《《Investment 8th Chap021》.doc

CHAPTER 21: OPTION VALUATION PROBLEM SETS 1. The value of a put option also increases with the volatility of the stock. We see this from the put-call parity theorem as follows: P = C – S0 + PV(X) + PV(Dividends) Given a value for S and a risk-free interest rate, then, if C increases because of an increase in volatility, P must also increase in order to maintain the equality of the parity relationship. 2. A $1 increase in a call option’s exercise price would lead to a decrease in the option’s value of less than $1. The change in the call price would equal $1 only if: (i) there were a 100% probability that the call would be exercised, and (ii) the interest rate were zero. 3. Holding firm-specific risk constant, higher beta implies higher total stock volatility. Therefore, the value of the put option increases as beta increases. 4. Holding beta constant, the stock with a lot of firm-specific risk has higher total volatility. The option on the stock with higher firm-specific risk is worth more. 5. A call option with a high exercise price has a lower hedge ratio. This call option is less in the money. Both d1 and N(d1) are lower when X is higher. 6. a. Put A must be written on the stock with the lower price. Otherwise, given the lower volatility of Stock A, Put A would sell for less than Put B. b. Put B must be written on the stock with the lower price. This would explain its higher price. c. Call B must have the lower time to expiration. Despite the higher price of Stock B, Call B is cheaper than Call A. This can be explained by a lower time to expiration. d. Call B must be written on the stock with higher volatility. This would explain its higher price. e. Call A must be written on the stock with higher volatility. This would explain its higher price. 7. Exercise Price Hedge Ratio 120 0/30 = 0.000 110 10/30 = 0.333 100 20/30 = 0.667 90 30/30 = 1.000 As the option becomes more in the money, the hedge ratio increases to a maximum of 1.0. 8. S d1 N(d1) 45 -0.0268