Problem 2. Suppose a share of stock currently trades for $50. A call option written on this stock with an exercise price of $50 trades for $2, and an otherwise identical put option also trades for $2. The options are both European and expire 1 month from today. A. Describe a trading strategy involving the call, the put, and the share that enables you to synthetically replicate a riskless pure discount bond1 with a face value equal to the exercise price on these options. B. What is the annualized riskless rate of interest implied by the prices of these various securities? C. Suppose that the annualized riskless rate of interest is 3%. Describe an arbitrage strategy that will enable you to make riskless profits with zero net investment. Calculate the profits that are earned, and also numerically confirm that the profits are riskless and do not involve any investment of your own money.

Problem 3. Suppose the current value of the SP 500 stock market index is 2,700. Currently, the annualized three-month t-bill yield is 2.37%, and annualized six-month t-bill yield is 2.45%. Furthermore, the consensus analyst forecast of the SP 500 dividend yield for the coming year is 2%. Calculate the forward price of the SP 500 index for three-month and six-month contracts, assuming continuously compounded interest rates and dividend yields.

Problem 4. The continuously compounded two-month interest rates in Switzerland and the United States are 1% and 2% respectively. The spot price of the Swiss franc is $0.9300. The forward price for a contract deliverable in two months is $0.9400. What arbitrage opportunities does this create? 1A pure discount bond is a bond which pays principal plus interest on the bond's maturity date.