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Pricing for Large Positions in Contingent Claims

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  • Scott Robertson
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    Abstract

    Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches infinity, the utility function's decay rate for large negative wealths is the primary driver of prices. For utilities with exponential decay, one may price like an exponential investor. For utilities with a power decay, one may price like a power investor after a suitable adjustment to the rate at which the position size becomes large. In a sizable class of diffusion models, limiting indifference prices are explicitly computed for an exponential investor. Furthermore, the large claim limit is seen to endogenously arise as the hedging error for the claim vanishes.

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    File URL: http://arxiv.org/pdf/1202.4007
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    Paper provided by arXiv.org in its series Papers with number 1202.4007.

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    Date of creation: Feb 2012
    Date of revision: Dec 2013
    Handle: RePEc:arx:papers:1202.4007

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    1. Laurence Carassus & Miklós Rásonyi, 2011. "Risk-averse asymptotics for reservation prices," Annals of Finance, Springer, Springer, vol. 7(3), pages 375-387, August.
    2. Monoyios, Michael, 2007. "The minimal entropy measure and an Esscher transform in an incomplete market model," Statistics & Probability Letters, Elsevier, Elsevier, vol. 77(11), pages 1070-1076, June.
    3. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(2), pages 99-123.
    4. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility-Based Pricing," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 19(1), pages 129-159.
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