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Pricing Index Options By Static Hedging Under Finite Liquidity

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  • JOHN ARMSTRONG

    (Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, UK)

  • TEEMU PENNANEN

    (Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, UK)

  • UDOMSAK RAKWONGWAN

    (Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, UK)

Abstract

We develop a model for indifference pricing in derivatives markets, where price quotes have bid–ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor’s views, risk preferences and financial position as well as on the price quotes. Computational techniques of convex optimization allow for fast computation of the hedging portfolios and prices as well as sensitivities with respect to various model parameters. We illustrate the techniques by pricing and hedging of exotic derivatives on S&P index using call and put options, forward contracts and cash as the hedging instruments. The optimized static hedges provide good approximations of the options payouts and the spreads between indifference selling and buying prices are quite narrow as compared with the spread between superhedging and subhedging prices.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:06:n:s0219024918500449
    DOI: 10.1142/S0219024918500449
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    References listed on IDEAS

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    1. Teemu Pennanen, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. 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.
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    Cited by:

    1. Teemu Pennanen & Udomsak Rakwongwan, 2020. "Optimal semi-static hedging in illiquid markets," Papers 2008.01463, arXiv.org.

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