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 14 to 22 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 Buy 0 4667 shares, Y $7 88 (borrow) Buy 0 3333 shares, Y $7 88 (borrow) Buy 0 6536 shares, Y $8 72 (borrow) Buy 0 4328 shares, Y $8 72 (borrow) None of the given answers Work 4 36x ye (0 06 0 25), 0 24x ye (0 06 0 25), x 0 33, 4 12 ye (0 06 0 25), y 7 88 What is the price of the call option $2 12 $2 76 $3 18 $3 24 $4 12 Work 0 33 30 7 88 2 12 What is the risk neutral probability that the stock price would be $36 0 538 0 362 0 682 0 493 0 551 Work P e (0 06 0 25) 0 8 1 2 0 8 0 538 What is the expected payoff of the call option (after 3 months) using risk neutral probabilities $5 65 $4 93 $3 82 $2 15 None of the given answers Work 4 0 538 2 15 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 0 6240 0 5813 0 4212 0 3333 0 2128 Now consider a two period binomial model Use the same information as in question 15 but now the call option expires after 3 3 6 months What is the price of the call option $2 28 $2 62 $3 14 $3 92 $4 27 Consider a European put option using the one period binomial model as in question 15 The strike price of the put is $28 What is the price of the put option $1 82 $2 14 $2 63 $3 87 $4 12 Consider a two period binomial model using the information in question 15 The put option is will expire after 3 3 6 months What is the price of the European put option with a strike price of $28 $3 47 $2 96 $2 37 $1 94 $1 82 If the above put option is an American put, what is its price $3 47 $2 96 $2 37 $1 94 $1 82 Please show calculations as I'm trying to figure out how to do these exercises Thanks

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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 14 to 22. 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?

Work: 4 = 36x + ye^(0.06*0.25), 0 = 24x + ye^(0.06*0.25), x = 0.33, 4 = 12 + ye^(0.06*0.25), y = -7.88

Work: 0.33 * 30 7.88 = 2.12

Work: P = e^(0.06*0.25) 0.8 / 1.2 0.8 = 0.538

What is the expected payoff of the call option (after 3 months) using risk neutral probabilities?

Work: 4 * 0.538 = 2.15

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?

Now consider a two period binomial model. Use the same information as in question 15 but now the call option expires after 3 + 3 = 6 months. What is the price of the call option?

Consider a European put option using the one period binomial model as in question 15. The strike price of the put is $28. What is the price of the put option?

Consider a two period binomial model using the information in question 15. The put option is will expire after 3 + 3 = 6 months. What is the price of the European put option with a strike price of $28?