Consider six-month European call and put options on a stock that pays no dividend. The current share price is $40 and the risk free rate is 10% per annum. The Black-Scholes implied volatility is 30% per annum.

a). Construct an ATM straddle using the call and put and compute the delta, gamma and theta for the straddle based on the Black-Scholes model.

b). What is the relation between the straddle’s delta, gamma and theta.