Reference no: EM133430160

Question: Using the Monte Carlo simulation method, estimate the price of a one-year, 45-strike, Eu-ropean put option on a stock that is trading for $60 today. The risk-free interest rate is equal to 2.5% per year and the stock pays dividends at a rate of 1.5% per year. Both rates are continuously compounded. The option is trading at an implied volatility of 55%. The simulated value of the stock's price on the option's maturity date is based on the following formula:

ST = S0e(r-q-σ2/2)T +σ√T ×N ORM SIN V (RAN D()),

where S0 is the stock price, T is the option's tenor expressed in years, r is the continuously- compounded risk-free rate, q is the stock's continuously compounded dividend yield, σ is the option's implied volatility, and NORMSINV(RAND()) is the combination of MS Excel functions that produces random draws from the standardized normal distribution.

(A) Using the above equation, draw a sample consisting of 10,000 simulated values for the stock's price on the option's maturity date, and show your simulated price distribution with a histogram.

(B) Estimate the option's price using the stock's first i) 1,000, ii) 2,000, iii) 5,000, and all iv) 10,000 simulated prices produced in A). For each subsample, report the option price estimate, its standard deviation, standard error, 95% confidence band, and pricing error, which corresponds to the difference between the estimate and the option's true price, based on the BSM formula. The price estimate's standard error (SE) is equal to the standard deviation (SD) of the option's discounted terminal payoffs divided by the square root of the sample size (N), i.e., SE = SD/√N . The 95% confidence band for the option's true price lies between ±1.96 × SE. Please, present your results in a neat 6 × 5 table with the statistics in the rows and the different sample sizes in the columns.