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Mathematics and Financial Economics
Erschienen in: Mathematics and Financial Economics 1/2014

01.01.2014

Event risk, contingent claims and the temporal resolution of uncertainty

verfasst von: Pierre Collin-Dufresne, Julien Hugonnier

Erschienen in: Mathematics and Financial Economics | Ausgabe 1/2014

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Abstract

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.
Vorheriger Artikel Asymptotic power utility-based pricing and hedging
Nächster Artikel Nonmyopic optimal portfolios in viable markets

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Fußnoten
1
This is reminiscent of [6] who show that, in the presence of transaction costs, the minimal amount necessary to dominate the pay-off of a call option is the value of the underlying itself. Other papers studying almost sure hedging in incomplete markets, albeit with different forms of incompleteness, include [4, 38, 40] and [32].
 
2
The utility based buying price is defined similarly. Utility based pricing has been used in the literature on transaction costs by [8, 17, 23] and [9] among others; and on incomplete/constrained markets by [10, 21, 37] and [43]. See [22] for a survey.
 
3
Vulnerable options have been studied by [31] and [26]. However, in these papers the default event is modeled as the first passage time of the writer’s assets value (assumed to be a diffusion) at some boundary. Defaultable contingent claims thus become default free knock-out barrier options and since every Brownian stopping time is predictable, default of the writer is a predictable process, i.e. does not come as a surprise.
 
4
This price was also central to the analysis of [28] who obtain it as a result of an APT-like diversification argument.
 
5
Duffie and Huang [14] and Collin-Dufresne and Hugonnier [1] investigate pricing in the presence of bilateral counterparty credit risk.
 
6
Since, for logarithmic agents, the late resolution prices provide reasonable approximation of the early resolution utility based prices we present only graphs for late resolution prices. These are also simpler to compute.
 
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Metadaten
Titel
Event risk, contingent claims and the temporal resolution of uncertainty
verfasst von
Pierre Collin-Dufresne
Julien Hugonnier
Publikationsdatum
01.01.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Mathematics and Financial Economics / Ausgabe 1/2014
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-013-0107-8