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

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...

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Bibliographic Details
Published in:Journal of the Korean Statistical Society 2011, 40(2), , pp.227-238
Main Authors: Song, Seongjoo, Jeong, Jaehong, Song, Jongwoo
Format: Article
Language:English
Subjects:
Applied Statistics
Asymptotic expansion
Bayesian Inference
Lévy process
Nonlinear regression
Option pricing
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
통계학
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Summary: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.
ISSN:1226-3192
2005-2863
DOI:10.1016/j.jkss.2010.10.001