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Antonio
Topic Author
Posts: 630
Joined: June 30th, 2004, 3:13 pm
Location: Imperial College London
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### Approximation of a multivariate gaussian probability

In order to estimate the convergence of Monte Caro methods on the pricing of rainbow options, I have to calculate the theorical valeu of the option. I already have the close formula of the option, but I need to calculate the two-dimension gaussian probability. As there doesn't exist any close formula, I'm looking for any approximation methods for it.Could anyone help me ?Thanks in advance

Gmike2000
Posts: 801
Joined: September 25th, 2003, 9:49 pm

### Approximation of a multivariate gaussian probability

dont know of any closed form approximation, but it is really easy to do this in matlab (use trapezoidal rule over a fine mesh).

daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### Approximation of a multivariate gaussian probability

Do you mean you want to compute M(a,b,r) where M() is the bivariate cumulative density function ?
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Antonio
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Posts: 630
Joined: June 30th, 2004, 3:13 pm
Location: Imperial College London
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### Approximation of a multivariate gaussian probability

Yes. That's what I wanted to do. But I found an approximation method in Hull's bookThanks

prospero
Posts: 47
Joined: March 16th, 2002, 4:00 am

### Approximation of a multivariate gaussian probability

there's an excellent article in the Summer '03 Journal of Computational Finance comparing different approximations of bivariate Normals. The one given in Hull's book didn't fare well, ended up as of the least accurate and slowest.

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