European Option Pricing under the Structural Time Series and Markov Regime-switching Model

Pao-Peng Hsu 1; Che-Yang Lin 2

doi:10.18282/ff.v7i1.453

Pao-Peng Hsu 1 1 Department of Tourism and Leisure Management and Department of Applied Finance, Yuanpei University of Medical Technology
Che-Yang Lin 2 2 Department and the Graduate Institute of Business Administration, Yuanpei University of Medical Technology

DOI: https://doi.org/10.18282/ff.v7i1.453

Keywords: Structural time series, Markov regime-switching process, HJM, European call option

Abstract

We present closed-form formulas for the valuation of a European call option whose underlying process is assumed to follow structural time series and the Markov regime-switching process through mean reversion described by a harmonic oscillator. In our model, each parameter has related corresponding economic meaning, and this leads to an easy analy-sis of the interplay between the option and business cycles. Forward rates are assumed under the Heath et al. (1992) HJM framework. The call option analytic formulas are obtained when the joint distribution of occupation times is specified and forward rates are restricted in a one-factor HJM model.

Author Biographies

Pao-Peng Hsu 1, 1 Department of Tourism and Leisure Management and Department of Applied Finance, Yuanpei University of Medical Technology

Department of Tourism and Leisure Management and Department of Applied Finance

Che-Yang Lin 2, 2 Department and the Graduate Institute of Business Administration, Yuanpei University of Medical Technology

Department and the Graduate Institute of Business Administration

References

Akar, C., Baskaya, Z., 2011. Detecting the long term cyclical behaviour of the Turkish stock market by means of spectral analysis. Research Journal of Finance and Economics, 67, 160-167.

Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. The Journal of Political Economy, 81, 637-654.

Buckle, R. A., Haugh, D., Thomson, P., 2002. Growth and volatility regime switching models for New Zealand GDP data. Wellington, New Zealand Treasury, Working Paper.

Chen, S. N., Chiang, M. H., Hsu, P. P., Li, C. Y., 2014. Valuation of quanto options in a Markovian regime-switching market: A Markov-modulated Gaussian HJM model. Finance Research Letters, 11, 161-172.

Chen, S. N., Hsu, P. P., Liang, K. Y. 2019. Option pricing and hedging in different cyclical structures: a two-dimensional Markov-modulated model, 25, 762-779.

Duan, J. C., 1995. The GARCH option pricing model. Mathematical Finance, 5, 13-32.

Galati, G., Hindrayanto, I., Koopman, S. J., Vlekke, M., 2016. Measuring financial cycles in a model-based analysis: Empirical evidence for the United States and the euro area. Economics Letters, 145, 83-87.

Glasserman, P., Kou, S. G., 2003. The term structure of simple forward rates with jump risk. Mathematical Finance, 13, 383-410.

Heath, D., Jarrow, R.A., Morton, A. J., 1992. Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60, 77-105.

Heston, S. L., Nandi, S., 2000. A closed-form GARCH option valuation model. Review of Financial Studies, 13, 585-625.

Janczura, J., Weron, R., 2010. An empirical comparison of alternate regime-switching models for electricity spot prices. Energy Economics, 32, 1059-1073.

Jones, C.I., 2016. The facts of economic growth. Handbook of Macroeconomics, 2, 3–69.

Jones, S., Tarp, F., 2017. What’s beneath the stylized facts of economic growth? Insights from a structured statistical decomposition. UNU-WIDER & University of Copenhagen, Denmark.

Kim, I. J., Kim, S., 2004. Empirical comparison of alternative stochastic volatility option pricing models: Evidence from Korean KOSPI 200 index options market. Pacific-Basin Finance Journal, 12, 117-142.

Koopman, S. J., Lucas, A., 2005. Business and default cycles for credit risk. Journal of Applied Econometrics, 20, 311-323.

Laine, M., 2019. Introduction to dynamic linear models for time series analysis. preprint arXiv:1903.11309.

McConnell, M.M., Perez-Quiros, G., 2000. Output fluctuations in the United States: What has changed since the early 1980s? American Economic Review 90, 1464–1476.

Merton, R. C., 1973. Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4, 141-183.

Moreno, M., Platania, F., 2011. Business Cycle and Interest Rates: Pricing and Risk Management under a New Term Structure Model. Available at SSRN: https://ssrn.com/abstract=1787018.

Raible, S., 2000. Lévy processes in Finance: Theory, numerics, and empirical facts. PhD Thesis, University of Freiburg.

Scott, L. O., 1997. Pricing stock options in a jump‐diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods. Mathematical Finance, 7, 413-426.