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Exam 25: Option Valuation

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Question 1

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Which one of the following statements related to the implied standard deviation (ISD) is correct?

A) The ISD is an estimate of the historical standard deviation of the underlying security.
B) ISD is equal to (1 − d₁) .
C) The ISD estimates the volatility of an option's price over the option's lifespan.
D) The value of ISD is dependent upon both the risk-free rate and the time to option expiration.
E) ISD confirms the observable volatility of the return on the underlying security.

F) A) and C)
G) A) and D)

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Question 2

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The implied standard deviation used in the Black-Scholes option pricing model is:

A) based on historical performance.
B) a prediction of the volatility of the return on the underlying asset over the life of the option.
C) a measure of the time decay of an option.
D) an estimate of the future value of an option given a strike price e.
E) a measure of the historical intrinsic value of an option.

F) C) and D)
G) B) and C)

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Question 3

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Use the information below to answer the following question. Alpha is considering a purely financial merger with Beta. Alpha currently has a market value of $14 million, an asset return standard deviation of 55 percent, and pure discount debt of $6 million that matures in four years. Beta has a market value of $6 million, an asset return standard deviation of 60 percent, and pure discount debt of $2 million that matures in four years. The risk free rate, continuously compounded, is 3.5 percent. The combined equity value of the two separate firms is $14,180,806. By what amount will the combined equity value change if the merger occurs and the asset return standard deviation of the merged firm is 45 percent?

A stock is selling for $62 per share. A call option with an exercise price of $65 sells for $3.85 and expires in three months. The risk-free rate of interest is 2.8 percent per year, compounded continuously. What is the price of a put option with the same exercise price and expiration date?

Assume the standard deviation of the returns on ABC stock increases. This change will ________ the value of the call options and ________ the value of the put options on ABC stock.

The current market value of the assets of AMN Co. is $47 million, with a standard deviation of 21 percent per year. The firm has zero-coupon bonds outstanding with a total face value of $35 million. These bonds mature in two years. The risk-free rate is 3.6 percent per year, compounded continuously. What is the value of d₁ as it applies to the Black-Scholes option pricing model?

The delta of a call option on a firm's assets is .624. How much will a project valued at $48,000 increase the value of equity?

In the Black-Scholes option pricing formula, N(d₁) is the probability that a standardized, normally distributed random variable is:

According to put-call parity, the present value of the exercise price is equal to the:

A stock is currently selling for $39 a share. The risk-free rate is 2.5 percent and the standard deviation is 26 percent. What is the value of d₁ of a 9-month call option with a strike price of $40?

Assume a stock price of $16.80, risk-free rate of 2.7 percent, standard deviation of 59 percent, N(d₁) value of .93116, and an N(d₂) value of .85708. What is the value of a 6-month call with a strike price of $10 given the Black-Scholes option pricing model?

When computing the value of a call option using the Black-Scholes option pricing model, d₂ is calculated as:

Webster United stock is priced at $35.79 per share. The 6-month $35 call options are priced at $1.40 and the risk-free rate is 3.2 percent, compounded continuously. What is the per share value of the 6-month put option?

A call option with an exercise price of $25 and 9 months to expiration has a price of $4.92. The stock is currently priced at $26.90, and the risk-free rate is 4.1 percent per year, compounded continuously. What is the price of a put option with the same exercise price and expiration date?

Use the information below to answer the following question. You own a lot in Key West, Florida, that you are considering selling. Similar lots have recently sold for $1.2 million. Over the past five years, the price of land in the area has varied with a standard deviation of 19 percent. A potential buyer wants an option to buy the land in the next 9 months for $1,310,000. The risk-free rate of interest is 7 percent per year, compounded continuously. How much should you charge for the option? Round your answer to the nearest $100.

If the price of the underlying stock decreases, then the value of the call options ________ and the value of the put options ________.

A call option matures in six months. The underlying stock price is $37 and the stock's return has a standard deviation of 27 percent per year. The annual risk-free rate is 3.4 percent, compounded continuously. The exercise price is $0. What is the price of the call option?

A decrease in which of the following will increase the value of a put option on a stock?

The estimate of the future volatility of the returns on the underlying asset that is computed using the Black-Scholes option pricing model is referred to as the:

This morning, Kate put a European protective put strategy in place when the cost of ABC stock was $29.15 per share and the 1-year $30 ABC put was priced at $1.05 per share. How much profit per share will she earn from this strategy if the stock is worth $28 a share on the put expiration date?