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 SDEs 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 an other financial instruments are often supposed to be driven by SDEs. 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.
An algorithm for step control in numerical solution of SDE
Laerte Sorini
;Maria Letizia Guerra
2000
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 SDEs 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 an other financial instruments are often supposed to be driven by SDEs. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
