DEFAULT AND SYSTEMIC RISK IN EQUILIBRIUM

We develop a finite horizon continuous time market model, where risk‐averse investors maximize utility from terminal wealth by dynamically investing in a risk‐free money market account, a stock, and a defaultable bond, whose prices are determined via equilibrium. We analyze the endogenous interaction arising between the stock and the defaultable bond via the interplay between equilibrium behavior of investors, risk preferences and cyclicality properties of the default intensity. We find that the equilibrium price of the stock experiences a jump at default, despite that the default event has no causal impact on the underlying economic fundamentals. We characterize the direction of the jump in terms of a relation between investor preferences and the cyclicality properties of the default intensity. We conduct a similar analysis for the market price of risk and for the investor wealth process, and determine how heterogeneity of preferences affects the exposure to default carried by different investors.     

Firm capital dynamics in centrally cleared markets

We develop a tractable continuous time model of multifirm capital dynamics in a centrally cleared market. Our framework jointly models the strategic interactions between business operations of firms and their trading activities. We show that the endogenous allocation of firm capital between trading and operations can be recovered as the unique fixed point of a system of quadratic equations. Our model predicts that (a) there exists a convex relationship between equilibrium margins and firm capital in the cross‐section, (b) market collateral demand is positively correlated with size concentration, and (c) size concentration is expected to increase over time. Using proprietary data on bilateral credit default swap exposures, we provide evidence that the convexity prediction is both economically and statistically significant and validate our model assumption that firms hedge excess risks.     

Equilibrium with Default and Endogenous Collateral

We study a two‐period general equilibrium model with incomplete asset markets and default. We make collateral endogenous by allowing each seller of assets to fix the level of collateral. Sellers are required to provide collateral whose first‐period value, per unit of asset, exceeds the asset price by an arbitrarily small amount. Moreover, borrowers are also required to be fully covered by the purchase, in the first period, of state‐by‐state default insurance. These insurance contracts are offered by lenders. The insurance cost or revenue is a linear charge and plays the role of a spread penalizing borrowers who will incur in default and benefiting lenders who will suffer default. Under these assumptions, equilibrium always exists.     

APPROXIMATE COMPLETENESS WITH MULTIPLE MARTINGALE MEASURES

We construct a financial market with countably many securities for which there are two equivalent martingale measures under which the market is approximately complete. Thus, approximate completeness does not in general guarantee unique consistent prices for nonmarketed claims. the construction also produces an economy with two agents and infinitely many traded goods which is in equilibrium but has no equilibrium when a new good (recognized by all as redundant) is tentatively traded.     

Sovereign debt as a contingent claim: a quantitative approach

We construct a dynamic equilibrium model with contingent service and adverse selection to quantitatively study sovereign debt. In the model, benefits of defaulting are tempered by higher future interest rates. For a wide set of parameters, the only equilibrium is one in which the sovereign defaults in all states; additional output losses, however, sustain equilibria that resemble the data. We show that due to the adverse selection problem, some countries choose to delay default to reduce loss of reputation. Moreover, although equilibria with no default imply greater welfare levels, they are not sustainable in highly indebted and volatile countries.     

WELL‐BEHAVED PRODUCTION ECONOMIES

We show that production economies are tâtonnement stable if consumers satisfy the weak axiom of revealed preference. To ensure that producer supply decisions are well defined, we restrict prices in the tâtonnement so that positive profits cannot occur but do allow supply decisions to be multi‐valued. The model therefore permits linear activities and hence the technologies that admit capital theory paradoxes. The result thus shows that if the consumer side of the economy is well behaved then capital theory paradoxes are irrelevant for stability. Other features of the Walrasian general‐equilibrium model that have aroused suspicion (e.g. that a price below its equilibrium value may have negative excess demand and thus temporarily move even lower in a tâtonnement) may be a sign of trouble but also have nothing to do with capital theory paradoxes. We show that these phenomena arise even when there is no choice of technique and there is an aggregate production function.     

One‐Way Compatibility,Two‐Way Compatibility and Entry in Network Industries

We study the strategic choice of compatibility between two initially incompatible network goods in a two‐stage game played by an incumbent and an entrant firm. Compatibility may be achieved by means of a converter. We derive a number of results under different assumptions about the nature of the converter (one‐way vs two‐way), the existence of property rights and the possibility of side payments. With incompatibility, entry deterrence occurs for sufficiently strong network effects. In the case of a two‐way converter, which can only be supplied by the incumbent, incompatibility will result in equilibrium unless side payments are allowed and the network externalities are sufficiently low. When both firms can build a one‐way converter and there are no property rights on the necessary technical specifications, the unique equilibrium involves full compatibility. Finally, when each firm has property rights on its technical specifications, full incompatibility is observed at the equilibrium with no side payments; when these are allowed the entrant sells access to its network to the incumbent which refuses to do the same and asymmetric one‐way compatibility results in equilibrium.     

