Option Pricing with Levy-Stable Processes Generated by Levy-Stable Integrated Variance

Quantitative Finance Vol. 9, No. 4, June 2009, pp 397–409

30 Pages Posted: 2 Oct 2007 Last revised: 11 Mar 2013

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Sam Howison

University of Oxford

Date Written: September 1, 2007

Abstract

We show how to calculate European-style option prices when the log-stock price process follows a Lévy-Stable process with index parameter 1_< alpha _< 2 and skewness parameter 1_< beta _< 2. Key to our result is to model integrated variance integral from t to T of sigma^2 as an increasing Lévy-Stable process with continuous paths in T.

Keywords: stable processes, Lévy, jumps, implied volatility, jumps

JEL Classification: G12, C00, G13

Suggested Citation

Cartea, Álvaro and Howison, Sam, Option Pricing with Levy-Stable Processes Generated by Levy-Stable Integrated Variance (September 1, 2007). Quantitative Finance Vol. 9, No. 4, June 2009, pp 397–409, Available at SSRN: https://ssrn.com/abstract=1018092

Álvaro Cartea (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Sam Howison

University of Oxford ( email )

Mathematical Institute
andrew Wiles Building, Woodstock Road
Oxford, OX2 6GG
United Kingdom

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