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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
مراجع
  • [1] A. Almendral and C. W. Oosterlee, Numerical valuation of options with jumps in the underlying, Appl. Numer. Math., 53 (2005), 1–18.
  • [2] L. Andersen and J. Andreasen, Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing, Rev. Deriv. Res., 4 (2000), 231–262.
  • [3] G. Bakshi, C. Cao, and Z. Chen, Empirical performance of alternative option pricing models, J. Finance, 52 (1997), 2003–2049.
  • [4] F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ., 81 (1973), 637–654.
  • [5] J. Cao, B. Wang, and W. Zhang, Valuation of European options with stochastic interest rates and transaction costs, Int. J. Comput. Math. 99 (2022), 227–239.
  • [6] J. C. Cox, J. E. Ingersoll, and S. A. Ross, An intertemporal general equilibrium model of asset prices, Econometrica, 53 (1985), 363–384.
  • [7] D. J. Duffy, Finite difference methods in financial engineering, John Wiley & Sons, Ltd., Chichester, 2006.
  • [8] J. J. Douglas, Alternating direction methods for three space variables, Numer. Math., 4 (1962), 41–63.
  • [9] J. J. Douglas, On the numerical integration of uxx + uyy = ut by implicit methods, J. Soc. Ind. Appl. Math., 3 (1955), 42–65.
  • [10] Jr. J. Douglas and J. H. H. Rachford, On the numerical solution of heat conduction problems in two and three space variables, Trans. Amer. Math. Soc. 82 (1956), 421–439.
  • [11] B. Düring and M. Fournie, High-order compact finite difference scheme for option pricing in stochastic volatility models, J. Comput. Appl. Math. 236 (2012), 4462–4473.
  • [12] E. Grannan and G. Swindle, Minimizing transaction costs of option hedging strategies, Math. Finance, 6 (1996), 341–364.
  • [13] T. Haentjens, Efficient and stable numerical solution of the Heston-Cox-Ingersoll-Ross partial differential equation by alternating direction implicit finite difference schemes, Int. J. Comput. Math. 90 (2013), 2409–2430.
  • [14] S. L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency pptions, Rev. Financ. Stud., 6 (1993), 327–343.
  • [15] S. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs, Rev. Futures Markets, 8 (1989), 222–239.
  • [16] J. Hull and A. White, Pricing interest-rate-derivative securities, Rev. Financ. Stud., 3 (1990), 573–592.
  • [17] J. Hull and A. White, The pricing of options on assets with stochastic volatilities, J. Finance, 42 (1987), 281–300.
  • [18] K. J. int Hout and C. Mishra, Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms, Appl. Numer. Math., 74 (2013), 83–94.
  • [19] M. K. Kadalbajoo, A. Kumar, and L. P. Tripathi, An efficient numerical method for pricing option under jumpdiffusion model, Int. J. Adv. Eng. Sci. Appl. Math., 7 (2015), 114–123.
  • [20] F. Kalsheker, Option Pricing Models with Stochastic Volatility and Jumps, 2009. MS thesis–University of Cape Town.
  • [21] S. G. Kou, A jump-diffusion model for option pricing, Manag. Sci., 48 (2002), 1086–1101.
  • [22] Y. Kwon and Y. Lee, A second-order finite difference method for option pricing under jump-diffusion models. SIAM J. Numer. Anal., 49 (2011), 2598–2617.
  • [23] H. Leland, Option pricing and replication with transactions costs, J. Finance, 40 (1985), 1283–1301.
  • [24] M. C. Mariani, I. SenGupta, and P. Bezdek, Numerical solutions for option pricing models including transaction costs and stochastic volatility, Acta Appl. Math., 118 (2012), 203–220.
  • [25] M. C. Mariani, I. SenGupta, and G. Sewell, Numerical methods applied to option pricing models with transaction costs and stochastic volatility, Quant. Finance, 15 (2015), 1417–1424.
  • [26] E. Mashayekhi, J. Damirchi, and A. R. Yazdanian, Numerical solution of HCIR equation with transaction costs using alternating direction implicit method, arXiv preprint arXiv:2306.01535, (2023).
