given the following information: S-60, K-65, volatility = 0.4 per yea. year, Tim
ID: 2807321 • Letter: G
Question
given the following information: S-60, K-65, volatility = 0.4 per yea. year, Time to expiration = 3M hat is the probability that a European call option on the stock will be 1 money upon expiration? (7 points) What is the probability that a European put option on the stock wi money upon expiration? (7 points) Use Black and Scholes formula to calculate the call price. (10 poa ( points) in-the- points) Use Put-Call Parity to calculate the put price using call price from (a Use Black and Scholes formula to calculate the put price. (10 points) e. either go up by 0 percent or down by 8 percent in one year. The risk-free rate is 4 percent. Assume Consider a binomial world in which the current stock price of 80 can a one-period world. Answer the following questions about a call with an ex ercise price of 80. a. What would be the call's price if the stock goes up? (3 points) b. What would be the call's price if the stock goes down? (3 points c. For a short position with every share of Call, how many shares of stocks should you buy to form a risk-free portfolio? (4 points) d. What is the value of the call? (6 points)Explanation / Answer
a)
Up price = 80*(1+10%) = 88
Call = 88 - 80 = 8
b)
Down price = 80*(1-8%) = 73.6
Call = 0
c)
hedge ratio = (8 - 0) / (88 - 73.6) = 0.56
d)
Call = 0.56*80 + (-0.56*88 + 8)/(1+4%) = 5.1282
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