Model Uncertainty and Liquidity

We investigate the dynamic portfolio problem of a market-maker for a derivative security whose preferences exhibit uncertainty aversion (Knightian uncertainty). The Choquet-expected utility implied by such preference is used to capture the feature that the trader is uncertain about which model should be used. The prices that emerge from the model are similar to standard models and have the feature that as uncertainty is removed, the derivative prices converge to standard prices. However, the optimal changes in the agent's portfolio that results from the option position are quite different than the standard hedge position. It is this feature that links uncertainty with market liquidity.

[1]  Myron S. Scholes.  Crisis and Risk Management , 2000 .

[2]  I. Gilboa.  Expected utility with purely subjective non-additive probabilities , 1987 .

[3]  Larry G. Epstein,et al.  Uncertainty, Risk-Neutral Measures and Security Price Booms and Crashes , 1995 .

[4]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[5]  A. Prati,et al.  Currency Crises and Uncertainty About Fundamentals , 2002, SSRN Electronic Journal.

[6]  Suleyman Basak,et al.  Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices , 1999 .

[7]  S. Werlang,et al.  Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio , 1992 .

[8]  S. Werlang,et al.  Excess volatility of stock prices and Knightian uncertainty , 1992 .

[9]  A. Kyle.  Continuous Auctions and Insider Trading , 1985 .

[10]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[11]  T. Ho,et al.  Optimal dealer pricing under transactions and return uncertainty , 1981 .

[12]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[13]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[14]  Larry G. Epstein,et al.  Intertemporal Asset Pricing Under Knightian Uncertainty , 1994 .

[15]  T. Sargent,et al.  Robust Permanent Income and Pricing , 1999 .

[16]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[17]  G. Choquet.  Theory of capacities , 1954 .

[18]  The crisis of 1998 and the role of the central bank , 2001 .

[19]  Sanford J. Grossman,et al.  Liquidity and Market Structure , 1988 .

[20]  F. Knight.  The economic nature of the firm: From Risk, Uncertainty, and Profit , 2009 .