An options trader purchases 1000 1-year at-the-money calls on a non-dividend paying stock with S0 = $100, α = 0.20, and σ = 0.25. Assume the options are priced according to the Black-Scholes formula and r = 0.05.
a. Use Monte Carlo (with 1000 simulations) to estimate the expected return, standard deviation, skewness, and kurtosis of the return on the call when it is held until expiration. Interpret your answers.
b. Repeat for an at-the-money put. Discuss.