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Simulation and Calibration of Options Prices under a Levy-Type Stochastic Dynamic and Semi Markov Market Switching Regimes Processes

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  • Patrick Assonken
  • Gangaram Ladde

Abstract

This work mainly highlights the benefits of derivative pricing in a semi Markov switching market. We explore the main differences between Markov and Semi Markov regime switching models. The three main problems we deal with are, (1) historical parameter calibration through the recently developed LLGMM method, (2) effects of semi Markov parameters on option prices and (3) comparison of Heston model, semi Markov regime model and Markov regime model calibration performances over both sequential option price calibration and the overall implied volatility surface of the market. Employing the LLGMM method, parameters of the spot price process described by a linear Levy-type stochastic differential equation under semi-Markov structural perturbations are calibrated to observed prices. From Fourier space time stepping and Carr and Madan methods, risk neutral parameters of the spot price are calibrated and interpreted. American and European style vanilla and exotic option prices are simulated. The presented results are shown in the context of a piecewise constant semi-Markov intensity matrix approximating a Weibull intensity matrix. We obtain that under the conditional minimum entropy martingale measure, option prices predictably increase as the regime risk increases through the intensity matrix of the semi Markov process. Calibration and simulation results demonstrate noticeable effects of semi-Markov parameters on option prices and a demonstrably better calibration fit of the Black Scholes model over the entire volatility surface, in a market with semi Markov regimes.

Suggested Citation

  • Patrick Assonken & Gangaram Ladde, 2017. "Simulation and Calibration of Options Prices under a Levy-Type Stochastic Dynamic and Semi Markov Market Switching Regimes Processes," Applied Economics and Finance, Redfame publishing, vol. 4(1), pages 93-126, January.
  • Handle: RePEc:rfa:aefjnl:v:4:y:2017:i:1:p:93-126
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    References listed on IDEAS

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    1. Patrick Assonken & G. S. Ladde, 2015. "Option Pricing With A Levy-Type Stochastic Dynamic Model For Stock Price Process Under Semi-Markovian Structural Perturbations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-72, December.
    2. Kyriakos Chourdakis, 2002. "Continuous Time Regime Switching Models and Applications in Estimating Processes with Stochastic Volatility and Jumps," Working Papers 464, Queen Mary University of London, School of Economics and Finance.
    3. Orlin Grabbe, J., 1983. "The pricing of call and put options on foreign exchange," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 239-253, December.
    4. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 6-83, Wharton School Rodney L. White Center for Financial Research.
    5. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 06-83, Wharton School Rodney L. White Center for Financial Research.
    6. P. E. Kloeden & Eckhard Platen, 1992. "Higher-order implicit strong numerical schemes for stochastic differential equations," Published Paper Series 1992-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. Biswas, Arunangshu & Goswami, Anindya & Overbeck, Ludger, 2018. "Option pricing in a regime switching stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 116-126.

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    More about this item

    Keywords

    Semi Markov; Regime switching; Option pricing; LLGMM method; Levy processes; Minimum entropy; equivalent martingale measure;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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