Heston's model is formulated in the language of stochastic processes (not my case at all) and translated to a PDE, where it is solved in Fourier space in closed form. The actual price of an option then is given by a Fourier inversion. The model gives a mean reverting behaviour for volatility and allows to reproduce 'volatility smiles' - both are stylish facts observable in markets (which the classical Black-Scholes model does not cover). Here I show ways, how evaluation can be done within Maple in reasonable time: the involved integrands are very time consuming for numerical evaluation, but that can be simplified a lot using the codegen packag. That should be interesting beyond financial applications, so subsequently I added some stuff about 'smiles' and 'term structures', which is well known, but may serve as motivation for those not reading finance text too often. Download 102_Heston_using_Maple.mws (78 KB) or get the worksheet as pdf (670 KB)

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