(2015.8.8 16:00 N613)Prof. Qiang Zhang:Pricing Options under Heston Model of Stochastic Volatility----Academy of Mathematics and Systems Science

Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Qiang Zhang,Department of Mathematics, City University of Hong Kong
Inviter:	Shunlong Luo
Title:	Pricing Options under Heston Model of Stochastic Volatility
Time & Venue:	2015.8.8 16:00-17:00 N613
Abstract:	The well-known Heston model for stochastic volatility captures   the reality of the movement of stock prices in our financial market.  However, the solutions for option prices under the stochastic volatility model are expressed in terms of integrals in the complex plane. There are difficulties in evaluating these expressions numerically. We present closed-form solutions for option prices and implied volatility under Heston model of stochastic volatility. We method is based on a multiple-scale analysis in singular perturbation theory. Our theoretical predictions are in excellent agreement with numerical solutions of the Heston model of stochastic volatility. We also show that our approximate solution is valid not only in the fast-mean-reverting regime, but also in the slow  mean-reverting regime. This means that the solutions in these two different regions can be approximated by the same function. We further  apply our new approach of multiple-scale analysis to pricing Asian  options  with stochastic volatility. The results are also in excellent  agreement  with the exact numerical solutions.