Three periods American call option with a strike price of K on a stock, with the...

 

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Three periods American call option with a strike price of K on a stock, with the respective payoff at each different node, is shown as Figure 2. Su Payoff: A Su Payoff:D Sud Payoff: G Payoff: B Sud So Payoff: E Sa Sud Payoff:0 Payoff:C S Payoff:0 S Payoff:0 Figure 2 You are given information about the option. It is optimal to exercise early at the node ud only. The continuously compounded annual risk-free rate and continuously compounded annual dividend yield rate is r and 8, respectively. Duration for each period is h. . The initial stock value is So. Sulaj is defined as the stock price after going upper node for i times and going lower node for j times, given that i,j = 0,1,2,... The probability of reaching the upper node is 0.70. Show that the premium of the American call option can be written as below: Co (A+BB+YC)e-rh + 0Ee-yrh hence, determine (x + y) * (a + y + 0). (10 marks) Given that the risk-free interest rate continuously compounded is r. Show that the difference between call and put prices for a non-dividend-paying stock under the one-period binomial tree satisfies the put-call parity. Co-Po So-Ke-rh (10 marks) Three periods American call option with a strike price of K on a stock, with the respective payoff at each different node, is shown as Figure 2. Su Payoff: A Su Payoff:D Sud Payoff: G Payoff: B Sud So Payoff: E Sa Sud Payoff:0 Payoff:C S Payoff:0 S Payoff:0 Figure 2 You are given information about the option. It is optimal to exercise early at the node ud only. The continuously compounded annual risk-free rate and continuously compounded annual dividend yield rate is r and 8, respectively. Duration for each period is h. . The initial stock value is So. Sulaj is defined as the stock price after going upper node for i times and going lower node for j times, given that i,j = 0,1,2,... The probability of reaching the upper node is 0.70. Show that the premium of the American call option can be written as below: Co (A+BB+YC)e-rh + 0Ee-yrh hence, determine (x + y) * (a + y + 0). (10 marks) Given that the risk-free interest rate continuously compounded is r. Show that the difference between call and put prices for a non-dividend-paying stock under the one-period binomial tree satisfies the put-call parity. Co-Po So-Ke-rh (10 marks)

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To show that the premium Of the American call option can be written as C0alpha Abeta Bgamma CexrhThe... View the full answer