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On a Markov chain approximation method for option pricing with regime switching
1. | School of Finance and Statistics, East China Normal University, Shanghai, 200241, China |
2. | School of Risk and Actuarial Studies and CEPAR, UNSW Business School, University of New South Wales, Sydney, NSW 2052, Australia |
3. | Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia |
4. | School of Finance and Statistics, Research Center of International Finance and Risk Management, East China Normal University, Shanghai 200241 |
References:
[1] |
P. Boyle and T. Draviam, Pricing exotic options under regime switching, Insurance: Mathematics and Economics, 40 (2007), 267-282.
doi: 10.1016/j.insmatheco.2006.05.001. |
[2] |
W. K. Ching, X. Huang, M. Ng and T. K. Siu, Markov Chains: Models, Algorithms and Applications, 2nd edition, Springer, New York, 2013.
doi: 10.1007/978-1-4614-6312-2. |
[3] |
J. C. Duan, E. Dudley, G. Gauthier and J. G. Simonato, Pricing discretely monitored barrier options by a Markov chain, The Journal of Derivatives, 10 (2003), 9-31. |
[4] |
J. C. Duan and J. G. Simonato, American option pricing under GARCH by a Markov chain approximation, Journal of Economics and Dynamic Control, 25 (2001), 1689-1718.
doi: 10.1016/S0165-1889(00)00003-8. |
[5] |
R. J. Elliott, L. Aggoun and J. Moore, Hidden Markov Models: Estimation and Control, Springer, New York, 1994. |
[6] |
R. J. Elliott, L. Chan and T. K. Siu, Option pricing and Esscher transform under regime switching, Annals of Finance, 1 (2005), 423-432. |
[7] |
R. J. Elliott, T. K. Siu and A. Badescu, On pricing and hedging options in regime-switching models with feedback effect, Journal of Economic Dynamics and Control, 35 (2011), 694-713.
doi: 10.1016/j.jedc.2010.12.014. |
[8] |
R. J. Elliott, C. C. Liew and T. K. Siu, Characteristic functions and option valuation in a Markov chain market, Computers and Mathematics with Applications, 62 (2011), 65-74.
doi: 10.1016/j.camwa.2011.04.050. |
[9] |
R. J. Elliott and T. K. Siu, A note on differentiability in a Markov chain market using stochastic flows, Stochastic Analysis and Applications, 33 (2015), 110-122.
doi: 10.1080/07362994.2014.975359. |
[10] |
K. Fan, Y. Shen, T. K. Siu and R. Wang, Pricing foreign equity option with regime-switching, Economic Modelling, 37 (2014), 296-305.
doi: 10.1016/j.econmod.2013.11.009. |
[11] |
K. Fan, Y. Shen, T. K. Siu and R. Wang, Pricing annuity guarantees under a double regime-switching model, Insurance: Mathematics and Economics, 62 (2015), 62-78.
doi: 10.1016/j.insmatheco.2015.02.005. |
[12] |
S. M. Goldfeld and R. E. Quandt, A Markov model for switching regressions, Jounal of Econometrics, 1 (1973), 3-16.
doi: 10.1016/0304-4076(73)90002-X. |
[13] |
J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57 (1989), 357-384.
doi: 10.2307/1912559. |
[14] |
R. H. Liu, Q. Zhang and G. Yin, Option pricing in a regime-switching model using the fast Fourier transform, Journal of Applied Mathematics and Stochastic Analysis, Article ID 18109 (2006), 1-22.
doi: 10.1155/JAMSA/2006/18109. |
[15] |
R. Norberg, The Markov chain market, ASTIN Bulletin, 33 (2003), 265-288.
doi: 10.2143/AST.33.2.503693. |
[16] |
S. R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell Publishers, United States, 1997. |
[17] |
R. E. Quandt, The estimation of parameters of linear regression system obeying two separate regimes, Journal of the American Statistical Assocation, 55 (1958), 873-880.
doi: 10.1080/01621459.1958.10501484. |
[18] |
Y. Shen and T. K. Siu, Pricing bond options under a Markovian regime-switching Hull-White model, Economic Modelling, 30 (2013), 933-940.
