# Derivative Security Analysis

Consider the following questions on the pricing of options on the stock of Hatters Yachts.

a. A share of Hatteras Yachts sells for $65 and has a standard deviation of 20 percent. The current risk-free rate is 4 percent and the stock pays two dividends: (1) $1.00 just prior to the option's expiration date, which is 91 days from now (exactly one-quarter of a year); and (2) a $1.00 dividend 182 days from now (i.e., exactly one-half year). Calculate the Black-Scholes value for a European-style call option with an exercise price of $60.

b. What would be the price of a 91-day European-style put option on Hatteras Yachts having the same exercise price?

c. Calculate the change in the call option's value that would occur if Hatteras' management suddenly decided to suspend dividend payments and this action had no effect on the price of the company's stock?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Part a) To calculate the price of the call, we use the black scholes calculator here: http://www.blackscholes.net/

Current price = 65

Exercise price = 60

Expected time to expire = 0.25

risk free = 4

dividend per share = 3.08% (this is because you get $1 in the first quarter and $1 in the 2nd quarter, so the annual dividend is $2, so 2/65 = 3.08%)

volatility = 20%.

This gives the price = 5.813.

Part c) Everything is the same as part a), except now dividend per share = 0%. Now the option is worth 6.22.

Part b) To calculate the price of the put, we use the call put parity formula, which states:

C - P = S - Ke^[-r(T-t)]

where C, P are the prices of call and put, S is current price, K is the strike price, r is risk free, T is time to maturity and t is current time.

We know that C = 5.813, S = 65, K = 60, r = 0.04, T = 0.25 and t = 0 (because we assume that we start at time 0)

This gives 5.813 - P = 65 - 60*e^(-0.04*0.25). This gives P = 0.216.

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