Exchange Option Pricing Under Variance Gamma-Like Models

Matteo Gardini and Piergiacomo Sabino

Applied Mathematical Finance, 2022, vol. 29, issue 6, 494-521

Abstract: In this article, we focus on the pricing of exchange options when the risk-neutral dynamic of log-prices follows either the well-known variance gamma or the recent variance gamma++ process introduced in Gardini et al. (2022. “The Variance Gamma++ Process and Applications to Energy Markets.” Applied Stochastic Models in Business and Industry 38 (2): 391–418. https://doi.org/10.1002/asmb.v38.2.). 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 tractabilities. 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.

Date: 2022
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DOI: 10.1080/1350486X.2023.2248791

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