Essays on Financial Intermediation in a Dynamic Setting PDF Download

Author: Ronaldo Carpio
Publisher:
ISBN: 9781267967695
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Languages : en
Pages :

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Book Description
The financial crisis of 2007-2009 demonstrated that financial intermediaries play a critical, if not yet well-understood, role in the economy. However, our theoretical understanding of what intermediaries do is currently incomplete. The papers in this dissertation seek to improve our theoretical knowledge by introducing models that explicitly capture the activities of a financial intermediary in a dynamic setting. The first paper tackles two fundamental theoretical questions about banks. The first question seems simple but is still unresolved: how should we model a banking firm? We develop a dynamic model of a banking firm based on the notion of banking as the inventory management of cash. A bank that makes loans and takes deposits is a dynamic, stochastic inventory management problem. The second question is an old issue that has again become relevant in the wake of the financial crisis: why do banks engage in maturity mismatch, the process of "borrowing short and lending long". We show how profit-maximizing behavior in an inventory management model can result in maturity mismatch. We present the dynamic model, solve it numerically, and use simulation to predict the bank's behavior in different environments. A limitation of this model is that interest rates and the supply of deposits are taken as exogenous. The second paper endogenizes these quantities for a simple model of an inventory-theoretic financial firm, a Ponzi scheme. As with an ordinary monopolistic firm, the "bank" faces a demand schedule and chooses the price it offers; here, the price is the interest rate, and demand is generated by an OLG population that chooses to borrow or lend using standard models of savings and portfolio choice. In this way we seek to endogenize interest rates, quantities of credit, and financial risk. An issue that arises in dynamic optimization models such as the ones above is that analytic solutions are rare and we must resort to numerical computation, Standard methods of solving dynamic programming problems are computationally expensive; the third paper presents two promising approaches that can potentially provide dramatic speedups in speed. The first method is based on pre-computing the inverse gradient and Lagrange multipliers of a known utility function; subsequent calls can simply look up the pre-computed maximizers, instead of having to call a numeric root-finding routine each time. The second method exploits the duality between concave functions and their Legendre-Fenchel transforms. The Bellman operator in primal space is isomorphic to a tractable scaling and addition operation in dual space. In special cases, we can obtain the value function of the solution in closed form; even when we cannot obtain a closed form solution, we can gain theoretical insight into the properties of the solution.