Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression

Seongjoo Song, Jaehong Jeong, Jongwoo Song

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4 Scopus citations


When the underlying asset price process follows a Lévy process, the market becomes incomplete, in which the option pricing can be a complicated problem. This paper proposes a method of asymptotic option pricing when the underlying asset price process follows a pure-jump Lévy process. We express the option price as the expected value of the discounted payoff and expand it at the Black-Scholes price assuming that the price process converges weakly to the Black-Scholes model. The price can be approximated by a formula with 4 parameters, which can easily be estimated using option prices observed in the market. The proposed price explains the market option data better than the Black-Scholes price in real data application with KOSPI 200.

Original languageEnglish
Pages (from-to)227-238
Number of pages12
JournalJournal of the Korean Statistical Society
Issue number2
StatePublished - Jun 2011

Bibliographical note

Funding Information:
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0023191 (S. Song) and No. 2010-0004196 (J. Song)).


  • Asymptotic expansion
  • Lévy process
  • Nonlinear regression
  • Option pricing


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