Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model

Baldeaux, Jan; Badran, Alexander

doi:10.48550/arxiv.1203.5903

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Sabr Local-stochastic Volatility1

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2015

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“…To the best of our knowledge, the above formula is the first explicit implied volatility expansion for the 3/2 model. The characteristic function of X t is given, for example, in Proposition 3.2 of Baldeaux and Badran (2012). We have…”

Section: Sabr Local-stochastic Volatilitymentioning

confidence: 99%

Explicit Implied Volatilities for Multifactor Local‐stochastic Volatility Models

Lorig

Pagliarani

Pascucci

2015

Mathematical Finance

123

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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. We also establish rigorous error estimates for these quantities. 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 four different model dynamics: constant elasticity of variance local volatility, Heston stochastic volatility, three-halves stochastic volatility, and SABR local-stochastic volatility.

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Section: Sabr Local-stochastic Volatilitymentioning

confidence: 99%