doi: 10.1016/j.econmod.2012.09.041. |
[19] |
Y. Shen, K. Fan and T. K. Siu, Option valuation under a double regime-switching model, Journal of Futures Markets, 34 (2014), 451-478.
doi: 10.1002/fut.21613. |
[20] |
J. G. Simonato, Computing American option prices in the lognormal jump-diffusion framework with a Markov chain, Finance Research Letters, 8 (2011), 220-226.
doi: 10.1016/j.frl.2011.01.002. |
[21] |
T. K. Siu, Regime Switching Risk: To Price or Not To Price? International Journal of Stochastic Analysis, Article ID 843246 (2011), 14 Pages. |
[22] |
T. K. Siu, Integration by parts and martingale representation for a Markov chain, Abstract and Applied Analysis, Article ID 438258 (2014), 11 Pages.
doi: 10.1155/2014/438258. |
[23] |
N. Song, W. K. Ching, T. K. Siu, E. S. Fung and M. K. Ng, Option valuation under a multivariate Markov chain model, Proceedings of CSO2010, Huangshan, IEEE Computer Society Proceedings, 1 (2010), 177-181.
doi: 10.1109/CSO.2010.73. |
[24] |
H. Tong, On a threshold model, in Pattern Recognition and Signal Processing (ed. C. H. Chen), NATO ASI Series E: Applied Sc. No. 29, The Netherlands: Sijthoff & Noordhoff, (1978), 575-586.
doi: 10.1007/978-94-009-9941-1_24. |
[25] |
H. Tong, Threshold Models in Non-linear Time Series Analysis, Springer-Verlag, Berlin, 1983.
doi: 10.1007/978-1-4684-7888-4. |
[26] |
J. van der Hoek and R. J. Elliott, American option prices in a Markov chain market model, Applied Stochastic Models in Business and Industry, 28 (2012), 35-59.
doi: 10.1002/asmb.893. |
[27] |
J. van der Hoek and R. J. Elliott, Asset pricing using finite state Markov chain stochastic discount functions, Stochastic Analysis and Applications, 30 (2012), 865-894.
doi: 10.1080/07362994.2012.704852. |
[28] |
F. L. Yuen and H. Yang, Option pricing with regime switching by trinomial tree method, Journal of Computational and Applied Mathematics, 233 (2010), 1821-1833.
doi: 10.1016/j.cam.2009.09.019. |
show all references
References:
[1] |
P. Boyle and T. Draviam, Pricing exotic options under regime switching, Insurance: Mathematics and Economics, 40 (2007), 267-282.
doi: 10.1016/j.insmatheco.2006.05.001. |
[2] |
W. K. Ching, X. Huang, M. Ng and T. K. Siu, Markov Chains: Models, Algorithms and Applications, 2nd edition, Springer, New York, 2013.
doi: 10.1007/978-1-4614-6312-2. |
[3] |
J. C. Duan, E. Dudley, G. Gauthier and J. G. Simonato, Pricing discretely monitored barrier options by a Markov chain, The Journal of Derivatives, 10 (2003), 9-31. |
[4] |
J. C. Duan and J. G. Simonato, American option pricing under GARCH by a Markov chain approximation, Journal of Economics and Dynamic Control, 25 (2001), 1689-1718.
doi: 10.1016/S0165-1889(00)00003-8. |
[5] |
R. J. Elliott, L. Aggoun and J. Moore, Hidden Markov Models: Estimation and Control, Springer, New York, 1994. |
[6] |
R. J. Elliott, L. Chan and T. K. Siu, Option pricing and Esscher transform under regime switching, Annals of Finance, 1 (2005), 423-432. |
[7] |
R. J. Elliott, T. K. Siu and A. Badescu, On pricing and hedging options in regime-switching models with feedback effect, Journal of Economic Dynamics and Control, 35 (2011), 694-713.
doi: 10.1016/j.jedc.2010.12.014. |
[8] |
R. J. Elliott, C. C. Liew and T. K. Siu, Characteristic functions and option valuation in a Markov chain market, Computers and Mathematics with Applications, 62 (2011), 65-74.
doi: 10.1016/j.camwa.2011.04.050. |
[9] |
R. J. Elliott and T. K. Siu, A note on differentiability in a Markov chain market using stochastic flows, Stochastic Analysis and Applications, 33 (2015), 110-122.
