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Zangoei Zadeh, Somayeh, Bani Asadi, Samaneh. (1405). Pricing European Options under Stochastic Delay and ng European Options under Stochastic Dela Price Jumps: A Hermite-Based Tau Approach. پژوهشنامه مدیریت اجرایی, (), -. doi: 10.22080/cjms.2026.31845.1851
Somayeh Zangoei Zadeh; Samaneh Bani Asadi. "Pricing European Options under Stochastic Delay and ng European Options under Stochastic Dela Price Jumps: A Hermite-Based Tau Approach". پژوهشنامه مدیریت اجرایی, , , 1405, -. doi: 10.22080/cjms.2026.31845.1851
Zangoei Zadeh, Somayeh, Bani Asadi, Samaneh. (1405). 'Pricing European Options under Stochastic Delay and ng European Options under Stochastic Dela Price Jumps: A Hermite-Based Tau Approach', پژوهشنامه مدیریت اجرایی, (), pp. -. doi: 10.22080/cjms.2026.31845.1851
Zangoei Zadeh, Somayeh, Bani Asadi, Samaneh. Pricing European Options under Stochastic Delay and ng European Options under Stochastic Dela Price Jumps: A Hermite-Based Tau Approach. پژوهشنامه مدیریت اجرایی, 1405; (): -. doi: 10.22080/cjms.2026.31845.1851

Pricing European Options under Stochastic Delay and ng European Options under Stochastic Dela Price Jumps: A Hermite-Based Tau Approach

Caspian Journal of Mathematical Sciences
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 شهریور 1405
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2026.31845.1851
نویسندگان
Somayeh Zangoei Zadeh* 1؛ Samaneh Bani Asadi2
1aDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,
تاریخ دریافت: 31 اردیبهشت 1405،  تاریخ بازنگری: 09 شهریور 1405،  تاریخ پذیرش: 10 شهریور 1405 
چکیده
This paper develops and analyzes a stochastic delayed model for the Black-Scholes equation that explicitly incorporates price jump phenomena. The primary objective is to provide a more accurate evaluation of European call option pricing in scenarios where the underlying asset price is governed by a Stochastic Delay Differential Equation (SDDE). Given that traditional Black-Scholes models often overlook the impact of sudden price jumps, which play a decisive role in the realities of capital markets, this study addresses this research gap by proposing a modified integro-differential framework. On the operational side, the numerical Tau method, utilizing Hermite polynomial bases, is employed to solve the resulting complex equation. This approach enhances computational precision by transforming the problem into a system of algebraic equations. The results from numerical examples, compared against analytical solutions, demonstrate the high accuracy and significant efficiency of the proposed model in capturing financial dynamics.
کلیدواژه‌ها
Tau method؛ delay Black- Scholes equation؛ stochastic integro-differential equation؛ European Option pricing problem؛ Hermitian polynomial
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