# CHAPTER 8: TRADING STRATEGES INVOLVING OPTIONS

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1 CHAPTER 8: TRADING STRATEGES INVOLVING OPTIONS Unless otherwise stated the options we consider are all European. Toward the end of this chapter, we will argue that if European options were available with every single possible strike price, any payoff function could in theory be created. 8. Strategies involving a single option and a stock The dashed line shows the relationship between profit and stock price for the individual securities comprising the portfolio, while the solid line shows the relationship between profit and stock price for the whole portfolio. In figure 8.a the investment strategy represented by this portfolio is known as writing a covered call. In figure 8.b we can see is the reverse of writing a covered call. In figure 8.c we see a protective put strategy, while in figure 8.d we see the reverse of a protective put. The profit patters have the same general shape as the profit patterns discussed in Chapter for short put, long put, long call, and short call, respectively. Put-call parity provides a way of understanding why this is so. For example, for figure 8.a: r T t c D Xe p S S c p D Xe This shows that a long position in a stock combined with a short position in a call is equivalent to a short put position plus an amount of cash. This explains why the profit patter is similar to that from a short put position. r T t 8. Spreads A spread trading strategy involves taking a position in two or more options of the same type. Bull Spreads This can be created by buying a call option on a stock with a certain strike price and selling a call option on the same stock with a higher strike price. Both options have the same expiration date. Figure 8-. or

6 The profit pattenr obtained with a strangle depends on how close the strike prices are together. The farther they are apart, the less the downside risk and the farther the stock price has to move for a profit to be realized. The sale of a strangle is sometimes referred to as a top vertical combination. 8.4 Other Payoffs If European options expiring at time T were available with every possible strike price, any payoff function at time T could in theory be obtained. The easiest way to see this is in terms of butterfly spreads. Figure 8.3 shows the payoff from a butterfly spread. This could be described as a spike. As X and X 3 become closer together, the spike becomes smaller. By judiciously combining together a large number of very small spikes, any payoff function can be approximated.

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