Problem
A bank risk manager tries to value a European put option. The current stock price is 100, the strike price 105, the time to maturity 2 years, the risk-free rate 0.05 and the volatility of the stock 0.4. Assume no dividends.
1. Calculate the value of this put option using the Black-Scholes formula. Provide the calculation of the different steps as discussed in the tutorial.
2. The bank manager also tries to value the put option using a Monte Carlo simulation. Simulate the stock price at the option expiration date for 1000 trials. Report the simulated stock price and the option payoff for the first 3 trials. Report your calculations and answers in 2 decimal digits.
3. Calculate the value of the put option using the Monte Carlo simulation with 1000 trials. Report how you calculated the option price after running the 1000 trials.
4. Compare your answer in 1 and 3. What could explain the price difference between these two methods? What advice could you give the risk manager to reduce the price difference between these two models?