513
Views
3
CrossRef citations to date
0
Altmetric
Research Article

An integral equation approach for pricing American put options under regime-switching model

&
Pages 1454-1479 | Received 28 Apr 2022, Accepted 05 Mar 2023, Published online: 20 Mar 2023

References

  • C. Alexander and L. Nogueira, Hedging with stochastic and local volatility, SSRN Electron. J.AUG 2004. https://doi.org/10.2139/ssrn.569083
  • M. Avellaneda and R. Buff, Combinatorial implications of nonlinear uncertain volatility models: the case of barrier options, Appl. Math. Finance 6(1) (1999), pp. 1–18.
  • R. Bansal and H. Zhou, Term structure of interest rates with regime shifts, J. Finance 57(5) (OCT 2002), pp. 1997–2043.
  • G. Barone-Adesi and R.E. Whaley, Efficient analytic approximation of American option values, J. Finance 42(2) (1987), pp. 301–320.
  • F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81(3) (1973), pp. 637–654.
  • N. Bollen, Valuing options in regime-switching models, J. Deriv. 6 (OCT 1999), pp. 38–50.
  • S. Boyarchenko and S. Levendorskii, American options in regime-switching models, SIAM J. Control Optim. 48 (JAN 2009), pp. 1353–1376.
  • P. Boyle, M. Broadie, and P. Glasserman, Monte Carlo methods for security pricing, J. Econ. Dyn. Control 21 (JUN 1997), pp. 1267–1321.
  • P. Boyle and T. Draviam, Pricing exotic options under regime switching, Insur. Math. Econ. 40 (FEB 2007), pp. 267–282.
  • P.P. Boyle, Options: A Monte Carlo approach, J. Financ. Econ. 4(3) (1977), pp. 323–338.
  • M. Broadie, P. Glasserman, and G. Jain, Enhanced Monte Carlo estimates for American option prices, J. Deriv. 5 (NOV 1997), pp. 25–44.
  • J. Buffington and R. Elliott, Regime switching and European options, Stoch. Anal. Appl. 280 (JAN 2002), pp. 73–82.
  • J. Buffington and R.J. Elliott, American options with regime switching, Int. J. Theor. Appl. Finance05 (NOV 2002), pp. 497–514.
  • D. Bunch and H. Johnson, The American put option and its critical stock price, J. Finance 55 (FEB 2000), pp. 2333–2356.
  • R. Caldana and G. Fusai, A general closed-form spread option pricing formula, J. Bank. Finance37(12) (2013), pp. 4893–4906.
  • P. Carr, Randomization and the American put, Rev. Financ. Stud. 11(3) (1998), pp. 597–626.
  • P. Carr, M. Stanley, and D. Madan, Option valuation using the fast Fourier transform, J. Comput. Finance 2 (4) (MAR 1999), pp. 61–73.
  • L. Chan and S.-P. Zhu, An analytic approach for pricing American options with regime switching, J. Risk Financ. Manag. 14(5) (2021), pp.188.
  • R. Company, V. Egorova, L. Jodar, and C. Vazquez, Computing American option price under regime switching with rationality parameter, Comput. Math. Appl. 72(3) (AUG 2016), pp. 741–754.
  • J. Dettman, Applied Complex Variables, Macmillan, Courier Corporation, 1965.
  • V. Egorova, R. Company, and L. Jodar, A new efficient numerical method for solving American option under regime switching model, Comput. Math. Appl. 71 (2016), pp. 224–237.
  • B. Engelmann, M.R. Fengler, M. Nalholm, and P. Schwendner, Static versus dynamic hedges: an empirical comparison for barrier options, Rev. Deriv. Res. 9(3) (2006), pp. 239–264.
  • C.-D. Fuh, R.-H. Wang, and J.-C. Cheng, Option pricing in a Black–Scholes model with Markov switching.The 4th International Conference on Financial Engineering and Statistical Finance. Taipei. 2002.
  • R. Geske and H. Johnson, The American put option valued analytically, J. Finance 39 (1984), pp. 1511–1524.
  • S.F. Gray, Modeling the conditional distribution of interest rates as a regime-switching process, J. Financ. Econ. 1(42) (1996), pp. 27–62.
  • X. Guo, Information and option pricings, Quant. Finance 1(1) (2001), pp. 38–44.
  • J.D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 57 (1989), pp. 357–384.
  • J.D. Hamilton, Analysis of time series subject to changes in regime, J. Econom. 45 (1990), pp. 39–70.
  • M. Hardy, A regime-switching model of long-term stock returns, N. Am. Actuar. J. 5 (2) (APR 2001), pp.41–53.
  • X.-J. He and S.-P. Zhu, How should a local regime-switching model be calibrated? J. Econ. Dyn. Control 78 (2017), pp. 149–163.
  • X.-J. He and S.-P. Zhu, On full calibration of hybrid local volatility and regime-switching models, J. Futures Mark. 38(5) (2018), pp. 586–606.
  • J.-Z. Huang, M. Subrahmanyam, G. Yu, and G.S. Co, Pricing and hedging American options: A recursive integration method, Rev. Financ. Stud. 9(1) (1996), pp. 277–300.
