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The β-variance gamma model

Content Provider	Springer Nature Link
Author	Schoutens, Wim Damme, Geert Van
Copyright Year	2010
Abstract	Kuznetsov (Ann Appl Prob, 2009) introduces a 10-parameter family of Lévy processes for which the Wiener-Hopf factors and the distribution of the running supremum (infimum) can be determined semi-analytically. In this text we will examine the numerical performance of this so-called β-family, both in the equity world and in the field of credit risk. In order to do this, we will calibrate a particular member of this family to a vanilla option surface (by means of the Fast Fourier Transform-technique due to Carr and Madan (J Comput Fin 2(4):61–73, 1999) and use the resulting parameters to determine the prices of a digital down-and-out barrier (DDOB) option, written on the same underlying. In a second experiment, we will try and calibrate the model to some real-life credit default swap (CDS) term structures. The parameters of the model under investigation are chosen such that its Lévy density is approximately equal to that of the famous Variance Gamma (VG) process, which will serve as a benchmark. Hence, the former will be referred to as the β-VG model. The option prices will be determined both semi-analytically [using the formulas derived by Kuznetsov (Ann Appl Prob, 2009)] and through a Monte-Carlo simulation. However, the CDS spreads will only be determined semi-analytically, due to the very close relation between pricing DDOB options and determining the par spread of a CDS. Furthermore, in both cases, the results will be compared with the ones obtained using the VG model [Cf. Schoutens (Lévy processes in finance: pricing financial derivatives, Wiley , Chichester, 2003) and, Cariboni and Schoutens (Levy processes in credit risk, Wiley, Chichester, 2009)]. It will turn out that, w.r.t. vanilla option prices, the β-VG model performs almost identically as the VG model, whereas the semi-analytical expressions by Kuznetsov (Ann Appl Prob, 2009) lead to a (fast and) accurate pricing of DDOB options and CDSs.
Starting Page	263
Ending Page	282
Page Count	20
File Format	PDF
ISSN	13806645
Journal	Review of Derivatives Research
Volume Number	14
Issue Number	3
e-ISSN	15737144
Language	English
Publisher	Springer US
Publisher Date	2010-07-24
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Levy processes Hitting probability Barrier options Finance/Investment/Banking
Content Type	Text
Resource Type	Article
Subject	Finance

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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