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In addition to the five factors discussed in the chapter, dividends also affect the price of...

In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black-Scholes option pricing model with dividends is: C=S × e−dt × N(d1) − E × e−Rt × N(d2) d1= [ln(S  /E ) +(R−d+σ2 / 2) × t ] (σ − t√)  d2=d1−σ × t√ All of the variables are the same as the Black-Scholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the stock. A stock is currently priced at $89 per share, the standard deviation of its return is 54 percent per year, and the risk-free rate is 6 percent per year, compounded continuously. What is the price of a call option with a strike price of $85 and a maturity of six months if the stock has a dividend yield of 2 percent per year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Solutions

Expert Solution

Price of a call option = $15.92

Workings:

Note:

The time to maturity is 6 months and the same is represented in years as 1/2 (6/12).

jeff jeffy answered 1 year ago
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