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arXiv · 1306.5447

Explicit implied volatilities for multifactor local-stochastic volatility models

Matthew Lorig·Stefano Pagliarani·Andrea Pascucci
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Abstract

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under five different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility, $3/2$ stochastic volatility, and SABR local-stochastic volatility.

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Matthew Lorig, Stefano Pagliarani, Andrea Pascucci. 2013-06-23. Explicit implied volatilities for multifactor local-stochastic volatility models. https://arxiv.org/abs/1306.5447

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