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Closed‐form approximations for spread options in Lévy markets
Author(s) -
Van Belle Jente,
Vanduffel Steven,
Yao Jing
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.2391
Subject(s) - inverse gaussian distribution , black–scholes model , exponential function , lévy process , mathematics , variance gamma distribution , mathematical economics , econometrics , variance (accounting) , valuation of options , economics , mathematical analysis , statistics , volatility (finance) , asymptotic distribution , accounting , distribution (mathematics) , estimator
We provide new closed‐form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, ie, when log‐returns are modeled as Brownian motions (Black‐Scholes model), variance gamma processes (VG model), or normal inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well‐known Margrabe formula (1978) that is valid in a Black‐Scholes model to the VG model under a homogeneity assumption.