DYNAMIC DEFAULTABLE TERM STRUCTURE MODELING BEYOND THE INTENSITY PARADIGM

The two main approaches in credit risk are the structural approach pioneered by Merton and the reduced‐form framework proposed by Jarrow and Turnbull and by Artzner and Delbaen. The goal of this paper is to provide a unified view on both approaches. This is achieved by studying reduced‐form approaches under weak assumptions. In particular, we do not assume the global existence of a default intensity and allow default at fixed or predictable times, such as coupon payment dates, with positive probability. In this generalized framework, we study dynamic term structures prone to default risk following the forward‐rate approach proposed by Heath, Jarrow, and Morton. It turns out that previously considered models lead to arbitrage possibilities when default can happen at a predictable time. A suitable generalization of the forward‐rate approach contains an additional stochastic integral with atoms at predictable times and necessary and sufficient conditions for an appropriate no‐arbitrage condition are given. For efficient implementations, we develop a new class of affine models that do not satisfy the standard assumption of stochastic continuity. The chosen approach is intimately related to the theory of enlargement of filtrations, for which we provide an example by means of filtering theory where the Azéma supermartingale contains upward and downward jumps, both at predictable and totally inaccessible stopping times.     

DEFAULT RISK AND DIVERSIFICATION: THEORY AND EMPIRICAL IMPLICATIONS

Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity's diffusion state variables as the only default risk premium. We show that this interpretation implies a restriction on the form of possible default risk premia, which can be justified through exact and approximate notions of "diversifiable default risk." The equivalence between the empirical and martingale default intensities that follows from diversifiable default risk greatly facilitates the pricing and management of credit risk. We emphasize that this is not an equivalence in distribution, and illustrate its importance using credit spread dynamics estimated in Duffee (1999) . We also argue that the assumption of diversifiability is implicitly used in certain existing models of mortgage-backed securities.     

Bilateralism, multilateralism, and the quest for global free trade

We develop an equilibrium theory of trade agreements in which both the degree and the nature (bilateral or multilateral) of trade liberalization are endogenously determined. To determine whether and how bilateralism matters, we also analyze a scenario where countries pursue trade liberalization on only a multilateral basis. We find that when countries have asymmetric endowments or when governments value producer interests more than tariff revenue and consumer surplus, there exist circumstances where global free trade is a stable equilibrium only if countries are free to pursue bilateral trade agreements. By contrast, under symmetry, both bilateralism and multilateralism yield global free trade.     

Viability and Equilibrium in Securities Markets with Frictions

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive lineaar pricing rule on the entirespace of contingent claims—an underlying frictionless linear pricing rule—that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches—a generalization of opportunities of arbitrage. When a market for a nonmarketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule—the supremum of the underlying frictionless linear pricing rules—for which the original equilibrium does not collapse when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules.     

Sovereign defaults: Information, investment and credit

Why would a sovereign government, immune from bankruptcy procedures and with few assets that could be seized in the event of a default, ever repay foreign creditors? And, correspondingly, why do foreign creditors lend to sovereigns? This paper finds general conditions under which, even in the absence of sanctions, lending to sovereigns can emerge in a single shot game. Furthermore, it shows that positive borrowing can be sustained both in pooling and separating equilibria. In this way, it makes clear that neither sanctions nor reputation considerations, the two classical explanations, are necessary to enforce repayment. Information revelation is the crucial mechanism for these results. The repayment/default decision is interpreted as a signal used by the government to communicate information to domestic and foreign agents about the fundamentals of the economy. Governments repay to affect agents' expectations about them. A default, through its effect on expectations about fundamentals, can generate a decline in foreign and domestic investment and a credit crunch in domestic credit markets. Governments repay to avoid these costs, but may default (in equilibrium) when hit by a negative shock.     

Defaultable debt, interest rates and the current account

World capital markets have experienced large scale sovereign defaults on a number of occasions. In this paper we develop a quantitative model of debt and default in a small open economy. We use this model to match four empirical regularities regarding emerging markets: defaults occur in equilibrium, interest rates are countercyclical, net exports are countercyclical, and interest rates and the current account are positively correlated. We highlight the role of the stochastic trend in emerging markets, in an otherwise standard model with endogenous default, to match these facts.     

