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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.
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