Search Results
Working Paper
Solving stochastic money-in-the-utility-function models
This paper analyzes the necessary and sufficient conditions for solving money-in-the-utility-function models when contemporaneous asset returns are uncertain. A unique solution to such models is shown to exist under certain measurability conditions. Stochastic Euler equations, whose existence is normally assumed in these models, are then formally derived. The regularity conditions are weak, and economically innocuous. The results apply to the broad range of discrete-time monetary and financial models that are special cases of the model used in this paper. The method is also applicable to ...
Working Paper
Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors
We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in Kamdem (2005) and are present also in at least thirty other papers referencing it, including the recent survey by Nadarajah, Zhang, and Chan (2014) on estimation methods for expected shortfall. In particular, we show that the correction we provide in the popular multivariate Student t setting eliminates understatement of expected shortfall by a factor varying from at least 4 to more than 100 across ...
Working Paper
Linear cointegration of nonlinear time series with an application to interest rate dynamics
We derive a definition of linear cointegration for nonlinear stochastic processes using a martingale representation theorem. The result shows that stationary linear cointegrations can exhibit nonlinear dynamics, in contrast with the normal assumption of linearity. We propose a sequential nonparametric method to test first for cointegration and second for nonlinear dynamics in the cointegrated system. We apply this method to weekly US interest rates constructed using a multirate filter rather than averaging. The Treasury Bill, Commercial Paper and Federal Funds rates are cointegrated, with two ...
Working Paper
Optimal Bidder Selection in Clearing House Default Auctions
Central counterparties' ability to hold successful default auctions is critically important to financial stability. However, due to the unique features of these auctions, standard auction theory results do not apply. We present a model of CCP default auctions that incorporates both the vital, but non-standard, objective of minimizing the likelihood it suffers reputationally damaging losses and the potential for information leakage to affect CCP members' private portfolio valuations. This gives insight into the key question of how CCPs should select auction participants. In particular, we ...
Working Paper
Central Clearing and Systemic Liquidity Risk
By stepping between bilateral counterparties, a central counterparty (CCP) transforms credit exposure. CCPs generally improve financial stability. Nevertheless, large CCPs are by nature concentrated and interconnected with major global banks. Moreover, although they mitigate credit risk, CCPs create liquidity risks, because they rely on participants to provide cash. Such requirements increase with both market volatility and default; consequently, CCP liquidity needs are inherently procyclical. This procyclicality makes it more challenging to assess CCP resilience in the rare event that one or ...
Working Paper
Monetary aggregation theory and statistical index numbers
This paper is the first of two from the Monetary Services Indices (MSI) Project at the Federal Reserve Bank of St. Louis. The second paper, Working Paper 96-008B, summarizes the methodology, construction and data sources for the an extensive new database of monetary services indices, often referred to as Divisia monetary aggregates, for the United States. This paper surveys the microeconomic theory of the aggregation of monetary assets, bringing together results that are not otherwise readily available in a single source. In addition to indices of the flow of monetary services, the Project's ...
Working Paper
Revisiting Risky Money
Risk was first incorporated into monetary aggregation over thirty-five years ago,using a stochastic version of the workhorse money-in-the-utility-function model.Nevertheless, the mathematical foundations of this stochastic model remain shaky.To firm the foundations, this paper employs a slightly richer probability conceptthan standard Borel-measurability, which enables me to prove the existence of awell-behaved solution and to derive stochastic Euler equations. This measurabilityapproach is long-established albeit less common in economics, possibly because the derivation of stochastic Euler ...