Valuing option under double Heston jump-diffusion model with stochastic interest rate and approximative fractional Brownian motion. (English) Zbl 1543.91105
Melliani, Said (ed.) et al., Recent advances in fuzzy sets theory, fractional calculus, dynamic systems and optimization. Contributions based on the presentations at the international conference on partial differential equations and applications, modeling and simulation, Beni Mellal, Morocco, from June 1–2, 2021. Cham: Springer. Lect. Notes Netw. Syst. 476, 393-403 (2023).
Summary: In the light of the current research, we propose a more general and realistic model based on approximative fractional Brownian motion studies. This framework presents an option pricing model under the double Heston jump-diffusion model, including approximative fractional motion with stochastic interest rate and stochastic intensity. The stochastic interest rate is determined using a two-factor Vašíček model. The negative interest rate is allowed for this model. Therefore, we are constructing a multi-factor model with a stochastic interest rate structure. We derive a closed-form pricing formula with an analytical solution for European options. Finally, some numerical results are presented to illustrate the value of a European call option comparing to other classical models.
For the entire collection see [Zbl 1515.35012].
For the entire collection see [Zbl 1515.35012].
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91G30 | Interest rates, asset pricing, etc. (stochastic models) |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
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