Presence Of Default Risk Research Articles

Sovereign risk and Dutch disease

I study how, in the presence of default risk, the Dutch disease amplifies an inefficiency in the sectoral allocation of capital. In a sovereign default model with commodities and production of traded and non-traded goods, default incentives increase when more capital is allocated to non-traded production. Households do not internalize this, giving rise to an inefficiently large non-traded sector. Commodity windfalls amplify this inefficiency through the classic Dutch disease mechanism. I characterize state-contingent subsidies that implement the efficient allocation and compare them to a simpler subsidy rule that ameliorates the externality. Evidence from spreads, natural-resource rents, and sectoral investment data support the main findings of the model.

Fairness principles for insurance contracts in the presence of default risk

AbstractWe use the theory of cooperative games for the design of fair insurance contracts. An insurance contract needs to specify the premium to be paid and a possible participation in the benefit (or surplus) of the company. We suppose that a convex commonotonic premium functional is used to value the aggregated liability of the insurance company. It results from the analysis that when a contract is exposed to the default risk of the insurance company, ex‐ante equilibrium considerations require a certain participation in the benefit of the company to be specified in the contracts. The fair benefit participation of agents appears as an outcome of a game involving the residual risks induced by the default possibility and using fuzzy coalitions.

Financing decisions: The case of convertible bonds

Research studying firms' motivations to issue convertible bonds remains far from complete. This paper aims to provide further understanding of firms' motives behind issuing convertible bonds. We propose a theoretical model that explains issuers' choice between convertibles and equity when raising a required amount of capital by comparing the cash flow streams of both alternatives in order to maximize the firm's value for the current shareholders. We derive a closed form solution of our theoretical model both in absence and presence of default risk. Our model suggests that issuing convertible bonds is preferred to a direct stock issuance if the expected return of convertible bonds is lower than the expected return of common stocks. Empirical findings confirm our theoretical predictions.

Valuing firm’s financial flexibility under default risk and bankruptcy costs: a WACC based approach

PurposeThe purpose of this paper is to present a model to value leveraged firms in the presence of default risk and bankruptcy costs under a flexible firm’s debt structure.Design/methodology/approachThe authors assume that the total debt of the firm is a combination of two debt components. The first component is an active debt component which is assumed to be proportional to the firm’s value. The second one is a passive predetermined risk-free debt component. The combination of the two debt categories makes the firm’s capital structure more realistic and allows us to include flexibility into the firm’s debt structure management. The firm’s valuation is performed using the discounted cash flow technique based on the weighted average cost of capital (WACC) method.FindingsThe model can be used to define active debt management strategies that can induce the firm to deviate from its capital structure target in order to preserve debt capacity for future funding needs. The firm’s valuation is performed by using the WACC method and a closed form valuation formula is provided. Such a formula can be used to value costs and benefits of financial flexibility.Research limitations/implicationsThe proposed approach provides a good compromise between mathematical complexity and model capability of interpreting the various economic and financial aspects involved in the firm’s debt structure puzzle.Practical implicationsThis model offers a realistic approach to practical applications where real financing decisions are characterized by a simultaneous use of these two debt categories. By comparing costs and benefits deriving from using unused debt capacity for future funding needs, the model provides a quantitative support to investigate if financial flexibility can add value to firms.Originality/valueTo the authors knowledge, the approach the authors propose is the first attempt to build a valuation scheme that accounts for firm’s financial flexibility under default risky debt and bankruptcy costs. Including financial flexibility, this model fills an important gap in the literature on this topic.

Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement

Since the 2008 global financial crisis, the banking industry has been using valuation adjustments to account for default risk and funding costs. These adjustments are computed separately and added together by practitioners as if the valuation equations were linear. This assumption is too strong and does not allow to model market features such as different borrowing and lending rates and replacement default closeout. Hence we argue that the full valuation equations are nonlinear, and this paper is devoted to studying the nonlinear valuation equations introduced in Pallavicini et al (2011).We illustrate all the cash flows exchanged by the parties involved in a derivative contract, in presence of default risk, collateralisation with re-hypothecation and funding costs. Then we show how to obtain semi-linear PDEs or Forward Backward Stochastic Differential Equations (FBSDEs) from present-valuing said cash flows in an arbitrage-free setup, and we study the well-posedness of these PDEs and FBSDEs in a viscosity and classical sense.Moreover, from a financial perspective, we discuss cases where classical valuation adjustments (XVA) can be disentangled. We show how funding costs are offset by treasury valuation adjustments when one takes a whole-bank perspective in the valuation, while the same costs are not offset by such adjustments when taking a shareholder perspective. We show that although we use a risk-neutral valuation framework based on a locally risk-free bank account, our final valuation equations do not depend on the risk-free rate. Finally, we show how to consistently derive a netting set valuation from a portfolio level one.

