Find approximately the variance of the random variable


Programming) Consider a European call option over an underlying asset whose price at time 0 is 105 dollars, with strike price K = 110 dollars, exercise time 1 year, interest rate equal to 5% (i.e. rT = 0.05), and a volatility such that σ √ T = 0.3

1. Compute the price of the call using the Monte Carlo method applied to the formula

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with 1000 simulations. Find (approximately) the variance of the random variable whose expectation you are trying to evaluate, and give a confidence interval for the desired quantity

2. Do the same computation (including the confidence interval) combining the same method applied to the formula for the price of the put,

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with the same number of simulations, and the call-put parity formula.

 

 

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Basic Computer Science: Find approximately the variance of the random variable
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