Efficient Monte Carlo simulation of security prices
Monte Carlo simulation schemes for solving stochastic differential equations of Itô type are considered. The authors study first- and second-order schemes of approximation of the stochastic equation. The main result of the paper consists in determining the optimal tradeoff between the stepsize \(h\) of the scheme and the order of convergence \(k\). The tradeoff between increasing the number of time-intervals and increasing the number of simulations is resolved for first-order discretization schemes as well as for second- and higher-order schemes. The results are illustrated by a simple option pricing example, an application of Monte Carlo methods to an asset pricing problem in continuous time security prices.
stochastic differential equations of Itô type
scientific article; zbMATH DE number 898161