TY - JOUR
T1 - Analytical computation of conditional moments in the extended Cox–Ingersoll–Ross process with regime switching
T2 - Hybrid PDE system solutions with financial applications
AU - Rujivan, Sanae
AU - Thamrongrat, Nopporn
AU - Juntanon, Parun
AU - Djehiche, Boualem
N1 - Publisher Copyright:
© 2024 International Association for Mathematics and Computers in Simulation (IMACS)
PY - 2025/3
Y1 - 2025/3
N2 - In this paper, we introduce a novel analytical approach for the computation of the nth conditional moments of an m-state regime-switching extended Cox–Ingersoll–Ross process driven by a continuous-time finite-state irreducible Markov chain. This approach is applicable for all integers n≥1 and m≥1, thereby ensuring wide-ranging utility. The key of our investigation is a complex hybrid system of inter-connected PDEs, derived through a utilization of the Feynman–Kac formula for regime-switching diffusion processes. Our exploration into the solutions of this hybrid PDE system culminates in the derivation of exact closed-form formulas for the conditional moments for diverse values of n and m. Additionally, we study the asymptotic characteristics of the first conditional moments for the 2-state regime-switching Cox–Ingersoll–Ross process, particularly focusing on the effects of the symmetry inherent in the Markov chain's intensity matrix and the implications of various parameter configurations. Highlighting the practicality of our methodology, we conduct Monte Carlo simulations to not only corroborate the accuracy and computational efficacy of our proposed approach but also to demonstrate its applicability to real-world applications in financial markets. A principal application highlighted in our study is the valuation of VIX futures and VIX options within a dynamic, mean-reverting, hybrid regime-switching framework. This exemplifies the potential of our analytical method to significantly impact contemporary financial modeling and derivative pricing.
AB - In this paper, we introduce a novel analytical approach for the computation of the nth conditional moments of an m-state regime-switching extended Cox–Ingersoll–Ross process driven by a continuous-time finite-state irreducible Markov chain. This approach is applicable for all integers n≥1 and m≥1, thereby ensuring wide-ranging utility. The key of our investigation is a complex hybrid system of inter-connected PDEs, derived through a utilization of the Feynman–Kac formula for regime-switching diffusion processes. Our exploration into the solutions of this hybrid PDE system culminates in the derivation of exact closed-form formulas for the conditional moments for diverse values of n and m. Additionally, we study the asymptotic characteristics of the first conditional moments for the 2-state regime-switching Cox–Ingersoll–Ross process, particularly focusing on the effects of the symmetry inherent in the Markov chain's intensity matrix and the implications of various parameter configurations. Highlighting the practicality of our methodology, we conduct Monte Carlo simulations to not only corroborate the accuracy and computational efficacy of our proposed approach but also to demonstrate its applicability to real-world applications in financial markets. A principal application highlighted in our study is the valuation of VIX futures and VIX options within a dynamic, mean-reverting, hybrid regime-switching framework. This exemplifies the potential of our analytical method to significantly impact contemporary financial modeling and derivative pricing.
KW - Closed-form formulas
KW - Conditional moments
KW - Extended CIR process with regime switching
KW - Hybrid system of PDEs
KW - Magnus expansion
KW - Pricing VIX futures
KW - Symmetry
UR - http://www.scopus.com/inward/record.url?scp=85205498454&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85205498454&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2024.09.032
DO - 10.1016/j.matcom.2024.09.032
M3 - Article
AN - SCOPUS:85205498454
SN - 0378-4754
VL - 229
SP - 176
EP - 202
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -