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Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets

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  • Cern›, Ales

    (Imperial College)

Abstract

This paper draws on the seminal article of Cochrane and Saa-Requejo (2000) who pioneered the calculation of option price bounds based on the absence of arbitrage and high Sharpe Ratios. Our contribution is threefold: We base the equilibrium restrictions on an arbitrary utility function, obtaining the C&S-R analysis as a special case with truncated quadratic utility. Secondly, we restate the discount factor restrictions in terms of Generalised Sharpe Ratios suitable for practical applications. Last but not least, we demonstrate that for ItÙ processes C&S-R price bounds are invariant to the choice of the utility function, and that in the limit they tend to a unique price determined by the minimal martingale measure.

Suggested Citation

  • Cern›, Ales, 2002. "Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets," Royal Economic Society Annual Conference 2002 41, Royal Economic Society.
    • Handle: RePEc:ecj:ac2002:41
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    Cited by:

    1. HENROTTE, Philippe, 2002. "Pricing kernels and dynamic portfolios," HEC Research Papers Series 768, HEC Paris.
    2. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
    3. Černý, Aleš & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2012. "On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 386-395.
    4. Oleg Bondarenko & Iñaki Longarela, 2009. "A general framework for the derivation of asset price bounds: an application to stochastic volatility option models," Review of Derivatives Research, Springer, vol. 12(2), pages 81-107, July.
    5. Mustafa Pınar, 2011. "Gain–loss based convex risk limits in discrete-time trading," Computational Management Science, Springer, vol. 8(3), pages 299-321, August.

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