Explicit Solutions to Optimal Risk-Averse Trading of Defaultable Bonds Under Heterogeneous Beliefs

by Tim S.T. Leung of the Johns Hopkins University

October 22, 2010

Abstract: This paper studies the problem of pricing and trading of defaultable bonds among investors with heterogeneous risk preferences and beliefs. Based on the utility indifference pricing methodology, we first construct the risk-averse bid-ask spread, which naturally widens as risk aversion or trading volume increases. In addition, we analyze the defaultable bond buyer's optimal static trading position under different market settings, including (i) when the market pricing rule is linear, and (ii) when the counterparty - single or multiple sellers - may have different risk preferences and beliefs. In each of these cases, we provide an explicit formula for the optimal trading position and examine the combined effects of risk aversions and beliefs. In particular, we find that belief heterogeneity, rather than the difference in risk aversion, is crucial to trigger a trade.

JEL Classification: G12, G13, C68.

AMS Classification: 91B16, 93E20, 91B70.

Keywords: optimal trading, indifference pricing, heterogeneous beliefs, structural credit risk

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