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

TL;DR

This paper introduces a multiscale stochastic volatility model with analytic pricing formulas that improves the accuracy and efficiency of pricing SPX and VIX options, capturing short-term market impacts.

Contribution

It develops a multiscale volatility model adding a fast scale factor to Heston, with approximate analytic formulas for efficient calibration and better fit to market data.

Findings

Reduces training errors for SPX options by 9.9% and VIX options by 13.2%.

Decreases test errors for SPX options by 13.0% and VIX options by 16.5%.

Highlights the importance of multiscale modeling for capturing short-term market effects.

Abstract

This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To capture the multiscale volatility of the financial market, our model adds a fast scale factor to the well-known Heston volatility and we derive approximate analytic pricing formulas for the options under the model. The analytic tractability can greatly improve the efficiency of calibration compared to fitting procedures with the finite difference method or Monte Carlo simulation. Our experiment using options data from 2016 to 2018 shows that the model reduces the errors on the training sets of the SPX and VIX options by 9.9% and 13.2%, respectively, and decreases the errors on the test sets of the SPX and VIX options by 13.0\% and 16.5\%, respectively, compared to the single-scale model of Heston. The error reduction is possible because the additional factor reflects short-term impacts on the market, which is difficult to achieve with only one factor. It highlights the necessity of modeling multiscale volatility.