Event risk, contingent claims and the temporal resolution of uncertainty

• Published in: Mathematics and financial economics Vol. 8; no. 1; pp. 29 - 69
• Main Authors: Collin-Dufresne, Pierre, Hugonnier, Julien
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2014; Springer Nature B.V
• Subjects: Applications of Mathematics; Arbitrage; Costs; Credit risk; Economic theory; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Expected utility; Finance; Hedging; Insurance; Macroeconomics/Monetary Economics//Financial Economics; Management; Mathematical analysis; Mathematics; Mathematics and Statistics; Mortgage backed securities; Prepayments; Prices; Quantitative Finance; Risk; Statistics for Business; Studies; Uncertainty; Utility functions; 60H30; Utility based valuation; G11; G10; Certainty equivalent; G13; 90A09; Credit risk; Temporal resolution of uncertainty; Event risk; 93E20; 90A10; Incomplete markets; D81
• ISSN: 1862-9679; 1862-9660
• DOI: 10.1007/s11579-013-0107-8

We study the pricing and hedging of contingent claims that are subject to Event Risk which we define as rare and unpredictable events whose occurrence may be correlated to, but cannot be hedged perfectly with standard marketed instruments. The super-replication costs of such event sensitive contingent claims (ESCC), in general, provide little guidance for the pricing of these claims. Instead, we study utility based prices under two scenarios of resolution of uncertainty for event risk: when the event is continuously monitored, or when it is revealed only at the payment date. In both cases, we transform the incomplete market optimal portfolio choice problem of an agent endowed with an ESCC into a complete market problem with a state and possibly path-dependent utility function. For negative exponential utility, we obtain an explicit representation of the utility based prices under both information resolution scenarios and this in turn leads us to a simple characterization of the early resolution premium. For constant relative risk aversion utility functions we propose a simple numerical scheme and study the impact of size of the position, wealth and expected return on these prices.