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.

Lorig, M., Pagliarani, S., Pascucci, A. (2017). Explicit implied volatilities for multifactor local-stochastic volatility models. MATHEMATICAL FINANCE, 27(3), 926-960 [10.1111/mafi.12105].

Explicit implied volatilities for multifactor local-stochastic volatility models

Pagliarani, Stefano;PASCUCCI, ANDREA
2017

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. 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.
2017
Lorig, M., Pagliarani, S., Pascucci, A. (2017). Explicit implied volatilities for multifactor local-stochastic volatility models. MATHEMATICAL FINANCE, 27(3), 926-960 [10.1111/mafi.12105].
Lorig, Matthew; Pagliarani, Stefano; Pascucci, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/601673
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