  • Y. Huang, P. Forsyth, and G. Labahn, Methods for pricing American options under regime switching, SIAM J. Sci. Comput. 33 (2011), pp. 2144–2168.
  • K. Jackson, S. Jaimungal, and V. Surkov, Fourier space time-stepping for option pricing with Levy models, J. Comput. Finance 12 (DEC 2008), pp. 1–29.
  • A.Q.M. Khaliq and R. Liu, New numerical scheme for pricing American option with regime-switching, Int. J. Theor. Appl. Finance 12(3) (2009), pp. 319–340.
  • I.J. Kim, The analytic valuation of American options, Rev. Financ. Stud. 3(4) (1990), pp. 547–572.
  • Y.-K. Kwok, Mathematical Models of Financial Derivatives, Springer, Berlin, 2008.
  • R. Liu, Regime-switching recombining tree for option pricing, Int. J. Theor. Appl. Finance 13(3) (2010), pp. 479–499.
  • R. Liu, Q. Zhang, and Y. Gang, Option pricing in a regime-switching model using the fast Fourier transform, J. Appl. Math. Stoch. Anal. 2006 (2006), pp. 1–22.
  • F.A. Longstaff and E.S. Schwartz, Valuing American options by simulation: A simple least-squares approach, Rev. Financ. Stud. 14(1) (2001), pp. 113–147.
  • X. Lu and E. Putri, A semi-analytic valuation of American options under a two-state regime-switching economy, Phys. A Stat. Mech. Appl. 538 (OCT 2019), pp. 122968.
  • L. MacMillan, Analytical approximation for the American put prices, Adv. Futures Options Res. 1 (1986), pp. 119–139.
  • G. Masi, Y. Kabanov, and W. Runggaldier, Mean-Variance hedging of options on stocks with Markov volatilities, Probab. Theory Appl. 39 (JAN 1994), pp. 172–182.
  • H. McKean, Appendix: A free boundary problem for the heating function arising from a problem in mathematical economics, Ind. Manag. Rev. 6 (JAN 1965), pp. 32–39.
  • R.C. Merton, Theory of rational option pricing, Bell J. Econ. Mgmt Sci. 4 (1973), pp. 141–183.
  • R.C. Merton, M.J. Brennan, and E.S. Schwartz, The valuation of American put options, J. Finance32(2) (1977), pp. 449–462.
  • S. Mitra and P. Date, Regime switching volatility calibration by the Baum–Welch method, J. Comput. Appl. Math. 234(12) (2010), pp. 3243–3260.
  • I. Noorani, F. Mehrdoust, and A. Nasroallah, A generalized antithetic variates Monte–Carlo simulation method for pricing of Asian option in a Markov regime-switching model, Math. Comput. Simul. 181 (2021), pp. 1–15.
  • C. Nwankwo, W. Dai, and R. Liu, Compact finite difference scheme with Hermite interpolation for pricing American put options based on regime switching model. arXiv preprint arXiv:1908.04900, August 2019.
  • E. Omberg, A note on the convergence of binomial-pricing and compound-option models, J. Finance42(2) (1987), pp. 463–469.
  • A. Ramponi, Spread option pricing in regime-switching jump diffusion models, Mathematics 10(9) (2022), pp.1574.
  • E.S. Schwartz, The valuation of warrants: Implementing a new approach, J. Financ. Econ. 4(1) (1977), pp. 79–93.
  • H. Song, J. Xu, J. Yang, and Y. Li, Projection and contraction method for the valuation of American options under regime switching, Commun. Nonlinear Sci. Numer. Simul. 109 (2022), pp. 106332.
  • L. Wu and Y.-K. Kwok, A front-fixing finite difference method for the valuation of American options, J. Financ. Eng. 6 (JAN 1997), pp. 83–97.
  • H. Yang, A numerical analysis of American options with regime switching, J. Sci. Comput. 44 (JUL 2010), pp. 69–91.
  • F. Yi, American put option with regime-switching volatility (finite time horizon) – variational inequality approach, Math. Methods. Appl. Sci. 31(12) (2008), pp. 1461–1477.
  • G.G. Yin and Q. Zhang, Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Springer, New York, 1998.
  • F.L. Yuen and H. Yang, Option pricing with regime switching by trinomial tree, J. Comput. Appl. Math. 233 (2010), pp. 1821–1833.
  • Q. Zhang and X. Guo, Closed-Form solutions for perpetual American put options with regime switching, SIAM J. Appl. Math. 64 (JAN 2004), pp. 2034–2049.
  • Y. Zheng and S.-P. Zhu, A generalized approach for pricing American options under regime-switching model (submitted), 2022.
  • S.-P. Zhu, A new analytical-approximation formula for the optimal exercise boundary of American put options, Int. J. Theor. Appl. Finance 09(07) (2006), pp. 1141–1177.
  • S.-P. Zhu, A. Badran, and X. Lu, A new exact solution for pricing European options in a two-state regime-switching economy, Comput. Math. Appl. 64(8) (2012), pp. 2744–2755.