Please show all work.

(a) Please calculate the annualized (252 trading days/year) historical volatility using the daily prices of NYSE Euronext, Inc. (NYX).

4/16	22.13
4/17	21.87
4/20	21.38
4/21	19.62
4/22	20.55
4/23	21.45

(b) (Continued from part a) The information about NYX and European call option is as follows: Current Stock Price = $22.81, Strike Price = $20, r_C=2.50% (continuously compounded interest rate), T = 21 days. Calculate the Black-Scholes model price for the European call option using the annualized historical volatility.

(c) Robert buys one call option contract on 100 shares of NYX with the strike price of $22.5 (the call price = $1.81 in the option market) and sell one call option contract with the strike price of $25 (the call price = $0.78). Both options contracts have the same maturity date. At option expiration, if the stock price of NYX is $24, what is the net profit/loss for all positions?

(d) (Continued from part c) Find the breakeven stock price for Roberts strategy.