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2006•BIROn (Birkbeck, University of London)Open access

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

Álvaro Cartea, Sam Howison

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Abstract

In this paper we show how to calculate European-style option prices when the log-stock price process follows a L´evy-Stable process with index parameter 1 ≤ α ≤ 2 and skewness parameter −1 ≤ β ≤ 1. Key to our result is to model integrated variance RT t σ2 sds as an increasing L´evy-Stable process with continuous paths.

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In this paper we show how to calculate European-style option prices when the log-stock price process follows a L´evy-Stable process with index parameter 1 ≤ α ≤ 2 and skewness parameter −1 ≤ β ≤ 1. Key to our result is to model integrated variance RT t σ2 sds as an increasing L´evy-Stable process with continuous paths.

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Available abstract

In this paper we show how to calculate European-style option prices when the log-stock price process follows a L´evy-Stable process with index parameter 1 ≤ α ≤ 2 and skewness parameter −1 ≤ β ≤ 1. Key to our result is to model integrated variance RT t σ2 sds as an increasing L´evy-Stable process with continuous paths.

Key concepts: Lévy process, Variance (accounting), Economics, Valuation of options, Stability (learning theory), Econometrics, Financial economics, Mathematical economics

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