to do what was necessary to succeed and still he failed. Why does this happen to so many traders sincerely dedicated to “making it work?” In most cases it is because although they were very well prepared when they began their new trading program, somewhere along the way they failed to do what was needed. They failed to have the discipline to pull the trigger (or to not pull the trigger as the  ase may be), and they either suffered a loss or missed a huge profit. With many traders this can cause an emotional “domino effect” where the trader’s primary focus is no longer on following his plan to achieve his long-term objectives. Instead, his primary objective becomes getting back at the markets for causing him to lose money or for taking off without him. Or maybe his objective is simply to get back to “break even” before walking away.Becoming bent on getting even is a perfectly natural response to a kick in the teeth. Unfortunately, it is also a sure-fire way to fail as a futures trader. A lack of discipline is defined as failing to do what you should do in a given circumstance. There is probably not a trader alive, successful or otherwise, who has never suffered because of his or her own lack of discipline at some critical moment. What separates those who make money in the long run from the other 90% is:

• The financial and emotional capabilities to survive a breach in discipline.
• The willingness to learn from mistakes and to never repeat a mistake already made.


A lack of discipline in futures trading is always a mistake. This is true even if your lack of discipline actually saves you money by skipping a trade or exiting early, or if it allows you to capture a windfall profit by taking a trade against your approach, doubling up on a losing trade or holding on after your trading method tells you to exit. Imagine, you fail to follow your plan and you come out ahead. This leaves you ahead financially for the moment but consider where this leaves you psychologically: “I broke my own rules and made some money.” All is well and good in the short run but what happens the next time a critical juncture is reached? Do you trust the approach that you spent so much time developing and refining (and which in the back of your mind “failed” you the last time around, while you, Mr. Super trader, instinctively knew it was going to fail so you heroically took matters into your own hands and won the day), or your own “gut” instincts?


The most cruel paradox in futures trading is that a trader’s short-term successes can plant the seeds of his long-term failure. Believe it or not, one of the worst things that can happen to a first time trader is to have great success right off the bat. In the long run you may actually be better off if you struggle a little at the outset, develop some respect for the markets and weather some early mistakes,
than if your first three trades are big winners and you decide you’ve got “the touch.”



 Why Do Traders Make Mistake


 A lack of discipline in trading is almost always the result of one or more of the three great obstacles to trading success:

• Fear
• Greed
• Ego


Every time a trader makes a decision regarding any element of his trading he is subject to the effects of fear, greed and ego. This does not imply that we all need hours of serious therapy. It is simply human nature taking over. We all want to make money (thus we feel greed) and we don’t want to lose money (thus we feel fear). Cutting a loss is extremely tough on the ego. Once you cut a loss on a trade there is no chance to recoup that loss without entering into an entirely new trade. This explains why cutting a loss is often such a difficult thing to do. How many people enjoy going around and voluntarily admitting mistakes, especially ones that cost them money? Not very many. It simply goes against human nature. Yet when trading futures it is often exactly the right thing to do


These emotions are at times so powerful that they can cause you to do all kinds of foolish things:


• You bail out of a trade prematurely with a small loss simply because you don’t want to risk a bigger loss (fear/ego).
• You stop trading altogether during a draw down—right before things turn around (fear).
• You take a profit prematurely because you don’t want to give it back, thereby missing a big profit (greed).
• You double up or increase your position size in an effort to get back to break-even or in an effort to “make a killing” (greed).

How To Avoid Mistake

Of the four biggest mistakes in futures trading, a lack of discipline is the most difficult mistake to avoid. The other mistakes detailed in this book can all be dealt with before you start a trading program. You can lay out every step of your trading program down to the last detail. But then you must pull the trigger. That is when Mistake #4 comes into play. As a result, the opportunities to make this
mistake are limitless. A lack of discipline occurs while you are in the line of fire.
Picture a new soldier who goes to military school, boot camp and engages in other extensive training. Then suddenly he finds himself in live combat for the first time with somebody shooting real bullets at him. Now consider an individual new to futures trading. 

LACK OF DISCIPLINE IN TRADERS

 

He has planned everything and knows exactly what needs to be done in order to ensure his long term survival. Then he suddenly finds himself in a difficult situation, with real money—his money—on the line. How people react in difficult situations cannot be known until that time arrives. Hopefully their planning and preparation will allow them to overcome any psychological obstacles. But you never know for sure how they will react until the moment of truth arrives.Just telling yourself to put fear and greed and ego aside won’t do the trick. You must identify the points within your own trading plan where you will most likely confront these obstacles and make plans to avoid their negative effects. For example, if your approach requires you to interpret chart patterns, you need to define your rules very carefully to remove as much subjectivity as possible. If you do not, you may find yourself interpreting the same pattern. differently at times. If your trading has not been going well lately it may be easy to find some perfectly justifiable reason not to take the next trade. Likewise, if you are planning to use mental stops you must prepare yourself to always follow through and to place orders as needed. If you fail to do so, then one bad trade can do you in.



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