Laerte Sorini
580 California St., Suite 400
San Francisco, CA, 94104
An Algorithm for Step Control in Numerical Solution of SDE
1998, IFAC Proceedings Volumes
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Abstract
The explicit solution of a Stochastic Differential Equation (SDE) can be obtained only when the drift and diffusion coefficients are linear. However a qualitative analysis can be done introducing numerical schemes for the approximation of SDEs solutions. In particular an algorithm for step control in numerical solution of SDE is presented here. Numerical solution of SDEs is applied to a large number of research's fields, among these finance is now one of the most interesting. In fact the dynamics of stock prices, interest rates, volatilities and other financial instruments are often supposed to be driven by SDEs. In the classical schemes of Euler and Milstein and in the more recent one due to Kloeden and Platen the discretization step is assumed to be constant. The approximation error becomes smaller as the length of step decreases but a too much small step implies higher computational time and this is not a desirable feature. The algorithm presented reduces the discretization step only when the trajectory shows quick variations and so the approximation error is reduced without increasing too much the number of iterations. Copyright ~ 1998lFAC
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