Sasha Cyganowski, Lars Grüne, Peter E. Kloeden:
MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance


( S.S. Nielsen, ed., Programming Languages and Systems in Computational Economics and Finance. Kluwer Academic Publishers, Dordrecht (2002), 441-460)
Abstract:
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.

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MAPLE Worksheets containing the examples from the paper:

Scalar Equations:  jump_scalar.mws   Vector Equations: jump_vector.mws


Note: The paper has two errors in the jump-procedure in Section 4:

The lines 

     tau:=stats[random, exponential[1]](1):
and

     else U:=exp(stats[random, normald[mu,sigma]](1)-1): fi:
must read

     tau:=stats[random, exponential[lambda]](1):
and

     else U:=exp(stats[random, normald[mu,sigma]](1))-1: fi:
respectively.

The worksheets above are corrected. 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!