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Beissner, Patrick; Rosazza Gianin, Emanuela (2018): The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time. Collaborative Research Center Transregio 190, Discussion Paper No. 72
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Abstract

Recent empirical studies suggest a downward sloping term structure of Sharpe ratios. We present a theoretical framework in continuous time that can cope with such a non-flat forward curve of risk prices. The approach departs from an arbitrage-free and incomplete market setting when different pricing measures are possible. Involved pricing measures now depend on the time of evaluation or the maturity of payoffs. This results in a time inconsistent pricing scheme. The dynamics can be captured by a time-delayed backward stochastic Volterra integral equation, which to the best of our knowledge, has not yet been studied.