Consider the mean-reverting process dSt = ( St)dt + StdWt. Create a time discretization of

Consider the mean-reverting process dSt = λ(μ ˆ’ St)dt + σStdWt. Create a time discretization of Δ = 1/252 and assume that the appropriate monthly model parameters are:
λ = 0.75
σ = 0.35
S0 = 40
Consider the cases where μ = 30 and μ = 50. Create a Monte-Carlo algorithm for pricing call options under this model. In order to do this, generate a random normal sample for each time step on each path in order to create an estimate for dSt at each time step. The stock price can be computed along each step as:

Here W is a normally distributed random variable with mean 0 and variance Δ.
Generate 1000 paths of 3 years by sampling daily. Using the Monte-Carlo paths generates calls prices for options at the following strikes: 30, 40, 50, 60, 70. Comment on the difference in prices caused by changing μ.

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