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Derivatives Ch 7 Solutions

In: Business and Management

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1. (Bull Spread) Buy one put with exercise price X1 and sell one put with exercise price X2. The profit equation is

( = Max(0, X1 – ST) – P1 – Max(0, X2 – ST) + P2

If ST < X1 < X2

( = X1 – ST – P1 – X2 + ST + P2

= X1 – X2 – (P1 – P2)

Recall from Chapter 3 that the difference between exercise prices is less than the difference between premiums. Since X1 < X2 and P1 < P2, the above profit is negative.

If X1 < ST < X2

( = – P1 – X2 + ST + P2

This figure increases dollar for dollar with ST. The breakeven is found by setting the profit to zero,

– P1 – X2 + ST* + P2 = 0

and solving for ST*

ST* = X2 + (P1 – P2)

If X1 < X2 ( ST

( = – P1 + P2

Since P2 > P1, this figure is positive.

The minimum profit occurs in the first profit range, ST < X1 < X2 and equals X1 – X2 – (P1 – P2). The maximum profit occurs in the third profit range, X1 < X2 < ST and equals – P1 + P2.

2. (Straddle) A straddle is a strategy based on the expectation that the market will have high volatility. If, however, everyone else in the market believes that the market will have high volatility, then the prices of the call and put will reflect the higher volatility, which will result in breakeven points further away from the current stock price. A straddle is most likely to be successful when the investor believes that the market will be more volatile than the everyone else in the market believes, and the investor’s expectations are more accurate.

3. (Box Spread) In internal rate of return (IRR) problems, the return from the investment is compared to the opportunity cost of capital. The investment is acceptable if the IRR exceeds the opportunity cost. In the box spread problem, the investment pays X2 – X1. The initial outlay is C1…...

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