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pjakubenas
Topic Author
Posts: 50
Joined: March 26th, 2002, 10:14 am

### Soluton to a HW/HW/Black model

Hello, everybody,Maybe someone can help me with this...We have a following modelwith with $W_{d}$, $W_{f}$, and $W_{X}$ (in general) correlated Brownian motions.A question: has anybody solved/seen this type of equations?I mean r_d and r_f are easy (just Ornshtein-Uhenbeck), what about X?More specifically, I would like to find how the correlations between the underlyingBrownian motions are related to the correlations Any sugestions are welcome.Sincerely Yours,Paulius Jakubenas

DrEvil
Posts: 36
Joined: April 22nd, 2004, 10:17 pm

### Soluton to a HW/HW/Black model

Yes, triplets of equations like this are quite commonly used (numerically) by FX quants for all sorts of FX derivatives, since each equation is a "classical" Ito process for the modelled rate.If I understand your question about the correlation, the IR-IR correlation only has to make the matrix positive definite, and Peter Jaeckel's book "Monte Carlo Methods in Finance" gives ideas on this.You can PM me if you'd like some details on what I've done with these types of models.

spv205
Posts: 478
Joined: July 14th, 2002, 3:00 am

### Soluton to a HW/HW/Black model

I would look at interest rate models, theory and practise [Brigo and Mercurio]- chapter 12, pricing equity derivatives under stochastic ratesthere they go through the equations (with only one interest rate)

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