The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate, in the context of bounded financial positions, the class of surplus-invariant acceptance sets. These are characterized by the fact that acceptability does not depend on the positive part, or surplus, of a capital position. We argue that surplus invariance is a reasonable requirement from a regulatory perspective, because it focuses on the interests of liability holders of a financial institution. We provide a dual characterization of surplus-invariant, convex acceptance sets, and show that the combination of surplus invariance and coherence leads to a narrow range of capital adequacy tests, essentially limited to scenario-based tests. Finally, we emphasize the advantages of dealing with surplus-invariant acceptance sets as the primary object rather than directly with risk measures, such as loss-based and excess-invariant risk measures, which have been recently studied by Cont, Deguest & He and by Staum, respectively.
This paper shows how to design incentive-based capital requirements that would prevent the bank from manufacturing tail risk. In the model, the senior bank manager may have incentives to engage in tail risk. Bank shareholders can prevent the manager from taking on tail risk via the optimal incentive compensation contract. To induce shareholders to implement this contract, capital requirements should internalize its costs. Moreover, bank shareholders must be given the incentives to comply with minimum capital requirements by raising new equity and expanding bank assets. Making bank shareholders bear the costs of compliance with capital regulation turns out to be crucial for motivating them to care about risk-management quality in their bank.
In this paper, we first show that for classical rational investors with correct beliefs and constant absolute or constant relative risk aversion, the utility gains from structured products over and above a portfolio consisting of the risk-free asset and the market portfolio are typically much smaller than their fees. This result holds irrespectively of whether the investors can continuously trade the risk-free asset and the market portfolio at no costs or whether they can just buy the assets and hold them to maturity of the structured product. However, when considering behavioural utility functions, such as prospect theory, or investors with incorrect beliefs (arising from probability weighting or probability misestimation), the utility gain can be sizable.
We generalize the Kou (2002) double exponential jump-diusion model in two directions. First, we independently displace the two tails of the jump size distribution away from the origin. Second, we allow for each of the displaced tails to follow a gamma distribution with an integer-valued shape parameter. Both extensions introduce additional exibility in the tails of the corresponding return distribution. Our model is supported by an equilibrium economy and we obtain closed-form solutions for European plain vanilla options. Our valuation function is computationally fast to evaluate and robust across the full parameter space. We estimate the physical model parameters through maximum likelihood and for a diverse sample of equities, commodities and exchange rates. For all assets under consideration, the original Kou (2002) model can be rejected in favor of our newly introduced asymmetrically displaced double gamma dynamics.
