Pricing exotic options under regime switching. (English) Zbl 1141.91420

Summary: This paper studies the pricing of options when the volatility of the underlying asset depends upon a hidden Markov process which takes discrete values. It is assumed that the regime switching process is generated by time-independent rate parameters and is independent of the Brownian motion. We derive the coupled Black-Scholes-type partial differential equations that govern the dynamics of several exotic options. These include European, Asian and lookback options. The difference in option prices with and without regime switching is substantial for lookback options and more moderate for European and Asian options.


91G20 Derivative securities (option pricing, hedging, etc.)
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[1] Alziary, B.; Decamps, J.P.; Koehl, P.F., A PDE approach to Asian options: analytical and numerical evidence, Journal of banking and finance, 21, 613-640, (1997)
[2] Andersem, T.G.; Benzoni, L.; Lund, J., An empirical investigation of continuous-time equity return models, Journal of finance, VLII, 1239-1284, (2002)
[3] Bakshi, G.; Cao, C.; Chen, Z., Empirical performance of alternative option pricing models, Journal of finance, 52, 2003-2049, (1997)
[4] Bates, D., Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options, Review of financial studies, 9, 69-107, (1996)
[5] Bollen, N.P.B., Valuing options in regime-switching models, Journal of derivatives, 6, 38-49, (1998)
[6] Di Masi, G.B.; Kabanov, Y.M.; Runggaldier, W.J., Mean-variance hedging of options on stocks with Markov volatility, Theory of probability and its applications, 39, 173-181, (1994) · Zbl 0836.60075
[7] Duan, J.C.; Popova, I.; Ritchken, P., Option pricing under regime switching, Quantitative finance, 2, 1-17, (2002)
[8] Goldman, M.B.; Sosin, H.B.; Gatto, M.A., Path-dependent options buy at the low, Sell at the high, Journal of finance, 34, 1111-1127, (1979)
[9] Guo, X., Information and option pricing, Quantitative finance, 1, 38-44, (2001) · Zbl 1405.91619
[10] Hamilton, J.D., A new approach to the economic analysis of non-stationary time series, Econometrica, 57, 357-384, (1989) · Zbl 0685.62092
[11] Hamilton, J.D., Analysis of time series subject to changes in regime, Journal of econometrics, 45, 39-70, (1990) · Zbl 0723.62050
[12] Hamilton, J.D.; Susmel, R., Autoregressive conditional heteroskedasticity and changes in regime, Journal of econometrics, 64, 307-333, (1994) · Zbl 0825.62950
[13] Hardy, M.R., A regime switching model of a long term stock-returns, North American actuarial journal, 3, 185-211, (2001) · Zbl 1083.62530
[14] Hardy, M.R., Investment guarantees: modelling and risk management for equity-linked life insurance, (2003), John Wiley and Sons New Jersey · Zbl 1092.91042
[15] Hull, J.; White, A., The pricing of options with stochastic volatilities, Journal of finance, 42, 281-300, (1987)
[16] Ingersoll, J.E., Theory of financial decision making, (1987), Rowman and Littlefield New Jersey
[17] Kemna, A.G.Z.; Vorst, A.C.F., A pricing method for options based on average asset values, Journal of banking and finance, 14, 113-129, (1990) · Zbl 0638.90013
[18] Merton, R., Option pricing when underlying stock returns are discontinuous, Journal of financial economics, 3, 125-144, (1976) · Zbl 1131.91344
[19] Naik, V., Option valuation and hedging strategies with jumps in the volatility of asset returns, Journal of finance, 48, 1969-1984, (1993)
[20] Rogers, L.C.G.; Shi, Z., The value of an Asian option, Journal of applied probability, 32, 1077-1088, (1995) · Zbl 0839.90013
[21] Scharfetter, D.L.; Gummel, H.K., Large signal analysis of a silicon Read diode oscillator, IEEE transactions on electron devices, ED-16, 64-77, (1969)
[22] Wilmott, P.; Dewynne, J.; Howison, S., Option pricing: mathematical models and computation, (1997), Oxford Financial Press Oxford
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