2022/07/01 by Matteo Gardini, Gardini, Matteo, Piergiacomo Sabino +1 · 1 citation
Economics, Econometrics and Finance · #Capital Investment and Risk Analysis #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #G.3 #G.5.1 #I.6 #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2207.00453
openalex publication_date 2022/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.