Rangarajan K. Sundaram

Of Smiles and Smirks: A Term-Structure Perspective

An extensive empirical literature in finance has documented not only the presence of anomalies in the Black-Scholes model, but also the term structures of these anomalies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts in the literature at addressing these anomalies have largely focused on two extensions of the Black-Scholes model: introducing jumps into the return process, and allowing volatility to be stochastic. We employ commonly used versions of these two classes of models to examine the extent to which the models are theoretically capable of resolving the observed anomalies. We find that each model exhibits some term structure patterns that are fundamentally inconsistent with those observed in the data. As a consequence, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models fare somewhat better than jumps.

Altering the Terms of Executive Stock Options

This paper examines the practice of resetting of the terms of previously-issued executive stock options. We identify the properties of the typical reset option, characterize the firms that have reset options, and develop a model to value options that may be reset. In our sample of 396 executives whose options had terms reset in 1992-95 period, a large majority had exercise prices reset to the market price. This resulted in a reduction of the typical options exercise price by about 40%. Slightly less than half of these options also had their maturities extended, generally receiving a new expiration of 10 years. We find that resetting has a strong negative relationship with firm performance even after correcting for industry performance. Resetting is also significantly more common among small firms than among large firms. However, few other industry- or firm-specific factors appear to matter. Finally, we find that the possibility of resetting does not have a large impact on the ex-ante value of an option award, but the ex-post gain can be substantial.

On the optimality of resetting executive stock options

Recent empirical work has documented the tendency of corporations to reset strike prices on previously-awarded executive stock option grants when declining stock prices have pushed these options out-of-the-money. This practice has been criticized as counter-productive since it weakens incentives present in the original award.We find that although the anticipation of resetting will typically result in a negative effect on initial incentives, resetting can still be an important, value-enhancing aspect of compensation contracts, even from an ex-ante standpoint. Indeed, we find a precise sense that some resetting is almost always optimal. We also characterize the conditions that affect the relative optimality resetting. We find, for example, that the relative advantages of resetting decrease as managerial ability to influence the resetting process increases, as the relative importance of external (industry-or economy-wide) factors in return generation increase, and as the direct or indirect cost of replacing the incumbent manager decrease. Our analysis, in summary, that the case against resetting is quite weak.

A Simple Approach to Three-Factor Affine Term Structure Models

RANGARAJAN SUNDARAM is assistant professor at New York University. his article develops a simple estimation approach for three-factor models of the term structure of interest rates, exploiting the exponential-affine structure of these models. The three factors in the model are the short-term rate of interest, the long-run mean of the short-term rate, and the volatility of the short-term rate. The objective of term structure modeling from a practitioner’s viewpoint is to develop a parsimonious representation of the yield curve matching the time series and cross-sectional variation of bond yields. The more factors, the richer the time series and cross-sectional properties of bond returns the model can accommodate. Of course, complexity is often traded off against parsimony for practical reasons of implementation. So far, practicality has kept researchers in the field from going beyond three-factor models. The simple estimation method in this article should make the implementation of three-factor models easier. Implementation of the model on data over a thirty-year period indicates that it captures known theoretical features and aspects of the term structure well. Duffle and Kan [1996] show that a wide range of choices of stochastic processes for interest rate factors yield bond pricing solutions of a form now widely called exponential-a

Cross-Country Variations in Capital Structures: The Role of Bankruptcy Codes

ne models. It is the affine form that we use in this article to develop our implementation methodology. Even though there are three factors, the affine class of solutions enables the use of a single equation maximum-likelihood model to approximate the multivariate estimation of a three-factor model. The model fits the data well, and also enables the filtering of the

