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Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps
Author(s) -
Deelstra Griselda,
Kozpınar Sinem,
Simon Matthieu
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2385
Subject(s) - markov chain , univariate , lévy process , markov process , jump , computer science , asset (computer security) , econometrics , valuation of options , inversion (geology) , mathematics , fourier transform , mathematical optimization , economics , multivariate statistics , statistics , physics , mathematical analysis , paleontology , computer security , quantum mechanics , structural basin , biology
This paper considers the evaluation of spread and basket options when the underlying asset prices are driven by Markov‐modulated Lévy processes with synchronous jumps. In particular, the asset prices may jump whenever there is a change of phase of the underlying Markov process. We further allow for dependence between the different price dynamics. In this general regime‐switching framework, we provide lower and upper bounds to the exact option prices based upon ideas from the literature without regime switching. These bounds are obtained via univariate Fourier inversion under the assumption that the joint characteristic functions of the Markov‐modulated Lévy processes are known. We study these obtained spread and basket option price approximations in different regime‐switching models. Several numerical experiments are included and these show that, especially, the lower bounds have a very high precision.