utup Ih the money") then the value of a Hint: Start with this-if X is any random variable then Elmax(X,0))2 EIXThen 5. Hedging. Consider the binomial model with u 1.1, 0.9 and Pu-0.6. Assume (b) Show that if co is the value of a call option struck at K, then -K. recognize that cr = max(ST-K,0). the index is currently at So no-arbitrage price of an ATM put option is $2.38. 100 and that the risk-free rate of interest is 5%. The (a) You sell the ATM put for $2.38 and don't hedge. What is your P&L in the up and down states? Assume that the proceeds from the sale of the option earn the risk-free rate of interest. (b) When hedging the short ATM put position, should you take a long or short position in the stock? Briefly explain. (c) Suppose you short o.3 shares to hedge the market risk. i. How much do you need to borrow/lend to make the initial cost of the portfolio (including the short ATM put position) equal to zero? ii. What is the P&L in the up and down states? ii. Briefly compare with the unhedged position. (d) Suppose you purchase shares as a hedge. Note that if