* L.Isella <L.Isella at myrealbox.com> [2006-02-04 15:03:10 +0000]:
> Dear All,
> I have not been active on the Maxima mailing list for a long time.
> I am interested in stochastic calculus for financial applications and I recall some discussion about an implementation of the Ito stochastic calculus for Maxima.
> I wonder if Maxima can do anything like deriving the distribution of a random variable following a certain stochastic process, at least in some cases.
Hi Lorenzo,
Check Andrei Zorin's Stochastic Calculus package for Maxima at
http://www.uic.nnov.ru/~zoav1/mac/sde-0.9.tar.gz
Hope this helps.
Milan
> For example, consider a stock S whose evolution is described by the geometric Brownian motion (BM) leading to Black and Scholes (BS) equation.
> A European option is defined by a certain payoff function depending on the underlying S and can be exercised only at a specific time, called maturity.
> As a consequence of the BM, stock returns are lognormally distributed.
> In the case of a complicated payoff, for which no analytical formula is available, one can still price the option e.g. by Monte Carlo simulating many lognormally distributed returns and take the option's expectation value.
> Depending on the process the stocks are expected to follow, their distribution will be different, but knowing it amounts to being able to price at least certain kinds of options.
> Many thanks
>
> Lorenzo
>
> Best regards
>
> Lorenzo
>
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