# On a semi-spectal method for pricing an option on a mean-reverting assset

## Next seminars

Supervisor
Leonard P. Bos - Department of Mathematics and Statistics, University of Calgary (Canada)
Date and time
Tuesday, June 21, 2005 at 5:30 PM - ore 17.00, te caffe` & C.
Place
Ca' Vignal - Piramide, Floor 0, Hall Verde
Programme Director
Stefano De Marchi
External reference
Publication date
May 31, 2005
Department

## Summary

We consider a risky asset following a mean-reverting stochastic process
of the form
$$dS=\alpha(L-S)dt+\sigma S dW.$$
We show that the (singular) diffusion equation which gives the value
of a European option on $S$ can be represented, upon
expanding in Laguerre polynomials, by a tridiagonal infinite matrix.
We analyse this matrix to show that the diffusion equation does
indeed have a solution and truncate the matrix to give a simple,
highly efficient method for the numerical calculation of
the solution.

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