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

Relatore
Leonard P. Bos - Department of Mathematics and Statistics, University of Calgary (Canada)

Data e ora
martedì 21 giugno 2005 alle ore 17.30 - ore 17.00, te caffe` & C.

Luogo
Ca' Vignal 3 - Piramide, Piano 0, Sala Verde

Referente
Stefano De Marchi

Referente esterno

Data pubblicazione
31 maggio 2005

Dipartimento

## Riassunto

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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