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Calibrated Parameters with Consistency for Option Pricing in the Two-state Regime Switching Black-Scholes Model  

Han, Gyu-Sik (Chonbuk National University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.36, no.2, 2010 , pp. 101-107 More about this Journal
Abstract
Among a variety of asset dynamics models in order to explain the common properties of financial underlying assets, parametric models are meaningful when their parameters are set reliably. There are two main methods from which we can obtain them. They are to use time-series data of an underlying price or the market option prices of the underlying at one time. Based on the Girsanov theorem, in the pure diffusion models, the parameters calibrated from the option prices should be partially equivalent to those from time-series underling prices. We call this phenomenon model consistency. In this paper, we verify that the two-state regime switching Black-Scholes model is superior in the sense of model consistency, comparing with two popular conventional models, the Black-Scholes model and Heston model.
Keywords
Parameter Calibration; Consistency; Regime Switching Black-Scholes Model; Girsanov Theorem; Heston Model;
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1 Black, F. and Scholes, M. (1973), The Pricing of Options and Corporate Liabilities, Journal of Politics and Economics, 81, 637-654.   DOI   ScienceOn
2 Kim, C. J. (1994), Dynamic Linear Models with Markov-Switching, Journal of Econometrics, 60, 1-22.   DOI
3 Yao, D. D., Zhan, Q., and Zhou, X. Y. (2006), A Regime-switching Model for European Options, appearing in Stochastic Processes, Optimization, and Control Theory : Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, Springer, New York.
4 Neftci, S. (2000), Introduction to Mathematics of Financial Derivatives, 2th edition, Academic Press, New York.
5 Ross, S. M. (2000), Introduction to Probability Models. Academic Press, London.
6 Heston, S. (1993), A Closed-form Solution for Options with Stochastic Volatility with Application to Bond and Currency Options, Review of Financial Studies, 6, 327-343.   DOI
7 Timmermann, A. (2000), Moments of Markov Switching Models, Journal of Econometrics, 96, 75-111.   DOI   ScienceOn
8 Hull, J. C. (2009), Option, Futures and Other Derivatives, 7th edition, Prentice Hall, New Jersey.
9 Javaheri, A. (2005), Inside Volatility Arbitrage : the Secrets of Skewness, John Wiley and Sons, Inc., New Jersey.
10 Hamilton, J. D. (1994), Time Series Analysis, Princeton University Press, New Jersey.
11 Andersen, L. B. G. (2007), Efficient Simulation of the Heston Stochastic Volatility Model, Working paper, Social Science Research Network.
12 Hamilton, J. D. (1989), A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle, Econometrica, 57, 357-384.   DOI   ScienceOn
13 Fuh, C. D. and Wang, R. H. (2002), Option pricing in a Black-Scholes with Markov Switching, Working Paper, Institute of Statistical Science, Taiwan.
14 Hamilton, J. D. (1988), Rational-Expectations Econometric Analysis of Changes in Regime : An Investigation of the Term Structure of Interest Rates, Journal of Economic Dynamics and Control, 12, 385-423.   DOI   ScienceOn
15 Das, S. R. and Sundaram, R. K. (2007), Higher-order Moments in Modeling Asset Price Processes in Finance, Working paper, National Bureau of Economic Research.
16 Bollen, N. P. B. (1998), Valuing Options in Regime-Switching Models, Journal of Derivatives, 6, 38-49.   DOI   ScienceOn
17 Cont, R. and Tankov, P. (2004), Financial Modeling with Jump Processes, Chapman and Hall/CRC, New York.
18 Cox, J., Ross, S., and Rubinstein M. (1979), Option Pricing : A Simplied Approach, Journal of Financial Economics, 7, 229-263.   DOI   ScienceOn