Abstract
We present and prove a triple sum series formula for the European call option price in a market model where the underlying asset price is driven by a Variance Gamma process. In order to obtain this formula, we present some concepts and properties of multidimensional complex analysis, with particular emphasis on the multidimensional Jordan Lemma and the application of residue calculus to a Mellin–Barnes integral representation in C3, for the call option price. Moreover, we derive triple sum series formulas for some of the Greeks associated to the call option and we discuss the numerical accuracy and convergence of the main pricing formula.
Highlights
The pricing of financial derivatives, such as options, is one of the pivotal tasks of mathematical finance, yet it can be an arduous task to develop a model that is consistent with the empirical evidence, soluble, and where its numerical estimation is neither erroneous nor time consuming
The model that we consider in this paper is a particular jump model, which assumes that the underlying asset price dynamics are described by a Lévy Process, namely the Variance Gamma process, which was first proposed by Dilip
In the market model that is driven by the Variance Gamma process, we have that the risky asset price at time T is given by ST = St e(r−q)τ −μτ + XVG (τ;C,G,M), (29)
Summary
The pricing of financial derivatives, such as options, is one of the pivotal tasks of mathematical finance, yet it can be an arduous task to develop a model that is consistent with the empirical evidence, soluble, and where its numerical estimation is neither erroneous nor time consuming.
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