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2014 | OriginalPaper | Buchkapitel

9. An Exact Formula for Pricing American Exchange Options with Regime Switching

verfasst von : Leunglung Chan

Erschienen in: Hidden Markov Models in Finance

Verlag: Springer US

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Abstract

This paper investigates the pricing of American exchange options when the price dynamics of each underlying risky asset are assumed to follow a Markov-modulated Geometric Brownian motion; that is, the appreciation rate and the volatility of each underlying risky asset depend on unobservable states of the economy described by a continuous-time hidden Markov process. We show that the price of an American exchange option can be reduced to the price of an American option. Then, we modify the result of Zhu and Chan (An analytic formula for pricing American options with regime switching. Submitted for publication, 2012), a closed-form analytical pricing formula for the American exchange option is given.

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Vorheriges Kapitel A Hidden Markov-Modulated Jump Diffusion Model for European Option Pricing

Nächstes Kapitel Parameter Estimation in a Weak Hidden Markov Model with Independent Drift and Volatility

Benth, F.E., Di Nunno, G., Khedher, A., Schmeck, M.D.: Pricing of spread options on a bivariate jump market and stability to model risk. Working paper, University of Oslo (2012)

Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Politi. Econ. 81, 637–659 (1973)CrossRef

Buffington, J., Elliott, R.J.: Regime switching and European options. In: Pasik-Duncan B. (eds.) Stochastic Theory and Control, Proceedings of a Workshop, Lawrence, pp. 73–81. Springer, Berlin (2002)

Buffington, J., Elliott R.J.: American options with regime switching. Int. J. Theor. Appl. Financ. 5, 497–514 (2002)CrossRef

Carmona, R., Durrleman, V.: Pricing and hedging spread options. SIAM Rev. 45(4), 627–685 (2003)CrossRef

Cheang, G.H.L., Chiarella, C.: Exchange options under jump-diffusion dynamics. Appl. Math. Financ. 18(3), 245–276 (2011)CrossRef

Dempster, M., Hong, S.: Spread option valuation and the fast Fourier transform. In: Geman, H., Madan, D., Pliska, S.R., Vorst, T. (eds.) Mathematical Finance, Bachelier Congress, vol. 1, pp. 203–220. Springer, Berlin (2000)

Deng, S., Li, M., Zhou, J.: Closed-form approximations for spread option prices and greeks. J. Deriv. 16(4), 58–80 (2008)

Elliott, R.J., Kopp, P.E.: Mathematics of Financial Markets. Springer, Berlin/Heidelberg/New York (1999)CrossRef

10.

Elliott, R.J., van der Hoek, J.: An application of hidden Markov models to asset allocation problems. Financ. Stoch. 3, 229–238 (1997)CrossRef

11.

Elliott, R.J., Aggoun, L., Moore J.B.: Hidden Markov Models: Estimation and Control. Springer, Berlin/Heidelberg/New York (1994)

12.

Elliott, R.J., Hunter, W.C., Jamieson, B.M.: Financial signal processing. Int. J. Theor. Appl. Financ. 4, 567–584 (2001)CrossRef

13.

Elliott, R.J., Malcolm, W.P., Tsoi, A.H.: Robust parameter estimation for asset price models with Markov modulated volatilities. J. Econ. Dyn. Control 27(8), 1391–1409 (2003)CrossRef

14.

Elliott, R.J., Chan, L.L., Siu, T.K.: Option pricing and Esscher transform under regime switching. Ann. Financ. 1(4), 423–432 (2005)CrossRef

15.

Elliott, R.J., Chan, L., Siu, T.K.: Option valuation under a regime-switching constant elasticity of variance process. Appl. Math. Comput. 219(9), 4434–4443 (2013)CrossRef

16.

Eydeland, A., Wolyniec, K.: Energy and Power Risk Management: New Developments in Modeling, Pricing and Hedging. Wiley, Hoboken (2003)

17.

Gounden, S., O’Hara, J.G.: An analytic formula for the price of an American-style Asian option of floating strike type. Appl. Math. Comput. 217, 2923–2936 (2010)CrossRef

18.

Guo, X.: Information and option pricings. Quant. Financ. 1, 38–44 (2001)CrossRef

19.

Hildebrand, F.B.: Advanced Calculus and Applications. Prentice Hall, Englewood Cliffs (1976)

20.

Hurd, T., Zhou, Z.: A Fourier transform method for spread option pricing. SIAM J. Financ. Math. 1, 142–157 (2009)CrossRef

21.

Kirk, E.: Correlation in energy markets. In: Kaminski, V. (ed.) Managing Energy Price Risk, pp. 71–78. Risk Publications, London (1996)

22.

Liao, S.J.: Homotopy Analysis Method in Nonlinear Differential Equations. Springer, Heidelberg/New York/Higher Education Press, Beijing (2012)CrossRef

23.

Liao, S.J., Zhu, S.P.: Solving the Liouville equation with the general boundary element method approach. Bound. Elem. Technol. XIII, 407–416 (1999)

24.

Margrabe, W.: The value of an option to exchange one asset for another. J. Financ. 33(1), 177–186 (1978)CrossRef

25.

Merton, R.: Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4, 141–183 (1973)CrossRef

26.

Odibat, Z.M.: A study on the convergence of homotopy analysis method. Appl. Math. Comput. 217, 782–789 (2010)CrossRef

27.

Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic, New York (1970)

28.

Ravindran, K.: Low-fat spreads. Risk 6(10), 56–57 (1993)

29.

Shimko, D.: Options on futures spreads: hedging, speculation and valuation. J. Futures Mark. 14(2), 183–213 (1994)CrossRef

30.

Siu, T.K., Erlwein, C., Mamon, R.: The pricing of credit default swaps under a Markov-modulated Mertons structural model. North Am. Actuar. J. 12(1), 19–46 (2008)

31.

Venkatramanan, A., Alexander, C.: Closed form approximations for spread options. Appl. Math. Financ. 18(5), 447–472 (2011)CrossRef

32.

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

33.

Yuen, F.L., Yang, H.: Pricing Asian options and equity-indexed annuities with regime switching by the trinomial tree method. North Am. Actuar. J. 14(2), 256–277 (2010)CrossRef

34.

Zhu, S.P.: An exact and explicit solution for the valuation of American put options. Quant. Financ. 6(3), 229–242 (2006)CrossRef

35.

Zhu, S.P., Chan, L.: An analytic formula for pricing American options with regime switching. Submitted for publication (2012)

36.

Zhu, S.P., Badran, A., Lu, X.: A new exact solution for pricing European options in a two-state regime-switching economy. Comput. Math. Appl. 64, 2744–2755 (2012)CrossRef

Titel: An Exact Formula for Pricing American Exchange Options with Regime Switching
verfasst von: Leunglung Chan
Verlag: Springer US
Buch: Hidden Markov Models in Finance
Print ISBN: 978-1-4899-7441-9

Electronic ISBN: 978-1-4899-7442-6

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-1-4899-7442-6_9