On the Number of State Variables in Options Pricing
Management Science
Sensitivity study of heston stochastic volatility model using GPGPU
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Currency option pricing with Wishart process
Journal of Computational and Applied Mathematics
A unified approach to pricing and risk management of equity and credit risk
Journal of Computational and Applied Mathematics
Mean-variance portfolio selection with correlation risk
Journal of Computational and Applied Mathematics
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State-of-the-art stochastic volatility models generate a “volatility smirk” that explains why out-of-the-money index puts have high prices relative to the Black-Scholes benchmark. These models also adequately explain how the volatility smirk moves up and down in response to changes in risk. However, the data indicate that the slope and the level of the smirk fluctuate largely independently. Although single-factor stochastic volatility models can capture the slope of the smirk, they cannot explain such largely independent fluctuations in its level and slope over time. We propose to model these movements using a two-factor stochastic volatility model. Because the factors have distinct correlations with market returns, and because the weights of the factors vary over time, the model generates stochastic correlation between volatility and stock returns. Besides providing more flexible modeling of the time variation in the smirk, the model also provides more flexible modeling of the volatility term structure. Our empirical results indicate that the model improves on the benchmark Heston stochastic volatility model by 24% in-sample and 23% out-of-sample. The better fit results from improvements in the modeling of the term structure dimension as well as the moneyness dimension.