Risk-Based Loan Pricing: Portfolio Optimization Approach with Marginal Risk Contribution

We consider a lender (bank) who determines the optimal loan price (interest rates) to offer to prospective borrowers under uncertain risk and borrower response. A borrower may or may not accept the loan at the price offered, and in the presence of default risk, both the principal loaned and the interest income become uncertain. We present a risk-based loan pricing optimization model, which explicitly takes into account marginal risk contribution, portfolio risk, and borrower's acceptance probability. Marginal risk assesses the amount a prospective loan would contribute to the bank's loan portfolio risk by capturing the interrelationship between a prospective loan and the existing loans in the portfolio and is evaluated with respect to the Value-at-Risk and Conditional-Value-at-Risk risk measures. We examine the properties and computational difficulties of the associated formulations. Then, we design a concavifiability reformulation method that transforms the nonlinear objective function of the loan pricing problems and permits to derive equivalent mixed-integer nonlinear reformulations with convex continuous relaxations. We discuss managerial implications of the proposed model and test the computational tractability of the proposed solution approach.

Chance-constrained optimization for pension fund portfolios in the presence of default risk

In this paper, we consider the portfolio optimization problem for a pension fund consisting of various government and corporate bonds. The aim of the problem is to maximize the fund’s cash position at the end of the time horizon, while allowing for the possibility of bond defaults. We model this problem as a stochastic discrete-time optimal control problem with a chance constraint that ensures all future outgoing commitments can be met with sufficiently high probability. We then introduce a corresponding deterministic formulation that is a conservative approximation of the original stochastic optimal control problem. This approximate problem can be solved using gradient-based optimization techniques. We conclude the paper with a simulation study.

Modelling Dynamic Redemption and Default Risk for LBO Evaluation: A Boundary Crossing Approach

We analyze corporate financial policies in leveraged buyouts (LBOs) in the presence of default risk. Our model captures the LBO-specific stepwise debt reduction, either with predetermined or cash-flow dependent (cash sweep) principal payments, and thus allows for dynamic redemption. These dynamics imply stochastic, discontinuous default boundaries. Our framework enables us to derive explicit-form solutions for the net present value (NPV) and the internal rate of return (IRR) of an LBO investment. We show that in scenarios with high entry debt and high redemption payments, the flexibility associated with dynamic redemptions creates value for investors, while fixed redemptions yield higher NPV and IRR values for moderate redemption due to lower debt yields. Moreover, we discuss optimal corporate financial policies implied by NPV or IRR maximization and find that the latter always results in increased leverage with higher default probability. The model of piecewise linear boundaries developed in this article is sufficiently flexible to be applied to a wide range of problems in corporate finance.

The Overhang Cost of Long and Short Term Debt in the Presence of Default Risk

This research studies the implications of short term debt for firm investment decisions on a sample of U.S. non-financial firms from 1985-2011. We argue that short term debt does not always help to reduce the overhang cost of leverage as is the case in Myers (1977) model. Our empirical results show that short term debt has a negative effect on subsequent investment, which is further amplified in the presence of high default risk. Moreover, a high proportion of short term debt also intensifies the negative impact of default risk on investment. This finding is consistent with our argument that short term debt overhang becomes more dominant than long term debt overhang when the firm faces high risk of bankruptcy. This finding provides another explanation for corporate failures during the 2007-2009 crisis in the U.S. It is the prolonged implications of the under-investment problem that delay recovery, and this problem is more severe for firms with short term debt because short term debt intensifies the negative impact of financial distress on firm investments. Finally, our results provide support for the model in Diamond and He (2011).

A stochastic maximum principle for backward control systems with random default time

This paper establishes a necessary and sufficient stochastic maximum principle for backward systems, where the state processes are governed by jump-diffusion backward stochastic differential equations with random default time. An application of the sufficient stochastic maximum principle to an optimal investment and capital injection problem in the presence of default risk is discussed.

