Document Type : Research Article
Authors
1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University Guilan, Rasht, Iran
2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Abstract
In this paper, we discuss the calibration of the geometric Brownian motion model equipped with Markov-switching factor. Since the motivation for this research comes from a recent stream of literature in stock economics, we propose an efficient estimation method to sample a series of stock prices based on the expectation-maximization algorithm. We also implement an empirical application to evaluate the performance of the suggested model. Numerical results through the classification of the data set show that the proposed Markov-switching model fits the actual stock prices and reflects the main stylized facts of market dynamics. Since the motivation for this research comes from a recent stream of literature in stock economics, we propose an efficient estimation method to sample a series of stock prices based on the expectation-maximization algorithm. Numerical results through the classification of the data set show that the proposed Markov-switching model fits the actual stock prices and reflects the main stylized facts of market dynamics. Since the motivation for this research comes from a recent stream of literature in stock economics, we propose an efficient estimation method to sample a series of stock prices based on the expectation-maximization algorithm.
Keywords
[2] M. Avellaneda, A. Levy, and A. Paras, Pricing and hedging derivative securities in markets with uncertain volatilities, Applied Mathematical Finance, 2 (1995), pp. 73-88.
[3] M. Avellaneda, R. Buff, Combinatorial implications of nonlinear uncertain volatility models: the case of barrier options, Applied Mathematical Finance, 6 (1999), pp. 1-18.
[4] T. Davig, Regime-switching debt and taxation, Journal of Monetary Economics, 51 (2004), pp. 837-859.
[6] E. Derman, I. Kani, The volatility smile and its implied tree, Goldman Sachs Quantitative Strategies Research Notes, 2 (1994), pp. 45-60.
[7] B. Dumas, J. Fleming, and R. E. Whaley, Implied volatility functions: Empirical tests, The Journal of Finance, 53 (1998), pp. 2059-2106.
[8] B. Dupire, Pricing with a smile, Risk, 7 (1994), pp. 18-20.
[9] R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov models: estimation and control, Springer Science & Business Media, 2008.
[10] B. Engelmann, M. R. Fengler, M. Nalholm, and P. Schwendner, Static versus dynamic hedges: an empirical comparison for barrier options, Review of Derivatives Research, 9 (2006), pp. 239-264.
[11] S. Fallah, F. Mehrdoust, American option pricing under double Heston stochastic volatility model: simulation and strong convergence analysis, Journal of Statistical Computation and Simulation, 89 (2019), pp. 1322-1339.
[12] S. Fallah, F. Mehrdoust, On the existence and uniqueness of the solution to the double Heston model equation and valuing Lookback option, Journal of Computational and Applied Mathematics, 350 (2019), pp. 412-422.
[13] S. Fallah, F. Mehrdoust, CEV model equipped with the long-memory, Journal of Computational and Applied Mathematics, 389 (2021), pp. 113359.
[14] G. A. Fink, Markov models for pattern recognition: from theory to applications, Springer Science & Business Media, 2014.
[15] S. Goutte, A. Ismail, and H. Pham, Regime-switching stochastic volatility model: estimation and calibration to VIX options, Applied Mathematical Finance, 24 (2017), pp. 38-75.
[16] P. S. Hagan, D. Kumar, A. S. Lesniewski, and D. E. Woodward, Managing smile risk, The Best of Wilmott, 1 (2002), pp. 249-296.
[17] M. Hahn, S. Fruhwirth-Schnatter, and J. Sass, Estimating models based on Markov jump processes given fragmented observation series, AStA Advances in Statistical Analysis, 93 (2009), pp. 403-425.
[18] J. D. Hamilton, Analysis of time series subject to changes in regime, Journal of Econometrics, 45 (1990), PP. 39-70.
[19] J. D. Hamilton, Regime switching models. In Macroeconometrics and time series analysis, Palgrave Macmillan, London, 2010.
[20] C. J. Kim, Dynamic linear models with Markov-switching, Journal of Econometrics, 60 (1994), pp. 1-22.
[21] Q. Luo, X. Mao, Stochastic population dynamics under regime switching Journal of Mathematical Analysis and applications, 334 (2007), pp. 69-84.
[22] F. Mehrdoust, I. Noorani, Forward price and tting of electricity Nord Pool market under regime-switching two-factor model, Mathematics and Financial Economics, (2021), pp. 1-43.
)