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Open Access research with a European policy impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the European Policies Research Centre (EPRC).

EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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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

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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.