Ex Ante Bargaining and Ex Post Enforcement in Trade Credit Supply: Theory and Evidence from China

If payment of goods is easily default, economic transaction may deeply suffer from the risk. This risky environment formed a mechanism that governs how economic transaction is realized, subsequently how trade credit is given. This paper distinguished ex ante bargaining and ex post enforcement, then modeled that bargaining power reduces trade credit ex ante, and ex post enforcement power and cash in hand of buyer can enhance both trade amount and trade credit in a presence of default risk. We modeled this relationship in order to organize findings from previous literature and from our original micro data on detailed transaction in China to consistently understand the mechanism governing trade credit. Then tested empirically a structure from the theoretical prediction with data. Results show that the ex post enforcement power of seller mainly determines size of trade credit and trade amount, cash in hand of the buyer can substitute with enforcement power; Bargaining power of seller is exercised to reduce trade credit and trade amount for avoiding default risk, but it simultaneously improves enforcement power as well. We found that ex post enforcement power consists of (ex ante) bargaining power on between two parties and intervention from the third party. However, its magnitude is far smaller than the direct impact to reduce trade credit and trade amount.

Sukuk spreads determinants and pricing model methodology

The investment concept of sukuk was created as an alternative to conventional bonds since interest-bearing instruments are prohibited under Islamic law. Sukuk (commonly referred to Islamic bonds) represent a proportional ownership of tangible assets or a pool of assets. However, the key to understanding these instruments as a financial innovation is to focus on their pricing and risk characteristics. The challenge for sukuk issuing entities becomes to provide an efficient pricing model, which is compliant with Islamic law principles. The aims of this paper are two-fold. Firstly, we explore empirically the determinants of sukuk yield spreads and we describe within a coherent empirical framework the economic implications of the links between sukuk yield spreads, stock market conditions and macroeconomic variables; Secondly, we provide a methodology for estimating the fair price of sukuk in the presence of default risk. This paper presents the first empirical study for the determinants of sukuk spreads using available data and it has several practical implications that are of value for investors, risk managers and the development of Islamic financial markets.

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Long-Term Contracts Under the Threat of Supplier Default

Contracting with suppliers prone to default is an increasingly common problem in some industries, particularly automotive manufacturing. We model this phenomenon as a two-period contracting game with two identical suppliers, a single buyer, deterministic demand, and uncertain production costs. The suppliers are distressed at the start of the game and do not have access to external sources of capital; hence, revenues from the buyer are crucial in determining whether default occurs. The production cost of each supplier is the sum of two stochastic components: a common term that is identical for both suppliers (representing raw materials costs, design specifications, etc.) and an idiosyncratic term that is unique to a given supplier (representing inherent firm capability). The buyer chooses a supplier and then decides on a single- or two-period contract. Comparing models with and without the possibility of default, we find that, without the possibility of supplier failure, the buyer always prefers short-term contracts over long-term contracts, whereas this preference is typically reversed in the presence of failure. Neither of these contracts coordinates the supply chain. We also consider dynamic contracts, in which the contract price is partially tied to some index representing the common component of production costs (e.g., commodity prices of raw materials such as steel or oil), allowing the buyer to shoulder some of the risk from cost uncertainty. We find that dynamic long-term contracts allow the buyer to coordinate the supply chain in the presence of default risk. We also demonstrate that our results continue to hold under a variety of alternative assumptions, including stochastic demand, allowing the buyer the option of subsidizing a bankrupt supplier via a contingent transfer payment or loan and allowing the buyer to unilaterally renegotiate contracts. We conclude that the possibility of supplier default offers a new reason to prefer long-term contracts over short-term contracts.

Technological Transfers, Limited Commitment and Growth

Evidence shows that there are substantial rich-to-poor international capital flows although not as abundant as differences in rates of return would suggest. These flows are procylcical: abundant in good times and scarce in bad times. Conventional growth models face certain difficulties in accounting for this pattern. In this paper, we propose a dynamic model of capital flows to developing countries which is qualitatively consistent with these empirical regularities. The model is based on three main premises: i) international lending contracts are imperfectly enforceable; ii) access to the international financial markets results in technological transfers to a developing country from the rest of the world; iii) some of the productivity gains associated with the access to external financing are perishable. We solve for transitional dynamics of the model economy with endogenously incomplete markets and compare the results with the solutions obtained from the perfect risk-sharing and autarkic environments. Our findings suggest that technological transfers may play a role of an important enforcement mechanism. In our framework, existence of substantial rich-to-poor capital flows is not inconsistent with the presence of default risk.

