Question
Consider a one period binomial model. The initial stock price is $30. Over the next 3 months, the stock price could either go up to
- Consider a one period binomial model. The initial stock price is $30. Over the next 3 months, the stock price could either go up to $36 (u = 1.2) or go down to $24 (d = 0.8). The continuously compounded interest rate is 6% per annum. Use this information to answer questions below. Consider a call option whose strike price is $32. How many shares should be bought or sold and how much money should be deposited or invested to replicate the payoff of the call option?
A.Buy0.4667 shares, Y = -$7.88 (borrow)
B.Buy0.3333 shares, Y = -$7.88 (borrow)
C.Buy0.6536 shares, Y = -$8.72 (borrow)
D.Buy0.4328 shares, Y = -$8.72 (borrow)
E.None of the above
2) What is the price of the call option?
A.$2.12
B.$2.76
C.$3.18
D.$3.24
E.$4.12
3) What is the risk-neutral probability that the stock price would be $36?
A.0.538
B.0.362
C.0.682
D.0.493
E.0.551
4) What is the expected payoff of the call option (after 3 months) using risk neutral probabilities?
A.$5.65
B.$4.93
C.$3.82
D.$2.15
E.None of the above
5) Suppose you wish to form a risk free portfolio by selling a call and buying a certain number of shares. How many shares should be bought for every call sold?
A.0.6240
B.0.5813
C.0.4212
D.0.3333
E.0.2128
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