2 research outputs found
A Fast Mean-Reverting Correction to Heston's Stochastic Volatility Model
We propose a multi-scale stochastic volatility model in which a fast
mean-reverting factor of volatility is built on top of the Heston stochastic
volatility model. A singular pertubative expansion is then used to obtain an
approximation for European option prices. The resulting pricing formulas are
semi-analytic, in the sense that they can be expressed as integrals.
Difficulties associated with the numerical evaluation of these integrals are
discussed, and techniques for avoiding these difficulties are provided.
Overall, it is shown that computational complexity for our model is comparable
to the case of a pure Heston model, but our correction brings significant
flexibility in terms of fitting to the implied volatility surface. This is
illustrated numerically and with option data
A Fast Mean-Reverting Correction to Heston's Stochastic Volatility Model
We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for European option prices. The resulting pricing formulas are semi-analytic, in the sense that they can be expressed as integrals. Difficulties associated with the numerical evaluation of these integrals are discussed, and techniques for avoiding these difficulties are provided. Overall, it is shown that computational complexity for our model is comparable to the case of a pure Heston model, but our correction brings significant flexibility in terms of fitting to the implied volatility surface. This is illustrated numerically and with option data.