Question: question 3 Consider a stock whose current price is S - $50. The volatility of its return is 20% per year and the risk free

question 3

Consider a stock whose current price is S - $50. The volatility of its return is 20% per year and the risk free rate of interest is 5% per year. (a) Simulate three values for the price of the stock after 6 months. Use the formula: S, = Sexp (r --o' )T +ovTZ, where Sr is the price of the stock after time I, r is the risk-free rate of interest, " is the volatility of the stock's return, Z is a sample from the standard normal distribution. Use the following three samples from the standard normal distribution: -0.300023, 1.27768 and 0.244257. [3 marks] (b) Consider a call option with maturity 7 - 6 months on the stock described above, with the strike price X = $50. What is the pay-off of this option under each of the above 3 simulations? [3 marks] (c) Consider the 3 simulations described above and another 3 additional simulations, in which the samples from the normal distribution are lower: 0.67042, 0.5537 and 0.42381. What is the price of the option described at (b) based on these 6 simulations? Justify your answer. [9 marks]

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