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Hello, I am trying to implement a vanilla European option pricer with Monte Carlo and compare its result to the BS analytical formula's result. I noticed that as I increase (from 1 million to 10 millions) the number of simulations, the MC result starts to diverge... Note that I...

thanks Alan.

Hello Alan, Thanks a lot for your reply. I understand the first part of your reply. One point remains confuse to me: what is the difference between a stochastic differential equation and a stochastic process? In the case above what is the SDE and what is the process? Regards, Julien.

Hello, I understand that by applying Ito's lemma to the following SDE dX = mu* X * dt + sigma * X * dW one obtains a solution to the above SDE which is as follows: X(t) =X (0) * exp(sigma * W(t) + ( mu- 0.5 * sigma^2)* t)) I have been told that I can use either of these equations (SDE...

Wonderful Alan! Thanks a lot. I get it now! Julien.

Hello Alan, Thanks. I got your reply this morning and I am working through it. I tried to compute the variance using the following formula: Var(X_2)=E(X^2)-E(X)^2 with E(X)^2 = mu_2^2 I get this: Var(X_2)=E[(lambda_21 U_1)^2 + 2 (lambda_21 U_1 lambda_22 U_2)+(lambda_22 U_2)^2] Is it...

Hello, Say I have two risk factors X_1 and X_2. Standard deviation for X_1 is sigma_1 and sigma_2 for X_2. Furthermore, X_1 has a mean of mu_1 and X_2 has a mean of mu_2. Correlation between X_1 and X_2 is rho. The system is as follows: X_1=mu_1 + lambda_{11} U_1 X_2=mu_2 + lambda_{21}...

I read in a book that the distance to default of a company is "2.978". Can anyone please tell me what is the unit implied behind this measure? Are they "years" for instance? Thanks in advance, Julien.