Question

14. 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 the remaining questions in this assignment. 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. Buy 0.4667 shares, Y = -$7.88 (borrow) B. Buy 0.3333 shares, Y = -$7.88 (borrow) C. Buy 0.6536 shares, Y = -$8.72 (borrow) D. Buy 0.4328 shares, Y = -$8.72 (borrow) E. None of the above

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Answer 1

14 - C - Invest in 0.6536 Shares at a price of $ 30 each and borrow $8.72 which will give current value of $30

16 - D - Risk neutral probability of the stock price would be $36 is 0.493, calculated as below :

Risk Neutral Probability (q) = (1 - probability of down (d)) / ((Probability of up (u) -probability of down (d))

= (1-0.8)/(1.2-0.8) = 0.2/.04 = 0.5

0.493 being the closest to 0.5, hence Risk Neutral Probability is 0.493