An Integrated Model for Hybrid Securities

We conduct a theoretical and empirical investigation of the impact of bankruptcy codes on firms’ capital-structure choices. In our theoretical framework, costs of financial distress are endogenously determined as a function of the bankruptcy code. Anticipated liquidation values emerge as the key variable in the capital structure-bankruptcy code link: among other things, the theory predicts that the difference in leverage between a debt-friendly bankruptcy code (such as the UK’s) and a more equity-friendly code (such as the US’s) should be a monotone function of liquidation values. We examine empirical support for the theory by comparing leverages in the US and the UK for the period 1990 to 2002. Our tests use two (inverse) proxies of liquidation values: asset-specificity of the firm, and the fraction of the firm’s assets that are intangibles. We find the theory is strongly backed by the data. The results are robust to considerations such as employing net leverage (debt net of cash holdings) and controlling for other firm characteristics that affect leverage.We develop a theoretical model of capital structure choice in which a central role is played by the bankruptcy code under which a company operates. We show that capital structure choices are substantially influenced by asset-specificity: firms with high assetspecificity will use a higher degree of leverage under a debt-friendly bankruptcy code than under an equity-friendly code, but the reverse is true for firms with low asset-specificity. Moreover, the dierence between the optimal debt levels under the two codes is itself an increasing function of the degree of asset-specificity. We test our model’s implications by comparing leverage ratios at the industry level in the US to those in the UK during the period 1990 to 2002. We find that our theoretical predictions are strongly confirmed by the data. Our results clarify and extend previous crosscountry empirical studies (notably Rajan and Zingales, 1995) that found mixed evidence on the relationship between the bankruptcy code and capital structure when data was aggregated over all industries.

Generalized Bandit Problems

We develop a model for pricing securities whose value may depend simultaneously on equity, interest-rate, and default risks. The framework may also be used to extract probabilities of default (PD) functions from market data. Our approach is entirely based on observables such as equity prices and interest rates, rather than on unobservable processes such as firm value. The model stitches together in an arbitrage-free setting a constant elasticity of variance (CEV) equity model (to represent the behavior of equity prices prior to default), a default intensity process, and a Heath-Jarrow-Morton (HJM) model for the evolution of riskless interest rates. The model captures several stylized features such as a negative relation between equity prices and equity volatility, a negative relation between default intensity and equity prices, and a positive relationship between default intensity and equity volatility. We embed the model on a discrete-time, recombining lattice, making implementation feasible with polynomial complexity. We demonstrate the simplicity of calibrating the model to market data and of using it to extract default information. The framework is extensible to handling correlated default risk and may be used to value distressed convertible bonds, debt-equity swaps, and credit portfolio products such as collateralized debt obligations (CDOs). Applied to the CDX INDU (credit default index--industrials) Index, we find the S&P 500 index explains credit premia.

Mispricing and Arbitrage in CDS Auctions

This chapter examines a number of extensions of the multi-armed bandit framework. We consider the possibility of an infinite number of available arms, we give conditions under which the Gittins index strategy is well-defined, and we examine the optimality of that strategy. We then consider some difficulties arising from “parallel search,” in which a decision-maker may pull more than one arm per period, and from the introduction of a cost of switching between arms.

Inventory Effects, the Winner’s Curse, and Bid Shading in Credit Default Swap Auction Outcomes

Credit default swaps were a major addition to the array of financial instruments available in the market. But as is typical for a fundamentally new product, the early designs had to be tweaked. First, it was necessary to eliminate ambiguity over what constitutes a credit event, and more recent changes enhanced liquidity by standardizing the contract terms and regularized how the payoff is determined following a default. This is now accomplished through a rather complicated twostage auction process. In this article, Gupta and Sundaram describe how the auction works and establish the existence of a striking and somewhat troubling pattern exhibited by prices of the underlying bonds at the time of the auction. In auctions where the first round shows an imbalance of selling over buying orders, the market price is higher on the day prior to the auction, drops sharply at the auction, and then shoots upward the next day. The reverse pattern happens in a buy auction. These patterns produce significant profits for simple trading rules, such as buying (selling) immediately after a sell (buy) auction.

CDS Credit-Event Auctions 1

This article studies bidding behavior in the novel and complex auctions that, since 2005, have determined recovery rates in the multi-trillion dollar credit default swap (CDS) market. We find that bids are substantially influenced by inventory effects (bidders’ CDS positions entering the auction), market illiquidity, and “winners curse” considerations. The economically and statistically significant extent of “bid-shading” induced by these factors explains why auction prices deviate significantly (on average >16%) from pre- and post-auction market prices for the same instruments even while auction-generated information is significantly informative for post-auction market price formation.