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Mashayekhi, Elham, Damirchi, Javad, Yazdanian, Ahmad. (1403). Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model. سامانه مدیریت نشریات علمی, 13(1), 339-356. doi: 10.22034/cmde.2024.58794.2490
Elham Mashayekhi; Javad Damirchi; Ahmad Reza Yazdanian. "Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model". سامانه مدیریت نشریات علمی, 13, 1, 1403, 339-356. doi: 10.22034/cmde.2024.58794.2490
Mashayekhi, Elham, Damirchi, Javad, Yazdanian, Ahmad. (1403). 'Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model', سامانه مدیریت نشریات علمی, 13(1), pp. 339-356. doi: 10.22034/cmde.2024.58794.2490
Mashayekhi, Elham, Damirchi, Javad, Yazdanian, Ahmad. Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model. سامانه مدیریت نشریات علمی, 1403; 13(1): 339-356. doi: 10.22034/cmde.2024.58794.2490

Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model

Computational Methods for Differential Equations
مقاله 25، دوره 13، شماره 1، فروردین 2025، صفحه 339-356    اصل مقاله (9.26 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.58794.2490
نویسندگان
Elham Mashayekhi1؛ Javad Damirchi1؛ Ahmad Reza Yazdanian* 2
1Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
2Faculty of Financial Sciences, Kharazmi University, Tehran, Iran.
چکیده
The standard model, which determines option pricing, is the well-known Black-Scholes formula. Heston in addition to Cox-Ingersoll-Ross which is called CIR, respectively, implemented the models of stochastic volatility and interest rate to the standard option pricing model. The cost of transaction, which the Black-Scholes method overlooked, is another crucial consideration that must be made when trading a service or production. It is acknowledged that by employing the log-normal stock diffusion hypothesis with constant volatility, the Black-Scholes model for option pricing departs from reality. The standard log-normal stock price distribution used in the Black-Scholes model is insufficient to account for the leaps that regularly emerge in the discontinuous swings of stock prices. A jump-diffusion model, which combines a jump process and a diffusion process is a type of mixed model in the Black-Scholes model belief. Merton developed a jump model as a modification of jump models to better describe purchasing and selling behavior. In this study, the Heston-Cox-Ingersoll-Ross (HCIR) model with transaction costs is solved using the alternating direction implicit (ADI) approach and the Monte Carlo simulation assuming the underlying asset adheres to the jump-diffusion case, then the outcomes are compared to the analytical solution. In addition, the consistency of the numerical method is proven for the model.
کلیدواژه‌ها
Option pricing؛ Stochastic volatility؛ Stochastic interest rate؛ Cost of transaction؛ Alternating direction implicit approach؛ Jump-diffusion process
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