Godin, Frédéric, Lai, Van Son and Trottier, Denis-Alexandre
(2019)
*Option pricing under regime-switching models: Novel approaches removing path-dependence.*
Insurance: Mathematics and Economics
.
ISSN 01676687
(In Press)

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Official URL: http://dx.doi.org/10.1016/j.insmatheco.2019.04.006

## Abstract

A well-known approach for the pricing of options under regime-switching models is to use the regime-switching Esscher transform (also called regime-switching mean-correcting martingale measure) to obtain risk-neutrality. One way to handle regime unobservability consists in using regime probabilities that are filtered under this risk-neutral measure to compute risk-neutral expected payoffs. The current paper shows that this natural approach creates path-dependence issues within option price dynamics. Indeed, since the underlying asset price can be embedded in a Markov process under the physical measure even when regimes are unobservable, such path-dependence behavior of vanilla option prices is puzzling and may entail non-trivial theoretical features (e.g., time non-separable preferences) in a way that is difficult to characterize. This work develops novel and intuitive risk-neutral measures that can incorporate regime risk-aversion in a simple fashion and which do not lead to such path-dependence side effects. Numerical schemes either based on dynamic programming or Monte-Carlo simulations to compute option prices under the novel risk-neutral dynamics are presented.

Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
---|---|

Item Type: | Article |

Refereed: | Yes |

Authors: | Godin, Frédéric and Lai, Van Son and Trottier, Denis-Alexandre |

Journal or Publication: | Insurance: Mathematics and Economics |

Date: | 30 April 2019 |

Digital Object Identifier (DOI): | 10.1016/j.insmatheco.2019.04.006 |

Keywords: | Option pricing; Regime-switching models; Hidden Markov models; Esscher transform; Path-dependence |

ID Code: | 985344 |

Deposited By: | Michael Biron |

Deposited On: | 17 May 2019 17:17 |

Last Modified: | 16 Apr 2021 01:00 |

## References:

Ang A., Timmermann A. Regime changes and financial marketsAnn. Rev. Financ. Econom., 4 (1) (2012), pp. 313-337

Azimzadeh P., Forsyth P.A., Vetzal K.R. Hedging costs for variable annuities under regime-switching Hidden Markov Models in Finance, Springer (2014), pp. 133-166

Bégin, J.-F., Gauthier, G., 2017. Price Bias and Common Practice in Option Pricing, Working paper. Simon Fraser University.

Bollen N.P. Valuing options in regime-switching models J. Derivat., 6 (1) (1998), pp. 38-49

Boyle P., Draviam T. Pricing exotic options under regime switching Insurance Math. Econom., 40 (2) (2007), pp. 267-282

Buffington J., Elliott R.J. American options with regime switching Int. J. Theor. Appl. Finance, 5 (05) (2002), pp. 497-514

Buffington J., Elliott R.J. Regime switching and European options Stochastic Theory and Control, Springer (2002), pp. 73-82

Bühlmann H., Delbaen F., Embrechts P., Shiryaev A.N. No-arbitrage, change of measure and conditional Esscher transforms CWI Quart., 9 (4) (1996), pp. 291-317

Bühlmann H., Delbaen F., Embrechts P., Shiryaev A.N. On esscher transforms in discrete finance models ASTIN Bull.: J. IAA, 28 (2) (1998), pp. 171-186

Christoffersen P., Elkamhi R., Feunou B., Jacobs K. Option valuation with conditional heteroskedasticity and nonnormality Rev. Financ. Stud., 23 (5) (2009), pp. 2139-2183

Di Masi G.B., Kabanov Y.M., Runggaldier W.J. Mean-variance hedging of options on stocks with Markov volatilities Theory Probab. Appl., 39 (1) (1995), pp. 172-182

Duan J.-C., Popova I., Ritchken P., et al. Option pricing under regime switching Quant. Finance, 2 (116–132) (2002), p. 209

Elliott R.J., Aggoun L., Moore J.B. Hidden Markov Models: Estimation and Control, Vol. 29 Springer Science & Business Media (1995)

Elliott R.J., Chan L., Siu T.K. Option pricing and Esscher transform under regime switching Annals of Finance, 1 (4) (2005), pp. 423-432

Elliott R.J., Madan D.B. A discrete time equivalent martingale measure Math. Finance, 8 (2) (1998), pp. 127-152

Elliott R.J., Siu T.K. Option pricing and filtering with hidden Markov-modulated pure-jump processes Appl. Math. Finance, 20 (1) (2013), pp. 1-25

Elliott R.J., Siu T.K., Badescu A. On pricing and hedging options in regime-switching models with feedback effect J. Econom. Dynam. Control, 35 (5) (2011), pp. 694-713

Elliott R.J., Siu T.K., Chan L., Lau J.W. Pricing options under a generalized Markov-modulated jump-diffusion model Stoch. Anal. Appl., 25 (4) (2007), pp. 821-843

Fan K., Shen Y., Siu T.K., Wang R. Pricing annuity guarantees under a double regime-switching model Insurance Math. Econom., 62 (2015), pp. 62-78

François P., Gauthier G., Godin F. Optimal hedging when the underlying asset follows a regime-switching Markov process European J. Oper. Res., 237 (1) (2014), pp. 312-322

Fuh C.-D., Ho K.W.R., Inchi H., Wang R.-H. Option pricing with Markov switching J. Data Sci., 10 (3) (2012), pp. 483-509

