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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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