Explicit Implied Volatilities for Multifactor Local-Stochastic Volatility Models

36 Pages Posted: 25 Jun 2013 Last revised: 28 Nov 2014

See all articles by Matthew Lorig

Matthew Lorig

University of Washington - Applied Mathematics

Stefano Pagliarani

DEAMS, Università di Trieste

Andrea Pascucci

University of Bologna - Department of Mathematics

Date Written: November 27, 2014

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.

Keywords: local-stochastic volatility, implied volatility, Heston, CEV, SABR

Suggested Citation

Lorig, Matthew and Pagliarani, Stefano and Pascucci, Andrea, Explicit Implied Volatilities for Multifactor Local-Stochastic Volatility Models (November 27, 2014). Available at SSRN: https://ssrn.com/abstract=2283874 or http://dx.doi.org/10.2139/ssrn.2283874

Matthew Lorig (Contact Author)

University of Washington - Applied Mathematics ( email )

Seattle, WA
United States

Stefano Pagliarani

DEAMS, Università di Trieste ( email )

Via Valerio n. 4/1
Trieste
Italy

HOME PAGE: http://www.cmap.polytechnique.fr/~pagliarani/

Andrea Pascucci

University of Bologna - Department of Mathematics ( email )

Piazzadi Porta San Donato, 5
Bologna, 40126
Italy

HOME PAGE: http://www.dm.unibo.it/~pascucci

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