Garcia R., Luger R., Renault E. Empirical assessment of an intertemporal option pricing model with latent variables J. Econometrics, 116 (1) (2003), pp. 49-83

Gerber H.U., Shiu E.S. Option pricing by esscher transforms (with discussion) Trans. Soc. Actuaries, 46 (1994), pp. 99-191

Gerber H.U., Shiu E.S. Actuarial bridges to dynamic hedging and option pricing Insurance Math. Econom., 18 (3) (1996), pp. 183-218

Goovaerts M.J., Laeven R.J. Actuarial risk measures for financial derivative pricing Insurance Math. Econom., 42 (2) (2008), pp. 540-547

Guo X. Information and option pricings Quant. Finance, 1 (1) (2001), pp. 38-44

Hamilton J.D. A new approach to the economic analysis of nonstationary time series and the business cycle Econometrica, 57 (2) (1989), pp. 357-384

Hardy M.R. A regime-switching model of long-term stock returns

N. Am. Actuar. J., 5 (2) (2001), pp. 41-53

Hardy M.R. Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance John Wiley & Sons, Ltd. (2003)

Harrison J., Kreps D.M. Martingales and arbitrage in multiperiod securities markets J. Econom. Theory, 20 (3) (1979), pp. 381-408

Ignatieva K., Song A., Ziveyi J. Pricing and hedging of guarantee minimum benefits under regime-switching and stochastic mortality

Insurance Math. Econom., 70 (2016), pp. 286-300

Ignatieva K., Song A., Ziveyi J. Fourier space time-stepping algorithm for valuing guaranteed minimum withdrawal benefits in variable annuities under regime-switching and stochastic mortality

ASTIN Bull.: J. IAA, 48 (1) (2018), pp. 139-169

Ishijima, H., Kihara, T., 2005. Option pricing with hidden Markov models, Institute of Finance, Waseda University.

Jin Z., Wang Y., Yin G. Numerical solutions of quantile hedging for guaranteed minimum death benefits under a regime-switching jump-diffusion formulation J. Comput. Appl. Math., 235 (8) (2011), pp. 2842-2860

Jobert A., Rogers L.C. Option pricing with Markov-modulated dynamics SIAM J. Control Optim., 44 (6) (2006), pp. 2063-2078

Lamberton D., Lapeyre B. Introduction to Stochastic Calculus Applied to Finance CRC Press (2007)

Liew C.C., Siu T.K. A hidden Markov regime-switching model for option valuation Insurance Math. Econom., 47 (3) (2010), pp. 374-384

Lin X., Tan K.S., Yang H. Pricing annuity guarantees under a regime-switching model N. Am. Actuar. J., 13 (3) (2009), pp. 316-332

Liu R., Zhang Q., Yin G. Option pricing in a regime-switching model using the fast Fourier transform Int. J. Stoch. Anal., 2006 (2006)

Mamon R.S., Rodrigo M.R. Explicit solutions to European options in a regime-switching economy Oper. Res. Lett., 33 (6) (2005), pp. 581-586

Naik V. Option valuation and hedging strategies with jumps in the volatility of asset returns J. Finance, 48 (5) (1993), pp. 1969-1984

Ng A.C.-Y., Li J.S.-H. Valuing variable annuity guarantees with the multivariate esscher transform Insurance Math. Econom., 49 (3) (2011), pp. 393-400

Ngai A., Sherris M. Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives Insurance Math. Econom., 49 (1) (2011), pp. 100-114

Ranjbar H.R., Seifi A. A path-independent method for barrier option pricing in hidden Markov models Physica A, 440 (2015), pp. 1-8

Shen Y., Siu T.K. Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model Insurance Math. Econom., 53 (3) (2013), pp. 757-768

Siu T.K. A hidden Markov-modulated jump diffusion model for european option pricing Hidden Markov Models in Finance, Springer (2014), pp. 185-209

Siu T.K., Fung E.S., Ng M.K. Option valuation with a discrete-time double Markovian regime-switching model Appl. Math. Finance, 18 (6) (2011), pp. 473-490

Siu C.C., Yam S.C.P., Yang H. Valuing equity-linked death benefits in a regime-switching framework ASTIN Bull.: J. IAA, 45 (2) (2015), pp. 355-395

Trottier D.-A., Godin F., Hamel E. Local hedging of variable annuities in the presence of basis risk ASTIN Bull.: J. IAA, 48 (2) (2018), pp. 611-646

Trottier D.-A., Godin F., Hamel E. On fund mapping regressions applied to segregated funds hedging under regime-switching dynamics Risks, 6 (3) (2018), p. 78

Wang C.-W., Yang S.S., Huang J.-W. Analytic option pricing and risk measures under a regime-switching generalized hyperbolic model with an application to equity-linked insurance Quant. Finance, 17 (10) (2017), pp. 1567-1581

Wang Y., Yin G. Quantile hedging for guaranteed minimum death benefits with regime switching Stoch. Anal. Appl., 30 (5) (2012), pp. 799-826

Yao D.D., Zhang Q., Zhou X.Y. A regime-switching model for European options Stoch. Processes, Optim. Control Theory: Appl. Financ. Eng. Queue. Netw. Manuf. Syst.(2006), pp. 281-300

Yuen F.L., Yang H. Option pricing in a jump-diffusion model with regime switching ASTIN Bull.: J. IAA, 39 (2) (2009), pp. 515-539

Zhang Q., Guo X. Closed-form solutions for perpetual American put options with regime switching SIAM J. Appl. Math., 64 (6) (2004), pp. 2034-2049

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