Markov-Modulated and Shifted Wishart Processes with Applications in Derivatives Pricing

Behzad-Hussein Azadie Faraz, Hamid Arian and Marcos Escobar-Anel ()
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Behzad-Hussein Azadie Faraz: Department of Mathematical Sciences, Sharif University of Technology, Azadi Street, P.O. Box 11155-9415, Tehran P932+H5X, Iran
Hamid Arian: School of Administrative Studies, York University, 4700 Keele St, Toronto, ON M3J 1P3, Canada
Marcos Escobar-Anel: Department of Statistical and Actuarial Sciences, Western University, 1151 Richmond Street, London, ON N6A 5B7, Canada

IJFS, 2025, vol. 13, issue 2, 1-31

Abstract: The popular Wishart (WI) processes, first introduced by Bru in 1991, exhibit convenient analytical properties for modeling asset prices, particularly a closed-form characteristic function, and the ability to jointly model stochastic volatility and correlation. These features tend to increase substantially during crisis periods, more than predicted by a Wishart dynamic. Moreover, the variance processes implied by the Wishart, similar to CIR models, have no buffer away from zero. In this paper, we introduced the Markov-Modulated Shifted Wishart processes (MMSW) and the embedded Shifted Wishart processes (SW) to address these shortcomings in the modeling of asset prices. We obtain analytical representations for several characteristic functions. We also estimate the parameters and evaluate the price of Spread options via the Fourier transform under the two new models compared to the standard Wishart. Our analyses demonstrate a significant impact of the MMSW process compared to the standard Wishart process of up to 7 % in Spread option prices.

Keywords: Markov Modulated processes; Shifted Wishart processes; stochastic correlation; continuum moment method estimation; spread options (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2025
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