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.
Mashayekhi, E., Damirchi, J., & Yazdanian, A. (2024). Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model. Computational Methods for Differential Equations, 13(1), 339-356. doi: 10.22034/cmde.2024.58794.2490
MLA
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". Computational Methods for Differential Equations, 13, 1, 2024, 339-356. doi: 10.22034/cmde.2024.58794.2490
HARVARD
Mashayekhi, E., Damirchi, J., Yazdanian, A. (2024). 'Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model', Computational Methods for Differential Equations, 13(1), pp. 339-356. doi: 10.22034/cmde.2024.58794.2490
VANCOUVER
Mashayekhi, E., Damirchi, J., Yazdanian, A. Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model. Computational Methods for Differential Equations, 2024; 13(1): 339-356. doi: 10.22034/cmde.2024.58794.2490
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