Suppose that a stock is currently trading at$85 and does not pay any dividend andthat the current 1-year risk-free rate is 5% (annualized). Suppose that over a given6-month period the stock will either go up 25% or down 20%

.(a) Use a two-step Binomial Tree to value an American call option with a strike priceof$90 that is expiring in 1-year. Be sure to show your work. You can use any of the three methods we discussed in class.

(b) Suppose you go long 5 of the options described above. What is the hedging strategy you would need to create a delta-hedged portfolio today (time 0)?

(c) Assume the counterparty who wrote you the option has a probability of default over the next six months of 3%, 6% from 6-months to 1-year from now, and are covery rate of 80%. Explain what a Credit Value Adjustment (CVA) is and how this would affect the value of the option if included For simplicity you can assume that the present value of the option is 10.21 from now until6-months and 9.00 from 6-months to 1-year.(d) Discuss how you could hedge this counterparty risk?3