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Calibrated Option Bounds

Author

Listed:
  • ALAN J. KING

    (IBM Research Division, Mathematical Sciences Department, Thomas J. Watson Research Center, PO Box 210, Yorktown Heights, NY 10598, USA)

  • MATTI KOIVU

    (Risk Management Division, European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany)

  • TEEMU PENNANEN

    (Department of Business Technology, Helsinki School of Economics, PL 1210, 00101 Helsinki, Finland)

Abstract

This paper proposes a numerical approach for computing bounds for the arbitrage-free prices of an option when some options are available for trading. Convex duality reveals a close relationship with recently proposed calibration techniques and implied trees. Our approach is intimately related to the uncertain volatility model of Avellaneda, Levy and Parás, but it is more general in that it is not based on any particular form of the asset price process and does not require the seller's price of an option to be a differentiable function of the cash-flows of the option. Numerical tests on S&P500 options demonstrate the accuracy and robustness of the proposed method.

Suggested Citation

  • Alan J. King & Matti Koivu & Teemu Pennanen, 2005. "Calibrated Option Bounds," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 141-159.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:02:n:s0219024905002925
    DOI: 10.1142/S0219024905002925
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    Citations

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    Cited by:

    1. Consiglio, Andrea & Zenios, Stavros A., 2018. "Pricing and hedging GDP-linked bonds in incomplete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 137-155.
    2. John Armstrong & Teemu Pennanen & Udomsak Rakwongwan, 2018. "Pricing Index Options By Static Hedging Under Finite Liquidity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-18, September.
    3. Consiglio, Andrea & De Giovanni, Domenico, 2008. "Evaluation of insurance products with guarantee in incomplete markets," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 332-342, February.
    4. John Armstrong & Teemu Pennanen & Udomsak Rakwongwan, 2018. "Pricing index options by static hedging under finite liquidity," Papers 1803.02486, arXiv.org.
    5. Martin Glanzer & Georg Ch. Pflug & Alois Pichler, 2017. "Incorporating statistical model error into the calculation of acceptability prices of contingent claims," Papers 1703.05709, arXiv.org, revised Jan 2019.
    6. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2014. "No-arbitrage bounds for financial scenarios," European Journal of Operational Research, Elsevier, vol. 236(2), pages 657-663.

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