# B give an expression of s t when t 1 c give the

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(b) Give an expression of S T when T =1. (c) Give the probability that the payoff of the bull spread (respectively the bear spread, the collar and the butterfly) is positive at T = 1 . (d) Are these assumptions realistic to model the stock price? Problem 2: [5marks] Forward contracts A stock is expected to pay a dividend of \$1 per share in 2 months and in 5 months. The stock price is \$60 and the risk-free rate is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a 6-month forward contract on the stock. (a)[ 2pts] What are the forward price and the initial value of the forward contract. Do not apply a formula from the lecture notes but redo the proof with arbitrage arguments. (b)[ 2pts] 3 months later, the price of the stock is \$48 and the risk free rate is still 8% per annum. What are the forward price and the value of the short position in the forward contract? To do the last 5 problems, you have to find the price of some derivatives. The only accepted method is to give an explicit replicating strategy. The price of the derivative is the price of the replicating strategy by the no-arbitrage principle. Problem 3: [4marks] Assume a market with a constant continuously compounded interest rate r offered by the bank and a risky stock S . Consider derivative with the payoff X T at T

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• Spring '09
• idk..
• fairly priced index

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