The effect of default options on choice—Evidence from online product configurators

Many firms use product configurators to enable customers to specify their desired products online. In such systems, defaults are pre-specified for levels of product features by the manufacturer or dealer. For example, when configuring a racing bike online, a default is predefined (e.g., the Shimano Ultegra model) for all required features (e.g., the gearshift levers). Such defaults, which may even adapt to previous choices, ensure that a functional and fully defined product emerges at the end of the configuration process. However, when designing sales systems, companies often fail to realize that these defaults also affect customer decision-making. We demonstrate the effect by a study that makes use of a fully simulated racing bike configurator. We find the following results: Moving the default of one feature (e.g. wheels) from the lowest to the highest level results in an increase in sales. In addition, the feature level defined as the default also acts as a reference point by increasing the sales of levels near to it. In order to maximize sales, the default should be set at the level of a feature that is between the medium and the highest price level. To conclude we discuss how manufacturers and dealers subtly yet powerfully influence the decision-making process with their sales systems.     

Banking relationship and default priority in consumer credit: Evidence from Thai microdata

Banks play an important role in consumer credit, and when borrowers face a decision on whether to default on mortgage or non-mortgage loans first, banking relationship may matter. Our study provides first evidence into the interplay between banking relationship and consumer default priority via credit bureau data of 1 million individuals in Thailand. We find that same-bank borrowers are less likely to default on mortgage loans first, and borrowers with longer banking relationship and lower switching cost are more likely to default on mortgage loans first (which is welfare-improving). Our results suggest that banking relationship can lead to better outcomes for defaulting borrowers even when switching cost is high.     

OPTIMAL INVESTMENT IN CREDIT DERIVATIVES PORTFOLIO UNDER CONTAGION RISK

We consider the optimal portfolio problem of a power investor who wishes to allocate her wealth between several credit default swaps (CDSs) and a money market account. We model contagion risk among the reference entities in the portfolio using a reduced‐form Markovian model with interacting default intensities. Using the dynamic programming principle, we establish a lattice dependence structure between the Hamilton‐Jacobi‐Bellman equations associated with the default states of the portfolio. We show existence and uniqueness of a classical solution to each equation and characterize them in terms of solutions to inhomogeneous Bernoulli type ordinary differential equations. We provide a precise characterization for the directionality of the CDS investment strategy and perform a numerical analysis to assess the impact of default contagion. We find that the increased intensity triggered by default of a very risky entity strongly impacts size and directionality of the investor strategy. Such findings outline the key role played by default contagion when investing in portfolios subject to multiple sources of default risk.     

Price limits,margin requirements,and default risk

This article investigates whether price limits can reduce the default risk and lower the effective margin requirement for a self‐enforcing futures contract by considering one more period beyond Brennan’s (1986) model to take into account the spillover of unrealized residual shocks due to price limits. The results show that, when traders receive no additional information, price limits can reduce the margin requirement and eliminate the default probability at the expense of a higher liquidity cost due to trading interruptions. Consequently, the total contract cost is higher than of that without price limits. When traders receive additional signals about the equilibrium price, we find that the optimal margin remains unchanged with or without the imposition of price limits, a result that is in conflict with Brennan’s assertion. Hence, we conclude that price limits may not be effective in improving the performance of a futures contract. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:573–602, 2000     

LOCAL RISK MINIMIZATION FOR DEFAULTABLE MARKETS

We study the local risk minimization approach for defaultable markets in a general setting where the asset price dynamics and the default time may influence each other. We find the Föllmer-Schweizer decomposition in this general setting and compute it explicitly in two particular cases, when default time depends on the risky asset's behavior and when only a dependence of discounted asset price on default time is occurring.     

The default heuristic in strategic decision making: When is it optimal to choose the default without investing in information search?

Many studies have shown that decision makers have a tendency to choose the default or standard action among several possible actions. The article develops a model to explore under what conditions it is optimal for a firm facing a strategic decision problem to choose the default action without investing in obtaining more information that allows a more accurate decision. The model shows that the strategy to follow the default without additional information (“the default heuristic”) is more likely to be optimal when the cost of obtaining information is higher, and when the variation in possible outcomes is lower. The model also analyzes the optimal level of information search, showing that if the firm chooses to obtain information at all, it will invest in more accurate information when the cost of obtaining information is lower and when the variation in possible outcomes is lower.