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

Mark Higgins

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arXiv · 1404.4028

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

Mark Higgins

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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.

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Mark Higgins. 2014-04-15. Stochastic Spot/Volatility Correlation in Stochastic Volatility Models and Barrier Option Pricing. https://arxiv.org/abs/1404.4028

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