Consistent and Efficient Pricing of SPX and VIX Options under Multiscale Stochastic Volatility

Jaegi Jeon

Abstract:

We provide consistent and efficient pricing for both Standard & Poor's 500
Index options and the Chicago Board Options Exchange's Volatility
Index options under a multiscale stochastic volatility model. To capture the
multiscale, our model adds a fast scale factor to Heston's volatility and we
derive approximate analytic formulas for the options under the model. The
analytic tractability can greatly improve the efficiency of calibration compared
to fitting procedures using a numerical scheme. Our experiment using options
data for 3 years shows that the model reduces about 20% of the errors for a
single‐scale model.