doi: 10.1080/07362994.2014.975359. |
[10] |
K. Fan, Y. Shen, T. K. Siu and R. Wang, Pricing foreign equity option with regime-switching, Economic Modelling, 37 (2014), 296-305.
doi: 10.1016/j.econmod.2013.11.009. |
[11] |
K. Fan, Y. Shen, T. K. Siu and R. Wang, Pricing annuity guarantees under a double regime-switching model, Insurance: Mathematics and Economics, 62 (2015), 62-78.
doi: 10.1016/j.insmatheco.2015.02.005. |
[12] |
S. M. Goldfeld and R. E. Quandt, A Markov model for switching regressions, Jounal of Econometrics, 1 (1973), 3-16.
doi: 10.1016/0304-4076(73)90002-X. |
[13] |
J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57 (1989), 357-384.
doi: 10.2307/1912559. |
[14] |
R. H. Liu, Q. Zhang and G. Yin, Option pricing in a regime-switching model using the fast Fourier transform, Journal of Applied Mathematics and Stochastic Analysis, Article ID 18109 (2006), 1-22.
doi: 10.1155/JAMSA/2006/18109. |
[15] |
R. Norberg, The Markov chain market, ASTIN Bulletin, 33 (2003), 265-288.
doi: 10.2143/AST.33.2.503693. |
[16] |
S. R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell Publishers, United States, 1997. |
[17] |
R. E. Quandt, The estimation of parameters of linear regression system obeying two separate regimes, Journal of the American Statistical Assocation, 55 (1958), 873-880.
doi: 10.1080/01621459.1958.10501484. |
[18] |
Y. Shen and T. K. Siu, Pricing bond options under a Markovian regime-switching Hull-White model, Economic Modelling, 30 (2013), 933-940.
doi: 10.1016/j.econmod.2012.09.041. |
[19] |
Y. Shen, K. Fan and T. K. Siu, Option valuation under a double regime-switching model, Journal of Futures Markets, 34 (2014), 451-478.
doi: 10.1002/fut.21613. |
[20] |
J. G. Simonato, Computing American option prices in the lognormal jump-diffusion framework with a Markov chain, Finance Research Letters, 8 (2011), 220-226.
doi: 10.1016/j.frl.2011.01.002. |
[21] |
T. K. Siu, Regime Switching Risk: To Price or Not To Price? International Journal of Stochastic Analysis, Article ID 843246 (2011), 14 Pages. |
[22] |
T. K. Siu, Integration by parts and martingale representation for a Markov chain, Abstract and Applied Analysis, Article ID 438258 (2014), 11 Pages.
doi: 10.1155/2014/438258. |
[23] |
N. Song, W. K. Ching, T. K. Siu, E. S. Fung and M. K. Ng, Option valuation under a multivariate Markov chain model, Proceedings of CSO2010, Huangshan, IEEE Computer Society Proceedings, 1 (2010), 177-181.
doi: 10.1109/CSO.2010.73. |
[24] |
H. Tong, On a threshold model, in Pattern Recognition and Signal Processing (ed. C. H. Chen), NATO ASI Series E: Applied Sc. No. 29, The Netherlands: Sijthoff & Noordhoff, (1978), 575-586.
doi: 10.1007/978-94-009-9941-1_24. |
[25] |
H. Tong, Threshold Models in Non-linear Time Series Analysis, Springer-Verlag, Berlin, 1983.
doi: 10.1007/978-1-4684-7888-4. |
[26] |
J. van der Hoek and R. J. Elliott, American option prices in a Markov chain market model, Applied Stochastic Models in Business and Industry, 28 (2012), 35-59.
doi: 10.1002/asmb.893. |
[27] |
J. van der Hoek and R. J. Elliott, Asset pricing using finite state Markov chain stochastic discount functions, Stochastic Analysis and Applications, 30 (2012), 865-894.
doi: 10.1080/07362994.2012.704852. |
[28] |
F. L. Yuen and H. Yang, Option pricing with regime switching by trinomial tree method, Journal of Computational and Applied Mathematics, 233 (2010), 1821-1833.
doi: 10.1016/j.cam.2009.09.019. |
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