This paper analyses the constant elasticity of volatility (CEV) model suggested by Chan et al. [K.C. Chan, G.A. Karolyi, F.A. Longstaff, A.B. Sanders, An empirical comparison of alternative models of the short-term interest rate, Journal of Finance 47 (1992) 1209–1227]. The CEV model without...

Stochastic differential equations with Markovian switching (SDEwMSs), one of the important classes of hybrid systems, have been used to model many physical systems that are subject to frequent unpredictable structural changes. The research in this area has been both theoretical and applied. Most...

We show how to simulate Brownian motion not on a regular time grid, but on a regular spatial grid. That is, when it first hits points in δZ for some δ0. Central to our method is an algorithm for the exact simulation of τ, the first time Brownian motion hits ±1. This work is motivated by...