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A reduced lattice model for option pricing under regime-switching

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Listed:
  • Massimo Costabile
  • Arturo Leccadito
  • Ivar Massabó
  • Emilio Russo

Abstract

We present a binomial approach for pricing contingent claims when the parameters governing the underlying asset process follow a regime-switching model. In each regime, the asset dynamics is discretized by a Cox–Ross–Rubinstein lattice derived by a simple transformation of the parameters characterizing the highest volatility tree, which allows a simultaneous representation of the asset value in all the regimes. Derivative prices are computed by forming expectations of their payoffs over the lattice branches. Quadratic interpolation is invoked in case of regime changes, and the switching among regimes is captured through a transition probability matrix. An econometric analysis is provided to pick reasonable volatility values for option pricing, for which we show some comparisons with the existing models to assess the goodness of the proposed approach. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Massimo Costabile & Arturo Leccadito & Ivar Massabó & Emilio Russo, 2014. "A reduced lattice model for option pricing under regime-switching," Review of Quantitative Finance and Accounting, Springer, vol. 42(4), pages 667-690, May.
    • Handle: RePEc:kap:rqfnac:v:42:y:2014:i:4:p:667-690
    DOI: 10.1007/s11156-013-0357-9
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    References listed on IDEAS

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    Cited by:

    1. Hainaut, Donatien, 2014. "Impulse control of pension fund contributions, in a regime switching economy," European Journal of Operational Research, Elsevier, vol. 239(3), pages 810-819.
    2. Youngchul Han & Geonwoo Kim, 2016. "Efficient Lattice Method for Valuing of Options with Barrier in a Regime Switching Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-14, October.
    3. L. Ramprasath, 2018. "A simpler algorithm to price American Lookback options in a discrete stochastic volatility model," Working papers 294, Indian Institute of Management Kozhikode.
    4. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    5. Yang, Qing-Qing & Ching, Wai-Ki & Gu, Jia-Wen & Siu, Tak-Kuen, 2018. "Market-making strategy with asymmetric information and regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 408-433.
    6. Cheng Few Lee & Yibing Chen & John Lee, 2020. "Alternative Methods to Derive Option Pricing Models: Review and Comparison," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 102, pages 3573-3617, World Scientific Publishing Co. Pte. Ltd..
    7. Milan Kumar Das & Anindya Goswami & Sharan Rajani, 2019. "Inference of Binary Regime Models with Jump Discontinuities," Papers 1910.10606, arXiv.org, revised Mar 2022.
    8. Liu, Yuanyuan & Wen, Zhexin, 2024. "Two-time-scale stochastic functional differential equations with wideband noises and jumps," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    10. Zhang, Ziqing, 2024. "Multi-regime foreign exchange rate model: Calibration and pricing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 204-218.
    11. Jang, Bong-Gyu & Tae, Hyeon-Wuk, 2018. "Option pricing under regime switching: Integration over simplexes method," Finance Research Letters, Elsevier, vol. 24(C), pages 301-312.
    12. Emilio Russo, 2020. "A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model," Risks, MDPI, vol. 8(1), pages 1-22, January.
    13. Lo, C.C. & Nguyen, D. & Skindilias, K., 2017. "A Unified Tree approach for options pricing under stochastic volatility models," Finance Research Letters, Elsevier, vol. 20(C), pages 260-268.
    14. Chien-Hsiu Lin & Shih-Kuei Lin & An-Chi Wu, 2015. "Foreign exchange option pricing in the currency cycle with jump risks," Review of Quantitative Finance and Accounting, Springer, vol. 44(4), pages 755-789, May.
    15. Laura Eslava & Fernando Baltazar-Larios & Bor Reynoso, 2022. "Maximum Likelihood Estimation for a Markov-Modulated Jump-Diffusion Model," Papers 2211.17220, arXiv.org.
    16. Milan Kumar Das & Anindya Goswami & Sharan Rajani, 2023. "Inference of Binary Regime Models with Jump Discontinuities," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 49-86, May.
    17. Hsuan-Chu Lin & Ren-Raw Chen & Oded Palmon, 2016. "Explaining the volatility smile: non-parametric versus parametric option models," Review of Quantitative Finance and Accounting, Springer, vol. 46(4), pages 907-935, May.
    18. Jung Ho Park & Kwangsoo Shin, 2018. "R&D Project Valuation Considering Changes of Economic Environment: A Case of a Pharmaceutical R&D Project," Sustainability, MDPI, vol. 10(4), pages 1-15, March.
    19. Elyas Elyasiani & Silvia Muzzioli & Alessio Ruggieri, 2016. "Forecasting and pricing powers of option-implied tree models: Tranquil and volatile market conditions," Department of Economics 0099, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".

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    More about this item

    Keywords

    Option pricing; Regime-switching; Binomial lattice; Discrete time models; G13; C52;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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