Answer Happy

Consider an investor who wishes to protect herself against a decrease in the price of stock S and so would like to buy a put option. She is considering two actively traded put options with the following characteristics: Option Strike price Maturity Current price P₁ 2 P₂ 2 So 100- = Assume that the per annum bank deposit rate is R = 1 + r= 1.03 and that today the stock price is 100 and it has the following process: t = 0 105 104 Su 110- = -Sa 90- = t = 1 - Suu = 121 -Sud - 99 = -Sdu = 99 Sdd = 81 5.3 4.85 t = 2 Time (years)

Please answer the following questions: Q1.1 (2 points) Value the put options using the risk-adjusted probabilities. Which put option should she buy? Q1.2 (2 points) Find the price of the Arrow-Debreu securities for each state of the world, for both t=1 and t=2 (i.e., Pu, Pd, Puu, Pud, Pdd). 0 0 0 0 0 Q1.3 (2 points) What is the price of a structured product that pays 1 in every state of the world, at both t=1 and t=2? Q1.4 (2 points) Find the physical probabilities with respect to S when performing a change of numeraire from R to S (i.e., probs, probs, probs, probs, probs). U d uu ud dd Q1.5 (2 points) Use the martingale approach to price a call option with a 1 period maturity that pays 5 in state u and 0 in state d.