  • [27] K. Matsuda, Introduction to Merton jump diffusion model, Department of Economics, The Graduate Center, The City University of New York, New York, (2004).
  • [28] R. C. Merton, Option pricing when underlying stock returns are discontinuous, J. Financ. Econ., 3 (1976), 125–144.
  • [29] T. H. Nguyen and S. Pergamenschchikov, Approximate hedging with proportional transaction costs in stochastic volatility models with jumps, (2015).
  • [30] T. H. Nguyen and S. Pergamenshchikov, Approximate hedging problem with transaction costs in stochastic volatility markets, Math. Finance, 27 (2017), 832–865.
  • [31] H. Niederreiter and J. Spanier, Monte Carlo and Quasi-Monte Carlo Methods 1998, Proceedings of a Conference Held at the Claremont Graduate University, Claremont, California, USA, JU. Springer-Verlag, 2000.
  • [32] D. W. Peaceman, Differential equations for flow in reservoirs, Fundamentals of numerical reservoir simulation: Amsterdam, Elsevier, 6 (1977), 1–34.
  • [33] D. W. Peaceman and Jr. H. H. Rachford, The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math., 3 (1955), 28–41.
  • [34] E. Pindza, K.C. Patidar, and E. Ngounda, Robust spectral method for numerical valuation of European options under Merton’s jump-diffusion model, Numer. Methods Partial Differential Equations, 30 (2014), 1169–1188.
  • [35] M. Safaei, A. Neisy, and N. Nematollahi, Generalized componentwise splitting scheme for option pricing under the Heston-Cox-Ingersoll-Ross model, J. Statist. Theory and Applications, 18 (2019), 425–438.
  • [36] I. SenGupta, Option pricing with transaction costs and stochastic interest rate, Appl. Math. Finance, 21 (2014), 399–416.
  • [37] A. Shidfar, K. Paryab, A. R. Yazdanian, and T. A. Pirvu, Numerical analysis for Spread option pricing model of markets with finite liquidity: first-order feedback model, Int. J. Comput. Math., 91 (2014), 2603–2620.
  • [38] S. E. Shreve, Stochastic calculus for finance II: Continuous-time models, Springer, New York, 2004.
  • [39] K. Sin, Numerical Methods for Derivative Pricing with Applications to Barrier Options, MS thesis–University of Waterloo, 2010.
  • [40] J. Sippel and S. Ohkoshi, All power to PRDC notes, Risk, 15 (2002), 31–33.
  • [41] G. D. Smith, Numerical solution of partial differential equations: finite difference methods, Oxford university press, New York, 1985.
  • [42] Y. Tian and H. Zhang, European option pricing under stochastic volatility jump-diffusion models with transaction cost. Comput. Math. Appl., 79 (2020), 2722–2741.
  • [43] B. Wang, Option pricing under the Heston-CIR model with stochastic interest rates and transaction costs, Thesis (Ph.D.)–Auckland University of Technology - New Zealand, 2019.
  • [44] W. Wang, Y. Chen, and H. Fang, On the variable two-step IMEX BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance, SIAM J. Numer. Anal., 57 (2019), 1289–1317.
  • [45] J. Wang, S. Wen, M. Yang, and W. Shao, Practical finite difference method for solving multi-dimensional BlackScholes model in fractal market, Chaos Solitons Fractals, 157 (2022), 111895.
  • [46] N. N. Yanenko, The method of fractional steps. The solution of problems of mathematical physics in several variables (Springer-Verlag, New York-Heidelberg, 1971). Translated from the Russian by T. Cheron. English translation edited by M. Holt.
  • [47] A. R. Yazdanian and T. A. Pirvu, Numerical analysis for Spread option pricing model in illiquid underlying asset market: full feedback model, (2014).
  • [48] K. Zhang and S. Wang, Pricing options under jump diffusion processes with fitted finite volume method, Appl. Math. Comput., 201 (2008), 398–413.
  • [49] Y. Zhao and W. Ziemba, Hedging errors with Leland’s option model in the presence of transaction costs, Finance. Res. Lett., 4 (2007), 49–58.
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