The main goal of this paper is to study sensitivity analysis, with respect to the parameters of the model, in the framework of time-inhomogeneous Lévy process. This is a slight generalization of recent results of Fournié et al. (Finance Stochast 3(4):391–412, 1999 ), El-Khatib and Privault (Finance Stochast 8(2):161–179, 2004 ), Bally et al. (Ann Appl Probab 17(1):33–66, 2007 ), Davis and Johansson (Stochast Process Appl 116(1):101–129, 2006 ), Petrou (Electron J Probab 13(27):852–879, 2008 ), Benth et al. (Commun Stochast Anal 5(2):285–307, 2011 ) and El-Khatib and Hatemi (J Statist Appl Probab 3(1):171–182, 2012 ), using Malliavin calculus developed by Yablonski (Rocky Mountain J Math 38:669–701, 2008 ). This relatively recent result will help us to provide tools that are necessary for the calculation of the sensitivities. We provide some simple examples to illustrate the results achieved. In particular, we discussed the time-inhomogeneous versions of the Merton model and the Bates model.
Additive processes Time-inhomogeneous lévy process Malliavin calculus Integration by parts formula Sensitivity analysis
Mathematics Subject Classification 2010
60H07 60H35 60G51
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