Consider the following information about a non-dividend paying stock.

Current Stock Price St	$55
Return Standard Deviation	40% per year
Dividend Rate	0% per year
Risk-free Rate (continuously compounded)	6% per year

1. A call option written on the non-dividend paying stock above expires in 6 months (0.5 year) and has an exercise price of $50. Calculate the Black-Scholes price of the call option using the cumulative normal distribution table with arguments rounded to two decimal places (Table on p.34 of Chapter 15-16 Lecture Slides or Table 16-2 on p.523 of the textbook).

2. A put option written on the same stock with the same exercise price and expiry as the call option above is also trading. Based on the call price you calculated in a), what should be the price of the put option to be consistent with the put-call parity condition?

3. Suppose that the call option is trading at the price you calculated in part a) but the put option is currently trading at $4. Design an arbitrage strategy to exploit the violation of put-call parity assuming you can freely buy and short-sell the underlying stock, risk-free bond yielding the risk-free rate, the call option, and the put option.

4. Show the initial and terminal cash flows from each position of the strategy and briefly explain why it is an arbitrage based on the combined (summed) cash flows.