Keeping Up with the Correlations: Stochastic Spot/Volatility Correlation and Exotic Pricing

TL;DR

This paper introduces a generalized Double Heston model with stochastic spot/volatility correlation, enabling efficient pricing of exotic options and capturing key market dynamics affecting barrier and volatility swap prices.

Contribution

It extends the Heston model to include stochastic correlation, providing a more accurate framework for pricing barrier derivatives and volatility swaps in FX markets.

Findings

Stochastic correlation increases out-of-the-money option prices.

Model captures positive correlation between implied volatility skew and spot moves.

Pricing impacts are comparable to bid/ask spreads.

Abstract

We consider a novel use case for the Double Heston model (Christoffersen et al,, 2009), where the two Heston sub-variances have different spot/volatility correlations but the same volatility of volatility and mean reversion speed. This parameterization generalizes the traditional Heston stochastic volatility model (Heston, 1993) to include stochastic spot/volatility correlation. It is an affine model, allowing European options to be priced efficiently by numerically integrating over a closed-form characteristic function. This model incorporates a key dynamic relevant for pricing barrier derivatives in the foreign exchange markets: a positive correlation between moves in implied volatility skew and moves in the spot price. We analyze that correlation and its impact on both barrier option pricing and volatility swap pricing. Those price impacts are comparable to or larger than the bid/ask spreads for these products. Adding stochastic spot/volatility correlation increases the prices of out-of-the-money knockout options and one touch options, assuming that the model is calibrated to market vanilla option prices. It also increases the fair strike of volatility swaps compared to the Heston model.