Approximating Explicitly the Mean-Reverting CEV Process
Approximating Explicitly the Mean-Reverting CEV Process
We are interested in the numerical solution of mean-reverting CEV processes that appear in financial mathematics models and are described as nonnegative solutions of certain stochastic differential equations with sublinear diffusion coefficients of the form<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:math>where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo><</mml:mo><mml:mi>q</mml:mi><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math>. Our goal is to construct explicit numerical schemes that …