Pricing of spread and exchange options in a rough jump-diffusion market

Donatien Hainaut
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Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2022012, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This article studies the pricing of spread and exchange options in a market made up of two risky assets driven by a rough Heston model with jumps. Firstly, we rewrite this non-Markov model as an infinite dimensional Markov process. We next consider a finite dimensional approximation and show that the characteristic function of log-returns admits a representation in terms of forward differential equations. By passing to the limit, we infer that the characteristic function of the rough jump Heston model depends on a hybrid system of ordinary and fractional differential equations. Bivariate options are next priced with a one or two dimensional discrete Fourier Transform. We conclude by a numerical illustration analyzing the impact of roughness on exchange and spread options.

Keywords: Rough volatility; fractional Brownian motion; Heston model; spread options (search for similar items in EconPapers)
Pages: 32
Date: 2022-03-24
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