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

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  • Tomáš Tichý

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

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    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.

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    Bibliographic Info

    Article provided by Charles University Prague, Faculty of Social Sciences in its journal Finance a uver - Czech Journal of Economics and Finance.

    Volume (Year): 56 (2006)
    Issue (Month): 7-8 (July)
    Pages: 361-379

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    Handle: RePEc:fau:fauart:v:56:y:2006:i:7-8:p:361-379

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    Related research

    Keywords: digital options; dynamic and static replication; internal time; Lévy models; replication error; stochastic environment; stochastic volatility; variance gamma process;

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    References

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    1. 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 637-54, May-June.
    2. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    3. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Economics Series Working Papers 2003-W12, University of Oxford, Department of Economics.
    4. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
    5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    6. Ole E. Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2001. "Some recent developments in stochastic volatility modelling," Economics Papers 2001-W25, Economics Group, Nuffield College, University of Oxford.
    7. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, 06.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    9. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:
    1. Tomáš Tichý, 2010. "Examination of Portfolio Currency Risk Estimation by Means of Lévy Models," Politická ekonomie, University of Economics, Prague, vol. 2010(4), pages 504-521.

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