Assume the Black-Scholes framework for a stock. You are given: i) The current stock price is 40 ii) The stock pays no dividends iii) The expected rate of appreciation is 16% iv) The stock' s volatility is 30% v) The Black-Scholes price of a 6-month 42-strike European call on the stock is 3.22 vi) The continuously compounded risk-free rate is 8% You just bought a 6 -month straddle which pays the absolute difference between the stock price after 6 months and 42 . Calculate the probability of having a positive profit after 6 months: Possible Answers Less than 0.35 At least 0.35 but less than 0.40 At least 0.40 but less than 0.45 At least 0.45 but less than 0.50 At least 0.50 For a futures index, you are given that: i) the time-t value of the index is F(t) ii) F(0)=75 iii) The index's volatility is 35% iv) The continuously compounded risk-free interest rate is 10% A European gap call option has a time-1 payoff of F(1)K if F(1)>85, and is 0 otherwise. Given that the current price of the gap call is 0 , find K