- [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.
|