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Exam 16: Option Valuation

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Question 31

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You calculate the Black-Scholes value of a call option as $3.50 for a stock that does not pay dividends, but the actual call price is $3.75. The most likely explanation for the discrepancy is that either the option is ________ or the volatility you input into the model is too ________.

A) overvalued and should be written; low
B) undervalued and should be written; low
C) overvalued and should be purchased; high
D) undervalued and should be purchased; high

E) A) and D)
F) B) and C)

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Question 32

Multiple Choice

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The time value of a call option is likely to decline most rapidly ________ days before expiration?

A) 10
B) 30
C) 60
D) 90

E) A) and D)
F) A) and C)

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Question 33

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Suppose you purchase a call and write a put on the same stock with the same exercise price and expiration. If prices are at equilibrium, the value of this portfolio is ________.

A hedge ratio of 0.70 implies that a hedged portfolio should consist of ________.

The percentage change in the call option price divided by the percentage change in the stock price is the ________ of the option.

Perfect dynamic hedging requires ________.

The ________ is the difference between the actual call price and the intrinsic value.

A high dividend payout will ________ the value of a call option and ________ the value of a put option.

The current stock price of Howard & Howard is $64, and the stock does not pay dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard deviation of H&H's stock is 20%. You want to purchase a call option on this stock with an exercise price of $55 and an expiration date 73 days from now. Using the Black-Scholes OPM, the call option should be worth ________ today.

In order for a binomial option price to approach the Black Scholes price, ________.

The current stock price of Alcoco is $70, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of Alcoco's stock is 40%. You want to purchase a call option on this stock with an exercise price of $75 and an expiration date 30 days from now. Based on the Black-Scholes OPM, the call option's delta will be ________.

The stock price of Harper Corp. is $33 today. The risk-free rate of return is 6%, and Harper Corp. pays no dividends. A put option on Harper Corp. stock with an exercise price of $30 and an expiration date 73 days from now is worth $0.95 today. A call option on Harper Corp. stock with an exercise price of $30 and the same expiration date should be worth ________ today.

If you have an extremely "bullish" outlook on the stock market, you could attempt to maximize your rate of return by ________.

Calculate the price of a European call option using the Black Scholes model and the following data: stock price = $56.80, exercise price = $55, time to expiration = 15 days, risk-free rate = 2.5%, standard deviation = 22%, dividend yield = 8%.

A stock with a current market price of $50 and a strike price of $45 has an associated call option priced at $6.50. This call has an intrinsic value of ________ and a time value of ________.

What aspect of the time value of money does the factor of e represent in the Black-Scholes option value formula?

A stock with a stock and exercise price of $20 can either increase to $26 or decrease to $18 over the course of one year. In a one-period binomial option model, given an interest rate of 5% and equal probabilities, what is the likely option price? (Use annual compounding.)

The Black-Scholes option-pricing formula was developed for ________.

The hedge ratio is often called the option's ________.

The current stock price of Howard & Howard is $64, and the stock does not pay dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard deviation of H&H's stock is 20%. You want to purchase a put option on this stock with an exercise price of $55 and an expiration date 73 days from now. Using Black-Scholes, the put option should be worth ________ today.