Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets

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 ItU 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.

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