MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance

S. Cyganowski, L. Grüne, P. E. Kloeden: MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance
in: Programming Languages and Systems in Computational Economics and Finance, S.S. Nielsen (ed.)
Kluwer Academic Publishers, Dordrecht, 2002, 441 - 460

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The occurrence of shocks in the financial market is well known and, since the 1976 paper of the Noble Prize laureate R.C. Merton, there have been numerous attempts to incorporated them into financial models. Such models often result in jump-diffusion stochastic differential equations. This chapter describes the use of MAPLE for such equations, in particular for the derivation of numerical schemes. It can be regarded as an addendum to the chapter in this book by Higham and Kloeden (Paper [8] on Peter Kloeden's page on MAPLE for SDEs), which can be referred to for general background and additional literature on stochastic differential equations and MAPLE.


MAPLE Worksheets containing the examples from the paper: (ZIP-FIle)

The paper has two errors in the jump-procedure in Section 4:
The lines
tau:=stats[random, exponential[1]](1):
else U:=exp(stats[random, normald[mu,sigma]](1)-1): fi:
must read
tau:=stats[random, exponential[lambda]](1):
else U:=exp(stats[random, normald[mu,sigma]](1))-1: fi:
Note that the second error affects the simulation results, hence the figures produced by the corrected worksheets now look different. Many thanks to Nick Yannios for reporting these errors!

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