# [Maxima] Maxima and Stochastic Calculus

Richard Fateman fateman at cs.berkeley.edu
Sat Feb 4 10:32:25 CST 2006

```This sounds like a numerical computation.  If so, perhaps a program
has already been written to solve it in C, or Fortran, or Matlab, ..
in which case it might be possible to call it from Maxima, or
translate it into Lisp, or rewrite it in Maxima's language, or hire
someone to do one of these tasks.
RJF

----- Original Message -----
From: "L.Isella" <L.Isella at myrealbox.com>
To: <maxima at math.utexas.edu>
Sent: Saturday, February 04, 2006 7:03 AM
Subject: [Maxima] Maxima and Stochastic Calculus

> 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.
> 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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