Large difference of results (homework 3)

[Di3goCH]

Hi all,

I am not sure if my results are ok, but I got a large difference between the methods we have to use (Numerical Integration and Monte Carlo Simulation) when I calculated the option's price. I got around 5 and 90 respectively.

Someone else got large differences? I am not sure if it could happen, or if the results should be more similar between them.

Thanks in advance

[birte0]

Typically, the results of monte carlo and numnerical integration for calculating the value of a call option should be similar (up to a small simulation error). Ideally, it would be helpful if you could share some insights into how you computed the call option value using each method.

[Di3goCH]

Hi, I have doubts about the numerical integration. x is the price at maturity and K the strike price

I calculate the integral of (x-K) * lognormal function with the parameters given in the exercise.

I use integrate.squad() to integrate the function from K to +infinite, because for x<K the buyer does not use the call option, since he can buy the stock for a price x that is lower than K, and finally I multiply the result of the integrations for the discount factor. Should I share the code here?

[cafawo]

I integrate over the Log-Normal PDF using from scipy.integrate import quad.

PS: 90 sounds better than 5.

[Di3goCH]

Thanks! I used that function for integration before, but the problem was with the function to integrate. I tried to use lognormal.pdf() from stats, but it didn't work because of something with the parameters. I used stast.lognormal.pdf(x,sigma,mu), anyway the results was much smaller. Finally, I got similar results to that from the Monte Carlo simulation (around 90) only by writing the whole function given in the homework.