Since the initiation of the New Basel Capital Accord (Basel II) in 1999, when operational risk was introduced to the regulatory landscape, the attention to this risk type has risen substantially. The Basel Committee on Banking Supervision (Basel Committee, 2006) defines operational risk as “risk of loss resulting from inadequate or failed internal processes, people and systems or from external events.” The fact that events like bookkeeping errors and terrorist attacks are covered by this characterization illustrates the broad range of risks relative to credit or market risk. Taking this heterogeneity of loss events into account, the Basel Committee categorizes losses into seven event types and eight business lines. Banks are supposed to calculate risk measures for each of these 7 × 8 = 56 combinations, such as “Internal Fraud” in “Trading and Sales” or “Damage to Physical Assets” in “Commercial Banking”.
The risk measure specified by the Basel Committee is the Unexpected Loss at a confidence level of 99.9%. Generally speaking, this refers to the 99.9% quantile of the loss distribution (possibly reduced by the Expected Loss, that is, the mean of the distribution), commonly known as the 99.9% Value–at–Risk (VaR). It measures the maximum loss that will not be exceeded with the specified confidence level and is a widely used risk measure since the 1990s. The total required risk capital under the Advanced Measurement Approaches (AMA) is obtained by summing over all 56 event–type/business–line VaRs, a strategy implicitly expecting the joint occurrence of all loss types involved or, in other words, assuming perfect positive correlation between all loss processes. To allow for non–perfect correlations, the Basel Committee permits a bank “...to use internally determined correlations [...] provided it can demonstrate to the satisfaction of the national supervisor that its systems for determining correlations are sound, implemented with integrity, and take into account the uncertainty surrounding any such correlation estimates (particularly in periods of stress).” (Basel Committee, 2006, p. 148). Dropping the highly unrealistic assumption of perfect dependence (i.e., summing the Unexpected Losses of all cells) and relying on realistic correlation estimates should decrease the calculated risk capital. Therefore, banks should have a strong interest in developing and establishing adequate assessment approaches. This expected decrease in estimated risk capital due to less than perfect correlations of the loss processes is the focus here. Specifically, we investigate whether a general rule can be established about risk–capital requirements and less than perfect correlations. Second, we analyze how the model specification affects such a rule.
A key finding from this study was that, in patients with bipolar disorder, obesity is a stronger influence on insulin resistance than is bipolar disorder itself. In other words, insulin resistance in these patients does not appear to be more severe after accounting for their obesity. This conclusion, however, should be tempered by the observation that these obese women with bipolar disorder had significantly more abdominal fat and were slightly more hypertensive than BMI-matched controls, allowing for the possibility that bipolar disorder may indeed be associated with altered metabolic profile.
Using tools to assess both energy expenditure and energy intake, this project indicates that, once these euthymic patients with bipolar disorder become obese, their energy imbalance is likely similar to non-patient controls. However, similar levels of insulin resistance in patients compared to BMI matched controls in this cross sectional study do not discount the possibility that bipolar disorder does not somehow predispose these patients towards weight gain and obesity. Comparing normal weight subjects perhaps provides some important clues in this regard.
In the standard competing auctions model, many sellers compete to sell a single good by offering auctions to buyers. In the first stage of the game sellers post auctions. In the second stage buyers choose one particular auction, place their bid and the good goes to the higest bidder paying the second highest bid. Both the resources available to buyers and the quantity of the good at each auction are exogenously given. In this paper we endogenize both. We first allow buyers to choose the amount of money they bring to an auction, trading off the cost of holding money with the expected surplus from participating in an auction. Second, we allow sellers to choose how much of their production good they want to put on auction, trading off the production cost of the advertised quantity against the expected number of potential buyers. Finally, we allow sellers to charge each buyer with a fee for participating to their auction. This fee, which can be positive or negative, trades off the additional revenue (or cost) from the fee with the number of buyers taking part into their auction. We use our model to study how monetary policy affects the equilibrium allocation of a competing auctions economy and derive recommendations for optimal monetary policy in this environment.
To conduct this exercise we embed the competing auctions framework into the Lagos and Wright (2005) model of monetary exchange with two&sided divisibility. This model is in the tradition of Kiyotaki and Wrightns (1991, 1993) environment in which a role for fiat money is determined endogenously from the frictions of the trading environment, i.e. money is essential for trade (Kocherlakota, 1998; Wallace, 2001). In terms of equilibrium we build on the limit equilibrium concept developed by Peters and Severinov (1997), and extends it to the context of a monetary economy. We build a competing auction environment, start with a finite number of buyers and sellers, characterize the posted contracts, payoffs and money holdings, and then take the limit of these expressions in the infinite game. This limit equilibrium enables to exploit the convergence properties of a competitive matching economy, especially that the deviation by one seller will not affect the payoff buyers can get by visiting him. This corresponds to the market utility property (Peters, 2000) by which the buyerns utility in competitive matching economies is determined by the market and is taken as given by sellers. Finally we assume rational expectations so that sellers believe that their payoff functions satisfy the market utility property.
