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Information and option pricings

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  • X. Guo
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    Abstract

    How can one relate stock fluctuations and information-based human activities? We present a model of an incomplete market by adjoining the Black-Scholes exponential Brownian motion model for stock fluctuations with a hidden Markov process, which represents the state of information in the investors' community. The drift and volatility parameters take different values depending on the state of this hidden Markov process. Standard option pricing procedure under this model becomes problematic. Yet, with an additional economic assumption, we provide an explicit closed-form formula for the arbitrage-free price of the European call option. Our model can be discretized via a Skorohod embedding technique. We conclude with an example of a simulation of IBM stock, which shows that, not surprisingly, information does affect the market.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/713665550
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 1 (2001)
    Issue (Month): 1 ()
    Pages: 38-44

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    Handle: RePEc:taf:quantf:v:1:y:2001:i:1:p:38-44

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    Web page: http://www.tandfonline.com/RQUF20

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    Cited by:
    1. Robert Elliott & Tak Siu & Leunglung Chan, 2008. "A PDE approach for risk measures for derivatives with regime switching," Annals of Finance, Springer, vol. 4(1), pages 55-74, January.
    2. Traian Pirvu & Huayue Zhang, 2013. "Investment and Consumption with Regime-Switching Discount Rates," Papers 1303.1248, arXiv.org.
    3. Sakkas, E. & Le, H., 2009. "A Markov-modulated model for stocks paying discrete dividends," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 19-24, August.
    4. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
    5. Traian A. Pirvu & Huayue Zhang, 2011. "On Investment-Consumption with Regime-Switching," Papers 1107.1895, arXiv.org.
    6. Godfrey Charles-Cadogan & John A. Cole, 2013. "Bankruptcy Risk Induced by Career Concerns of Regulators," Papers 1312.7346, arXiv.org.
    7. Su, Xiaonan & Wang, Wensheng & Hwang, Kyo-Shin, 2012. "Risk-minimizing option pricing under a Markov-modulated jump-diffusion model with stochastic volatility," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1777-1785.
    8. Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alexandru, 2011. "On pricing and hedging options in regime-switching models with feedback effect," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 694-713, May.
    9. Tak Kuen Siu & Hailiang Yang Unim & John W Lau, 2007. "Option Pricing When the Regime-Switching Risk is Priced," CRIEFF Discussion Papers 0713, Centre for Research into Industry, Enterprise, Finance and the Firm.
    10. Robert Elliott & Leunglung Chan & Tak Siu, 2006. "Risk measures for derivatives with Markov-modulated pure jump processes," Asia-Pacific Financial Markets, Springer, vol. 13(2), pages 129-149, June.
    11. Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alex, 2010. "On mean-variance portfolio selection under a hidden Markovian regime-switching model," Economic Modelling, Elsevier, vol. 27(3), pages 678-686, May.
    12. Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.
    13. Qi-min, Zhang, 2011. "Convergence of numerical solutions for a class of stochastic age-dependent capital system with Markovian switching," Economic Modelling, Elsevier, vol. 28(3), pages 1195-1201, May.
    14. Shen, Yang & Siu, Tak Kuen, 2013. "Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 757-768.
    15. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    16. Nikita Ratanov, 2008. "Option Pricing Model Based on a Markov-modulated Diffusion with Jumps," Papers 0812.0761, arXiv.org.
    17. Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu & Harry Zheng, 2012. "On Pricing Basket Credit Default Swaps," Papers 1204.4025, arXiv.org.
    18. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    19. Liew, Chuin Ching & Siu, Tak Kuen, 2010. "A hidden Markov regime-switching model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 374-384, December.

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