Provide an analysis of the effectiveness of dynamic hedging of an options position.

For each of the price trajectory, perform delta-hedging. What are the hedging costs for the case in which option closes out-of-the-money, and for the case in which option closes in-the-money, respectively?

Assume the stock price follows a geometric Brownian motion with expected return, =0, and volatility =0.5, simulate two price trajectories using St+t=Stexp{(0.52)t+t}, where is a standard normal random variable, t=1/252 (daily increment), and time horizon is one year. For the first price trajectory, we want the price at maturity to be less than the strike price, i.e., STK, such that the call option closes in-the-money. Plot the two price trajectories on the same graph. Note: since the price trajectories are randomly generated, you may need to repeat the simulation multiple times until you find one that fits the criterion. Assume the stock price follows a geometric Brownian motion with expected return, =0, and volatility =0.5, simulate two price trajectories using St+t=Stexp{(0.52)t+t}, where is a standard normal random variable, t=1/252 (daily increment), and time horizon is one year. For the first price trajectory, we want the price at maturity to be less than the strike price, i.e., STK, such that the call option closes in-the-money. Plot the two price trajectories on the same graph. Note: since the price trajectories are randomly generated, you may need to repeat the simulation multiple times until you find one that fits the criterion