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Arbitrage pricing with incomplete markets

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  • Mark Britten-Jones
  • Anthony Neuberger

Abstract

This paper presents a new arbitrage-free approach to the pricing of derivatives, when the price process of the underlying security does not conform to the standard assumptions. In comparision to the Black-Scholes price process we relax the requirements of i) continuity; ii) constant volatility; and iii) infinite trading possibilities. We retain the assumption that the average volatility of price changes over the option's life is known, and we require that price jumps not be greater than some specified size. With only these assumptions we show that the no-arbitrage bound on a European call option's value approaches the Black-Scholes price as the maximum jump size approaches zero. We present a simple numerical method for the calculation of option pricing bounds for any specified maximum jump size, and discuss implications of our model for hedging, and the estimation of volatility.

Suggested Citation

  • Mark Britten-Jones & Anthony Neuberger, 1996. "Arbitrage pricing with incomplete markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 347-363.
    • Handle: RePEc:taf:apmtfi:v:3:y:1996:i:4:p:347-363
    DOI: 10.1080/13504869600000016
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    References listed on IDEAS

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    1. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Ivan Degano & Sebastian Ferrando & Alfredo Gonzalez, 2015. "Trajectory based models. Evaluation of minmax pricing bounds," Papers 1511.01207, arXiv.org, revised Dec 2016.
    2. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2015.
    3. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 21, July-Dece.
    4. Sergei Fedotov & Sergei Mikhailov, 1998. "Option Pricing Model for Incomplete Market," Papers cond-mat/9807397, arXiv.org, revised Aug 1998.
    5. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, December.
    6. Sebastian E. Ferrando & Alfredo L. Gonzalez & Ivan L. Degano & Massoome Rahsepar, 2014. "Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals," Papers 1407.1769, arXiv.org, revised Nov 2015.
    7. Sergei Fedotov & Sergei Mikhailov, 2001. "Option Pricing For Incomplete Markets Via Stochastic Optimization: Transaction Costs, Adaptive Control And Forecast," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 179-195.
    8. I. L. Degano & S. E. Ferrando & A. L. Gonzalez, 2020. "No-Arbitrage Symmetries," Papers 2008.06184, arXiv.org.

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