Model Uncertainity And Liquidity

The paper investigates portfolio strategies and derivative market making when the trader does not know the correct model. One of the puzzles from last summer's LTCM collapse was that when the Russian government defaulted, liquidity dried up. Antidotal evidence suggests that people were unable to trade emerging market debt (as well as corporate bonds) at any price. The drop in the yield of treasury bonds and the rise in the credit spread has been called a "flight to quality." In the paper "small" shocks can leads to a market collapse (lack of liquidity and trade) as the result of uncertainty people have about the "model" of the world. For example, banks that trade derivatives typically assume some model for the stochastic process for an underlying security (e.g., in Black-Scholes this is a log-normality assumption). In the context of the model they price a contract for a customer and hedge their position. In addition to this formal process, banks typically add an ad hoc heuristic to manage the "unforeseen risk." This is the "stress testing" or "value at risk" calculations.In the paper we model uncertainty as Knightian Uncertainty (or more formally the preference of uncertainty aversion). Knightian Uncertainty (and The Choquet integral implied by such preferences) incorporates that risk (the outcome of a coin toss) and uncertainty (the unknown probability that the coin falls heads) enter ones preferences differently. The most well know manifestation of this behavior is the Allais Paradox. Specifically in our paper, we look a the dynamic portfolio problem under Knightian Uncertainty of a derivative market maker. The most striking result (so far) is that while the prices implied by these preferences are quite similar to standard models, the portfolios can be dramatically different. Under Knightian Uncertainty, the position taken in the underlying securities in the "hedge" portfolio can be much larger and even of a different sign. It is this fact that leads us to explore how model uncertainty is closely linked to liquidity. The deeper issues we hope to get at is how the market helps participants "learn" about the right model. In particular, we are exploring how market trade can act to reduce or increase the amount of uncertainty.