\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

A lattice method for option evaluation with regime-switching asset correlation structure

The first authors are supported by the Adam Smith Business School of the University of Glasow

Abstract Full Text(HTML) Figure(6) / Table(6) Related Papers Cited by
  • This paper develops a lattice method for option evaluation in the presence of regime shifts in the correlation structure of assets, aiming at investigating whether the option prices reflect such shifts. We try to investigate whether option prices reflect switches in the correlation between the underlying asset of an option and risk-free rates.We develop and test two models.In the first model we allow all the parameters to follow a regime-switching process while in the second model, in order to isolate the regime-switching correlation effect on the option prices, we allow only the correlation to follow a regime-switching process. We use pentanomial lattices to represent the evolution of the regime-switching underlying assets. This is then applied in our empirical analysis, which focuses on crude oil. We use grid- and patternsearch based techniques to fit our models. Our findings suggest that prices of market traded options reflect the regime-switches and that a model which considers these switches produces significantly more accurate results than a single-regime model. We demonstrate that there is an asymmetry between parameter values obtained from historical data (backward looking) and those that are implied by traded options (for- ward looking) by employing the Kim filter to estimate our model.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Binomial tree

    Figure 2.  Pentanomial tree

    Figure 3.  Sensitivity of Call Option value to Transition Probabilities

    Figure 4.  Sensitivity of Call Option Value to the Regime Parameters

    Figure 5.  Sensitivity of option price to the regime resistance of the two regimes

    Figure 6.  Sensitivity of Option Price to the regime switching correlation

    Table 1.   

    Jump Probability Underlying Asset Price
    Up $ \pi_{u} $ $ S_{u} $
    Horizontal $\pi_{0} $ $ S $
    Down $ \pi_{d} $ $ S_{d} $
     | Show Table
    DownLoad: CSV

    Table 2.   

    Event Probability Underlying Asset Price
    Asset 1 Asset 2
    $ E_{1} $ $ \pi_{1} $ $ S_{p}u_{p} $ $ S_{b}u_{b} $
    $ E_{2} $ $ \pi_{2} $ $ S_{p}u_{p} $ $ S_{b}d_{b} $
    $ E_{3} $ $ \pi_{3} $ $ S_{p}d_{p} $ $ S_{b}d_{b} $
    $ E_{4} $ $ \pi_{4} $ $ S_{p}d_{p} $ $ S_{b}u_{b} $
    $ E_{5} $ $ \pi_{5} $ $ S_{p} $ $ S_{b} $
     | Show Table
    DownLoad: CSV

    Table 3.   

    Strike Price Market Price Predicted by Lattice Predicted by BS
    16 4.9 3.881616 3.9936
    17 2.85 3.127282 3.0613
    18 2.35 2.373772 2.2162
    19 1.65 1.629733 1.5029
    20 0.95 0.949999 0.9500
    21 0.4 0.399999 0.5587
    22 0.2 0.200003 0.3059
    23 0.2 0.136097 0.1565
    24 0.1 0.105053 0.0750
    25 0.15 0.088113 0.0339
    Sum of absolute differences 1.110163 2.573241
     | Show Table
    DownLoad: CSV

    Table 4.   

    Strike Price Market Price Predicted by Lattice Predicted by BS
    16 5 4.4153631 4.3208036
    17 3.8 3.7998973 3.5464351
    18 2.45 2.3996588 2.8585724
    19 2.25 1.9270998 2.2636265
    20 1.6 1.5997621 1.7622281
    21 1.35 1.3087541 1.3499542
    22 0.95 1.0205032 1.0186664
    23 1.05 1.1713058 0.7580323
    24 0.6 0.6000609 0.5569055
    25 0.5 0.4960518 0.4043912
    Sum of absolute differences 0.4890502 1.1145081
     | Show Table
    DownLoad: CSV

    Table 5.   

    Strike Price Market Price Predicted by Lattice Predicted by BS
    16 5 4.4153631 4.3208036
    17 3.8 3.7998973 3.5464351
    18 2.45 2.3996588 2.8585724
    19 2.25 1.9270998 2.2636265
    20 1.6 1.5997621 1.7622281
    21 1.35 1.3087541 1.3499542
    22 0.95 1.0205032 1.0186664
    23 1.05 1.1713058 0.7580323
    24 0.6 0.6000609 0.5569055
    25 0.5 0.4960518 0.4043912
    Sum of absolute differences 0.4890502 1.1145081
     | Show Table
    DownLoad: CSV

    Table 6.   

    Strike Price Predicted
    16 4.9 1.625144372
    17 2.85 1.269327353
    18 2.35 0.940833993
    19 1.65 0.626509398
    20 0.95 0.420399871
    21 0.4 0.245524212
    22 0.2 0.158808617
    23 0.2 0.079890983
    24 0.1 0.045583587
    25 0.15 0.023566284
     | Show Table
    DownLoad: CSV
  • [1] N. P. B. Bollen, Valuing options in regime-switching models, Journal of Derivatives, 6 (1998), 38-49. 
    [2] N. P. B. BollenS. F. Gray and R. E. Whaley, Regime switching in foreign exchange rates: Evidence from currency option prices, Journal of Econometrics, 94 (2000), 239-276. 
    [3] P. P. Boyle, A Lattice Framework for Option Pricing with Two State variables, Journal of Financial and Quantitative Analysis, 1988.
    [4] J. C. CoxS. A. Ross and M. Rubinstein, Option pricing: A Simplified approach, Journal of Financial Economics, 7 (1979), 229-263. 
    [5] J. C. Duan, A GARCH option pricing model, Mathematical Finance, 5 (1995), 13-32.  doi: 10.1111/j.1467-9965.1995.tb00099.x.
    [6] J. C. DuanI. Popova and P. Ritchken, Option pricing under regime switching, Quantitative Finance, 2 (2002), 116-132.  doi: 10.1088/1469-7688/2/2/303.
    [7] S. F. Gray, Modeling the conditional distribution of interest rates as a regime-switching process, Journal of Financial Economics, 42 (1996), 27-62. 
    [8] J. D. Hamilton, Rational expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates,, Journal og Econometric Dynamics and Control, 12 (1988), 385-423.  doi: 10.1016/0165-1889(88)90047-4.
    [9] J. Hull and A. White, The pricing of options assets with stochastic volatilities, The Journal of Finance, 42 (1987), 281-300. 
    [10] C. J. Kim, Dynamic linear models with Markov-switching,, Journal of Econometrics, 60 (1994), 1-22.  doi: 10.1016/0304-4076(94)90036-1.
    [11] C. J. Kim, Charles R.Nelson State-Space Models with Regime Switching. Classical and Gibbs-Sampling Approaches with Applications, Massachusetts Institution of Technology, United States of America, 1999.
    [12] V. Naik, Option valuation and hedging strategies with jumps in the volatility of asset returns, The Journal of Finance, 47 (1993), 1969-1984. 
    [13] G. W. Swhwert, Business cycles, financial crises, and risky asset volatility, Carnegie-Rochester Conference Series on Public Policy, 31 (1989), 83-126. 
    [14] C. M. TurnerR. Startz and C. R. Nelson, A markov model of heteroscedasticity, riskm and learning in the risky asset market, Journal of Financial Economics, 25 (1989), 3-22. 
    [15] D. D. Yao, Q. Zhang and X. Y. Zhou, A regime-switching model for european option pricing,, Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, Springer US, 94 (2006), 281–300. doi: 10.1007/0-387-33815-2_14.
  • 加载中

Figures(6)

Tables(6)

SHARE

Article Metrics

HTML views(2106) PDF downloads(332) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return