0
$\begingroup$

I'm trying to find a way to price a triple product forward with payoff XYZ at time T using risk-neutral pricing. But I don't really have a math background and I have trouble finding a way to account for correlation with 3 assets.

I know that for 2 assets with SDEs:

dX= a1dt + b1dz1

dY = a2dt + b2dz2

We have:

enter image description here

But how could we translate this expression when we have 3 assets instead of 2?

I looked for it online but examples were always given with 2 assets.

Thanks a lot :)

$\endgroup$
2
$\begingroup$

What you need is the Cholesky decomposition of the covariance matrix.

For a symmetric matrix $\Sigma$, the Cholesky matrix $L$ has the property

$$ \Sigma = LL^T $$ where $L$ is a matrix with zeros above the main diagonal.

In your case,

$$ d\begin{pmatrix}X\\Y\\Z\end{pmatrix}=\ldots + Ldz $$ where $L$ is the lower Cholesky matrix.

You can find a general $3x3$ example at Rosetta code and a $3x3$ online calculator at Wolfram alpha

$\endgroup$
1
  • $\begingroup$ Thanks, I'll look into it :) $\endgroup$ – Rheromaster Dec 3 '20 at 15:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.