OPTION PRICING FOR TRUNCATED LÉVY PROCESSES

Svetlana Boyarchenko · Sergei Zakharovich Levendorskii

284 citations0/0 files storedInternational Journal of Theoretical and Applied Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Probability and Risk Models

Abstract

A general class of truncated Lévy processes is introduced, and possible ways of fitting parameters of the constructed family of truncated Lévy processes to data are discussed. For a market of a riskless bond and a stock whose log-price follows a truncated Lévy process, TLP-analogs of the Black–Scholes equation, the Black–Scholes formula, the Dynkin derivative and the Leland's model are obtained, a locally risk-minimizing portfolio is constructed, and an optimal exercise price for a perpetual American put is computed.

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References

1997Processes of normal inverse Gaussian type 1985Option Pricing and Replication with Transactions Costs 1998New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model

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2002Optimal stopping and perpetual options for Lévy processes 2002Perpetual American Options Under Lévy Processes 2004PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES 2002Barrier options and touch-and-out options under regular Lévy processes of exponential type 2004Fast deterministic pricing of options on Lévy driven assets 2010Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes 2001Normal Modified Stable Processes 2013Tempered stable distributions and processes

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