A Theoretical Inspection of the Market Price for Default Risk

While there are now a number of empirical studies on the subject, very little is known on the market price for default risk from a theoretical perspective. This paper is a first step in the direction of an equilibrium model for the pricing of defaultable securities in an incomplete market setup. We first provide an explicit characterization of the set of equivalent martingale measures consistent with no arbitrage in the presence of default risk, as well as a necessary and sufficient condition for a convenient separation between adjustments for market risk and default risk. That result allows us to spell out an unambiguous definition of the market price for default risk as the logarithm of the ratio of the risk-adjusted probability of default to the original probability of default. It also suggests the following question: how should the original probability of default be adjusted to account for agents' risk-aversion? We address this question in a dynamic continuous-time equilibrium setup, and obtain a defaultable version of a standard consumption-based capital asset pricing model. In particular, we confirm the intuition that the correlation between default risk and market risk is a key ingredient of the equilibrium price for default risk, and obtain a quantitative estimate of the magnitude of the effect. Our model is consistent with empirical findings in that it predicts that the term structure of credit spreads can be upward sloping with a non-zero intercept. The theory is illustrated by an application to the valuation of employee compensation packages, which may be regarded as peculiar, yet natural, examples of defaultable securities.

Insurer Contract Nonperformance in a Market with Adverse Selection

ABSTRACT In this study we examine the impact of insurer contract nonperformance upon Wilson's adverse selection equilibrium where consumers exhibit constant absolute risk aversion. When the market equilibrium retains its original form (i.e., pool or separation), premiums and coverage levels generally fall, although the change in coverage level for good risks is ambiguous when the equilibrium is separating. When the market equilibrium changes form, the change in premium and coverage levels is generally ambiguous, although one can determine that good risk premiums go down when the equilibrium shifts from pooling to separating and that bad risk premiums and coverage levels go down when the equilibrium shifts from separating to pooling. Interestingly, we find that although the introduction of insurer default risk makes good risks worse off, this is not necessarily true for bad risks. Bad risks can be better off because the decrease in the price differential between types can make pooling relatively attractive to good risks in the presence of default risk. INTRODUCTION In a world with complete insurance markets, a risk adverse individual, facing fair prices, will fully insure her wealth across all states of the world. When insurance markets are incomplete, this result need not hold, and an individual's behavior will depend, among other things, upon the correlation of insurable and non-insurable risks (Doherty and Schlesinger, 1983a, 1983b; Mayers and Smith, 1983). The breakdown in the standard analysis is perhaps most severe when the uninsurable risk is itself created by the purchase of insurance, that is when there is a risk of contract nonperformance by the insurer.' Doherty and Schlesinger (1990) show that a risk averter will not purchase full coverage at fair prices, that coverage purchased is not, in general, a monotonic function of the risk of insurer default, coverage purchased is not necessarily negatively related to the level of loading, individuals who are more risk averse (in the sense of Ross,1981) need not purchase insurance, and (when default is partial) there is no monotonic relationship between the level of coverage and the extent of recovery. The consequences of contract nonperformance upon standard insurance results are thus quite severe. It is also well recognized in the literature that the operation of insurance markets is significantly affected by adverse selection (e.g., Rothschild and Stiglitz, 1976, Wilson, 1977, and Spence, 1978). Wilson's (1977) model of adverse selection suggests that the equilibrium will either involve a pooling contract or a pair of separating contracts. If a pool results, it provides the coverage level optimal to the good risks at the pool price. Separation occurs when the better risks prefer a limited coverage contract (with the better risk coverage level sufficiently limited that higher risks prefer a full coverage contract at a price fair to the higher risks) at a price fair to the better risks to any contract at a price fair to the overall pool. Adverse selection insurance markets may be significantly impacted when background risk (Agarwal, 1995) or severity risk (Doherty and Schlesinger, 1995; Ligon and Thistle, 1996) are present. The primary difference between these studies and ours is the correlation between insurable losses and the additional risk introduced; we explore the impact of contract nonperformance upon a market with adverse selection. We analyze the impact of the introduction of a third (default) state of the world upon the nature of the Wilson equilibrium (pooling or separating), including its impact on the level of coverage, the premium paid, and societal welfare. We find, as did Doherty and Schlesinger (1990), that contract nonperformance often generates indeterminate results compared to standard models, even with strong restrictions on preferences. However, these ambiguities imply that nonperformance may have a surprising impact on insurance markets, including the possibility that some consumers may be better off in the presence of default risk. …

