Stochastic Spot/Volatility Correlation in Stochastic Volatility Models and Barrier Option Pricing

TL;DR

This paper introduces a new stochastic model for barrier option pricing where the spot/volatility correlation is a separate mean-reverting stochastic process, providing an efficient approximation method validated against Monte Carlo simulations.

Contribution

It proposes a novel stochastic correlation model for barrier options and develops an efficient semi-static vega replication approximation method.

Findings

Approximation aligns well with Monte Carlo in markets with modest risk-neutral drift.

Model allows independent stochastic control of spot/volatility correlation.

Efficient pricing method reduces computational complexity.

Abstract

Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local volatility/stochastic volatility mixture model, where the mixture parameter tunes that covariance. This paper defines an alternate model where the spot/volatility correlation is a separate mean-reverting stochastic variable which is itself correlated with spot. We also develop an efficient approximation for barrier option and one touch pricing in the model based on semi-static vega replication and compare it with Monte Carlo pricing. The approximation works well in markets where the risk neutral drift is modest.