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6. One of the assumption we have made is that the risk-free interest rate is constant. In this problem, we will relax that assumption! Consider thoe following two period binomial model with a random interest rate rn. In this model, we define the risk-neutral pricing formula by 1+rn - d where p_- n1Tn Can you explain this formula?) Let V2 be a call option with expiration date t-2 and strike price K-7. a) Fill in the following binomial tree SIHH] = 16 V2HT 4 Vo S2[TT] ½TTIb) Suppose you sold the option for Vo at timet 0. However, you now regret your decision and now want to hedge against the risk you are now facing. Compute the am ount of stock you should purchase. Д0 Ao. so that at time1, regardless of what happens to the stock, the value of your portfolio is Vi 1- c) Suppose the first coin toss is a head: i.e. w,-H. Calculate how much stock you should buy now, Ді (H), to ensure that at t-2, the value of your portfolio is (S2-7)+.

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