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arXiv · 2207.00453

Exchange option pricing under variance gamma-like models

Matteo Gardini·Piergiacomo Sabino
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Abstract

In this article we focus on the pricing of exchange options when the dynamic of logprices follows either the well-known variance gamma or the recent variance gamma++ process introduced in Gardini et al [19]. In particular, for the former model we can derive a Margrabe's type formula whereas, for the latter one we can write an "integral free" formula. Furthermore, we show how to construct a general multidimensional versions of the variance gamma++ processes preserving both the mathematical and numerical tractability. Finally we apply the derived models to German and French energy power markets: we calibrate their parameters using real market data and we accordingly evaluate exchange options with the derived closed formulas, Fourier based methods and Monte Carlo techniques.

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Matteo Gardini, Piergiacomo Sabino. 2022-07-01. Exchange option pricing under variance gamma-like models. https://arxiv.org/abs/2207.00453

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