A Debt Management Problem with Bankruptcy Risk and Currency Devaluation

A debt repayment strategy is modeled as an interaction between a sovereign state and a pool of risk-neutral investors. The problem of optimal debt management introduced expands on the models derived in [2, 3, 1] and [4]. At each time, the government decides which fraction of the gross domestic product must be used to repay the debt, and how much to devalue its currency. The total yearly income (GDP) of the borrower is governed by a stochastic process. When the debt-to-income ratio x(t) reaches a threshold x ∗ , bankruptcy instantly occurs. Moreover, we assume that the borrower may go bankrupt at a random time before the debt reaches x ∗ . We explore the derivation and analysis of the model through the lens of optimal control in infinite time horizon with exponential discount. The resulting stochastic control system depends not only on the present time t but on all future times. For a given bankruptcy threshold x ∗ , existence of an equilibrium solution is obtained by a topological argument. Our results show that the optimal control strategy does not use currency devaluation for debt values below a threshold

A Stochastic Model of Optimal Debt Management and Bankruptcy

A problem of optimal debt management is modeled as a noncooperative interaction between a bor- rower and a pool of lenders, in an infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio x(t) reaches a given size x^* , bankruptcy instantly occurs. The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of their investment. For a given bankruptcy threshold x^ 17 , existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting. The paper also analyzes how the expected total cost to the borrower changes, depending on different values of x^ 17

A Stochastic Model of Optimal Debt Management and Bankruptcy

A problem of optimal debt management is modeled as a noncooperative interaction between a bor- rower and a pool of lenders, in an infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio x(t) reaches a given size x^* , bankruptcy instantly occurs. The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of their investment. For a given bankruptcy threshold x^∗ , existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting. The paper also analyzes how the expected total cost to the borrower changes, depending on different values of x^∗

A model of debt with bankruptcy risk and currency devaluation

The paper studies a system of Hamilton-Jacobi equations, arising from a stochastic optimal debt management problem in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of risk-neutral lenders. In this model, the borrower is a sovereign state that can decide how much to devaluate its currency and which fraction of its income should be used to repay the debt. Moreover, the borrower has the possibility of going bankrupt at a random time and must declare bankruptcy if the debt reaches a threshold x*. When bankruptcy occurs, the lenders only recover a fraction of their capital. To offset the possible loss of part of their investment, the lenders buy bonds at a discounted price which is not given a priori. This leads to a nonstandard optimal control problem. We establish an existence result of solutions to this system and in turn recover optimal feedback payment strategy $u*(x)$ and currency devaluation $v*(x)$. In addition, the behavior of $(u*,v*)$ near $0$ and x* is studied.Comment: 23 page

Credit Risk in a Network Economy

We develop a structural model of credit risk in a network economy. In particular, we are able to account for complex counterparty relationships,where one company may be indirectly affected by the credit risk of another company in the network. In this re-spect,we generalize Jarrow and Yu (2001)and Collin-Dufresne,Goldstein and Hugonnier (2003),but do so in the rich context of a structural form model. We provide closed form formulae for the price of risky debt and equity,which depend upon the lending/borrowing relationships in the economy. Our model applies to completely general lender/borrower relationships,including looping relationships. Our formulae can apply to cases where not only ?nancial ?ows but also operations are dependent across ?rms. In order to achieve these results,we use queueing theory. This paper thus represents one of the ?rst applications of queueing theory to ?nance.Credit Risk; Capital Structure; Queueing Networks

Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach

This paper analyzes corporate bond valuation of a straight bond, and the convertibility feature, when interest rates are stochastic and the firm value is determined by the interaction of a series of stochastic variables. The sensitivity of the corporate dValuation, options, bond, equity

LIFETIME LEVERAGE CHOICE FOR PROPRIETARY FARMERS IN A DYNAMIC STOCHASTIC ENVIRONMENT

This article reviews various models that may be used to explain optimal leverage choice for the proprietary farmer in a stochastic dynamic environment and develops a new model that highlights the risk of failure rather than the usual concept of risk as the variability of wealth. The model suggests that in addition to the usual factors, farm financial leverage is affected by age, wealth, and the opportunity cost of farming.Farm Management,

Empirical Implementation of a 2-Factor Structural Model for Loss-Given-Default

In this study we develop a theoretical model for ultimate loss-given default in the Merton (1974) structural credit risk model framework, deriving compound option formulae to model differential seniority of instruments, and incorporating an optimal foreclosure threshold. We consider an extension that allows for an independent recovery rate process, representing undiversifiable recovery risk, having a stochastic drift. The comparative statics of this model are analyzed and compared and in the empirical exercise, we calibrate the models to observed LGDs on bonds and loans having both trading prices at default and at resolution of default, utilizing an extensive sample of losses on defaulted firms (Moody’s Ultimate Recovery Database™), 800 defaults in the period 1987-2008 that are largely representative of the U.S. large corporate loss experience, for which we have the complete capital structures and can track the recoveries on all instruments from the time of default to the time of resolution. We find that parameter estimates vary significantly across recovery segments, that the estimated volatilities of recovery rates and of their drifts are increasing in seniority (bank loans versus bonds). We also find that the component of total recovery volatility attributable to the LGD-side (as opposed to the PD-side) systematic factor is greater for higher ranked instruments and that more senior instruments have lower default risk, higher recovery rate return and volatility, as well as greater correlation between PD and LGD. Analyzing the implications of our model for the quantification of downturn LGD, we find the ratio of the later to ELGD (the “LGD markup”) to be declining in expected LGD, but uniformly higher for lower ranked instruments or for higher PD-LGD correlation. Finally, we validate the model in an out-of-sample bootstrap exercise, comparing it to a high-dimensional regression model and to a non-parametric benchmark based upon the same data, where we find our model to compare favorably. We conclude that our model is worthy of consideration to risk managers, as well as supervisors concerned with advanced IRB under the Basel II capital accord.LGD; credit risk; default; structural model

The impact of alternative bank monitoring policies on corporate investment and financing decisions

Much of the benefit from bank loans is generated by the specialized monitoring and information gathering role provided by financial institutions, including their role in facilitating the reorganization of firms experiencing financial distress. Despite these numerous benefits, it is somewhat surprising that aggregate trends suggest that the corporate sector has decreased its reliance on bank loans. We model the relationship between alternative bank monitoring policies and corporate investment and financing decisions. Rather than taking the monitoring characteristics of the bank as fixed, we examine the effects of changes in bank monitoring policies. We provide insights into how the banking sector evolves through time.Banks and banking ; Corporations - Finance