[Maxima] Maxima and Stochastic Calculus
L.Isella at myrealbox.com
Sat Feb 4 09:03:10 CST 2006
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.
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