HullFund8eCh11ProblemSolutions(3)

Problem 11.26

What trading position is created from a long strangle and a short straddle when both have the same time to maturity? Assume that the strike price in the straddle is halfway between the two strike prices of the strangle.

A butterfly spread (together with a cash position) is created.

Problem 11.27 (Excel file)

Describe the trading position created in which a call option is bought with strike price K1 and a put option is sold with strike price K2 when both have the same time to maturity and K2 > K1. What does the position become when K1 = K2?

The position is as shown in the diagram below (for K1 = 25 and K2 = 35). It is known as a range forward and is discussed further in Chapter 15. When K1 =K2, the position becomes a regular long forward.

Figure S11.6 Trading position in problem 11.24

Problem 11.28

A bank decides to create a five-year principal-protected note on a non-dividend-paying stock by offering investors a zero-coupon bond plus a bull spread created from calls. The risk-free rate is 4% and the stock price volatility is 25%. The low-strike-price option in the bull spread is at the money. What is the maximum ratio of the high strike price to the low strike price in the bull spread. Use DerivaGem.

Assume that the amount invested is 100. (This is a scaling factor.) The amount available to create the option is 100-100e-0.04×5=18.127. The cost of the at-the money option can be calculated from DerivaGem by setting the stock price equal to 100, the volatility equal to 25%, the risk-free interest rate equal to 4%, the time to exercise equal to 5 and the exercise price equal to 100. It is 30.313. We therefore require the option given up by the investor to be worth at least 30.313?18.127 = 12.186. Results obtained are as follows:

Strike Option Value 125 150 175 165 21.12 14.71 10.29 11.86

Continuing in this way we find that the strike must be set below 163.1. The ratio of the high strike to the low strike must therefore be less than 1.631 for the bank to make a profit. (Excel’s Solver can be used in conjunction with the DerivaGem functions to facilitate calculations.)

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