Please answer the two questions in full. Thank you!

STERN SCHOOL OF BUSINESS - UNDERGRADUATE DIVISION NEW YORK UNIVERSITY C15.0043-001 Futures and Options Professor Menachem Brenner PROBLEM SET 5 1. Assume that the spot price of gold is $1250 per ounce, six month at-the-money European puts and calls are selling for $88 each and the continuous compounding annualized riskless interest rate for the next 6 months is 0.5 percent. a. Are there any opportunities for arbitrage profits? If so, what is the strategy? b. Using the prices of the put and the call and the current price of the underlying asset, what is the implied riskless rate? 2. Assume that the current price of spot gold is 1200. In the next two periods the price of gold is expected to either go up by 5% or decline by 5% each period. The risk-free rate is 2% each period. a. What is the value of a European call option on gold which matures in one period with a strike price of 1200? What is the hedge ratio? What is the value of a put option with the same strike price? b. What is the value of a call option on gold which matures in two periods with a striking price of 1200? What are the hedge ratios? What is the value of a put option with the same strike? Compare the values of the options with the option values obtained in a. 1