Picture of wind turbine against blue sky

Open Access research with a real impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

The Energy Systems Research Unit (ESRU) within Strathclyde's Department of Mechanical and Aerospace Engineering is producing Open Access research that can help society deploy and optimise renewable energy systems, such as wind turbine technology.

Explore wind turbine research in Strathprints

Explore all of Strathclyde's Open Access research content

The Euler-Maruyama approximation for the asset price in the mean-reverting-theta stochastic volatility model

Baduraliya, Chaminda and Mao, Xuerong (2012) The Euler-Maruyama approximation for the asset price in the mean-reverting-theta stochastic volatility model. Computers and Mathematics with Applications, 64 (7). pp. 2209-2223. ISSN 0898-1221

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

Stochastic differential equations (SDEs) have been used to model an asset price and its volatility in finance. Lewis (2000) [10] developed the mean-reverting-theta processes which can not only model the volatility but also the asset price. In this paper, we will consider the following mean-reverting-theta stochastic volatility model dV(t)=α2(μ2−V(t))dt+σ2V(t)βdw2(t). We will first develop a technique to prove the non-negativity of solutions to the model. We will then show that the EM numerical solutions will converge to the true solution in probability. We will also show that the EM solutions can be used to compute some financial quantities related to the SDE model including the option value, for example.