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Model Dependency of the Digital Option Replication – Replication under an Incomplete Model (in English)

Author

Listed:
  • Tomáš Tichý

    (Faculty of Economics, VŠB-TU Ostrava, Czech Republic)

Abstract

The paper focuses on the replication of digital options under an incomplete model. Digital options are regularly applied in the hedging and static decomposition of many path-dependent options. The author examines the performance of static and dynamic replication. He considers the case of a market agent for whom the right model of the underlying asset-price evolution is not available. The observed price dynamic is supposed to follow four distinct models: (i) the Black and Scholes model, (ii) the Black and Scholes model with stochastic volatility driven by Hull and White model, (iii) the variance gamma model, defined as time changed Brownian motion, and (iv) the variance gamma model set in a stochastic environment modelled as the rate of time change via a Cox-Ingersoll-Ross model. Both static and dynamic replication methods are applied and examined within each of these settings. The author verifies the independence of the static replication on underlying processes.

Suggested Citation

  • Tomáš Tichý, 2006. "Model Dependency of the Digital Option Replication – Replication under an Incomplete Model (in English)," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 56(7-8), pages 361-379, July.
    • Handle: RePEc:fau:fauart:v:56:y:2006:i:7-8:p:361-379
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    File URL: http://journal.fsv.cuni.cz/storage/1063_s_361_379.pdf
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
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    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. MacBeth, James D & Merville, Larry J, 1979. "An Empirical Examination of the Black-Scholes Call Option Pricing Model," Journal of Finance, American Finance Association, vol. 34(5), pages 1173-1186, December.
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    Citations

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    Cited by:

    1. Tomáš Tichý, 2008. "Posouzení vybraných možností zefektivnění simulace Monte Carlo při opčním oceňování [Examination of selected improvement approaches to Monte Carlo simulation in option pricing]," Politická ekonomie, Prague University of Economics and Business, vol. 2008(6), pages 772-794.
    2. Tomáš Tichý, 2010. "Posouzení odhadu měnového rizika portfolia pomocí Lévyho modelů [Examination of Portfolio Currency Risk Estimation by Means of Lévy Models]," Politická ekonomie, Prague University of Economics and Business, vol. 2010(4), pages 504-521.
    3. Augusto Blanc-Blocquel & Luis Ortiz-Gracia & Rodolfo Oviedo, 2023. "Hedging At-the-money Digital Options Near Maturity," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.
    4. Vasilios N. Katsikis & Spyridon D. Mourtas, 2020. "ORPIT: A Matlab Toolbox for Option Replication and Portfolio Insurance in Incomplete Markets," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 711-721, December.

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    More about this item

    Keywords

    digital options; dynamic and static replication; internal time; Lévy models; replication error; stochastic environment; stochastic volatility; variance gamma process;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G20 - Financial Economics - - Financial Institutions and Services - - - General
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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