Relatore:
Leonard P. Bos
- Department of Mathematics and Statistics, University of Calgary (Canada)
martedì 21 giugno 2005
alle ore
17.30
ore 17.00, te caffe` & C.
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.
