Option Pricing in the Moderate Deviations Regime

20 Pages Posted: 5 Apr 2016

See all articles by Peter Friz

Peter Friz

Technische Universität Berlin (TU Berlin)

Stefan Gerhold

Vienna University of Technology

Arpad Pinter

Vienna University of Technology

Date Written: April 5, 2016

Abstract

We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options. First and higher order small-time moderate deviation estimates of call prices and implied volatility are obtained. The expansions involve only simple expressions of the model parameters, and we show in detail how to calculate them for generic local and stochastic volatility models. Some numerical examples for the Heston model illustrate the accuracy of our results.

Keywords: density expansions in small time, option pricing in small time, moderate deviations

JEL Classification: G13

Suggested Citation

Friz, Peter and Gerhold, Stefan and Pinter, Arpad, Option Pricing in the Moderate Deviations Regime (April 5, 2016). Available at SSRN: https://ssrn.com/abstract=2759347 or http://dx.doi.org/10.2139/ssrn.2759347

Peter Friz

Technische Universität Berlin (TU Berlin) ( email )

Straße des 17
Juni 135
Berlin, 10623
Germany

Stefan Gerhold (Contact Author)

Vienna University of Technology ( email )

Karlsplatz 13
Vienna
Austria

Arpad Pinter

Vienna University of Technology ( email )

Karlsplatz 13
Vienna
Austria

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