A Taylor Series Approach to Pricing and Implied Volatility for Local–Stochastic Volatility Models

18 Pages Posted: 9 Jun 2016

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: December 19, 2014

Abstract

Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local–stochastic volatility setting. Our price approximations require only a normal cumulative distribution function and our implied volatility approximations are fully explicit (ie, they require no special functions, no infinite series and no numerical integration). As such, approximate prices can be computed as efficiently as Black– Scholes prices, and approximate implied volatilities can be computed nearly instantaneously.

Keywords: Taylor series, local–stochastic volatility, time-dependent drift, diffusion coefficients

Suggested Citation

Lorig, Matthew and Pagliarani, Stefano and Pascucci, Andrea, A Taylor Series Approach to Pricing and Implied Volatility for Local–Stochastic Volatility Models (December 19, 2014). Journal of Risk, Vol. 17, No. 2, 2014, Available at SSRN: https://ssrn.com/abstract=2791417

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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