Corporate capital structure and pension-funding strategy

This article provides an integrated analysis of pension funding and corporate financing strategies in the presence of default risk. The article shows that when the marginal personal income tax rate is constant, the financing decision with respect to pension funding is influenced entirely by tax considerations. When the marginal personal income tax is progressive, the optimal financing of pension funding depends on the cyclical nature of the firm (as characterized by the sign of beta), the riskiness of pension assets, and ERISA regulations concerning the pension-benefit guaranty rate, the marginal pension insurance premium and the firm's legal responsibility for its unfunded pension obligations. It is shown that a necessary condition for partial pension funding is that the marginal insurance premium imposed by PBGC must be less than actuarially fair, and a necessary condition for pension funding to be financed by both debt and equity is that beta must be positive.

Inflation, Tax Rates, and Investment with Endogenous Financial Behavior

Since Modigliani and Miller's [24] famous article there has been an extensive theoretical debate over the role of corporate financial policy in determining real investment [3; 5; 8; 13; 22; 27; 28]. Auerbach [1] and Feldstein, Green, and Sheshinski [9] assume that an interior debt to total capital ratio exists at the firm level which minimizes the cost of funding investment. This position can be theoretically justified if one allows for the presence of default risk with incomplete financial markets [3], bankruptcy costs [5; 13], or corporate tax shield substitutes for debt [5]. Miller [22], on the other hand, downplays the importance of capital market imperfections and argues that while in an economy with personal and corporate taxes an interior corporate sector debt ratio will exist, at the firm level the choice of financial mix remains irrelevant. Despite the theoretical attention devoted to this topic, virtually no attempts have been made to establish an empirical model for the debt ratio.' Such a model could prove useful in explaining asset yields and real investment or, more ambitiously, in testing the alternative theories of financial policy determination mentioned above. The lack of effort in this area is surprising since many economists apparently believe that the debt ratio is quite important in determining real capital formation and resource allocation [7; 10; 11; 12; 20; 26]. Theory alone cannot be used to support this contention since, even if one does not accept the Modigliani-Miller reasoning and believes instead that financial policy is chosen optimally, the effect of a change in financial policy on the cost of funds will be approximately (to the first order) zero. This is a direct consequence of the envelope theorem which states that a marginal change in a choice variable leaves the objective function unchanged. Only an empirical study of discrete changes can determine the importance of financial policy for real investment. In a recent study [25] we estimated a reduced form model of the corporate sector debt ratio. The evidence in that paper supports the notion that increases in the nominal interest rate will encourage firms to increase their debt ratio due to the tax advantages of bond financing and that

Credit Rationing and Financial Disorder

We develop a model of lender behavior in the presence of default risk and moral hazard that determines default premiums and identifies the conditions under which borrowers are rationed. A hypothesis regarding a cognitive bias in the formation of expectations provides a dynamic component to our analysis and allows us to explain how an economy becomes vulnerable to a financial crisis and why vulnerability may increase over time. UNTIL RECENTLY, THE POSTWAR literature on financial disorder has consisted almost exclusively of the work of Hyman Minsky.1 Minsky's complex and richly detailed explanation of financial instability places special emphasis on the impact of an unsustainable economic expansion on the financial structure. He argues that rising interest rates and expectational factors that prevail during an investment boom will cause a shift toward finance in which debt-service payments rise relative to income receipts, cash and near-cash assets decline as a proportion of total assets, and asset prices reflect euphoric expectations. The shift toward speculative finance makes the system more vulnerable to crisis by reducing the capacity of the financial system to withstand a shock. Although we are in broad agreement with Minsky's description of the manifestations of financial vulnerability, we develop a much simpler explanation for why the system becomes more vulnerable over time. We emphasize creditor behavior in formulating, and acting on, shock probabilities rather than the business cycle as the mechanism through which the vulnerability of the system may increase. And we argue that an abrupt increase in the extent of credit rationing is the central feature of a financial crisis. Our analytic framework is constructed from ideas drawn from two disparate areas of research. From the literature on credit rationing, we develop a model of the microeconomics of lending decisions in the presence of default risk and moral hazard. This model enables us to relate default premiums to subjective expectations of default and the borrower's capital and to establish the conditions under which borrowers will be rationed. From the empirical literature on decisionmaking under uncertainty, we draw our hypotheses regarding the way in which lenders formulate expectations of default. Once the model is assembled, we