Consider the following options, which have the same two-year maturity and are written on the same stock. The firm does not pay dividends. 

Put option P1 has a strike price Xp1 = $50 

Put option P2 has a strike price Xp2 = $100 

Call option C1 has a strike price Xc1 = $100 

Call option C2 has strike price Xc2 = $50 

Your broker offers two trading strategies that can be derived from the options above. 

Strategy A: Long two puts P1 and long two calls C1 

Strategy B: Long two calls C2 and long two puts 

A. Which strategy would you choose if the two strategies have the same costs? Explain your answer.  

You now collect more information about the available securities. The stock has an implied volatility of 45% p.a.. The current risk-free rate is 1% p.a. The current stock price is $56. B. Calculate the value of the call option C1 using the Black-Scholes formula. Explain why such a deep out-of-the-money option still has a positive value. 

C. Calculate the cost of strategy B using the Black-Scholes formula.