Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Prof. Qiang Zhang,Department of Mathematics, City University of Hong Kong
Pricing Options under Heston Model of Stochastic Volatility
Time & Venue:
2015.8.8 16:00-17:00 N613
The well-known Heston model for stochastic volatility capturesthe 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 slowmean-reverting regime. This means that the solutions in these two different regions can be approximated by the same function. We furtherapply our new approach of multiple-scale analysis to pricing Asianoptionswith stochastic volatility. The results are also in excellentagreementwith the exact numerical solutions.
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