DURATION,DEFAULT RISK,AND THE TERM STRUCTURE OF INTEREST RATES

We examine the interactive effect of default and interest rate risk on duration of defaultable bonds. We show that duration for defaultable bonds can be longer or shorter than default‐free bonds depending on the relation between default intensity and interest rates. Empirical evidence indicates that in most cases duration for defaultable bonds is much shorter than for their default‐free counterparts because of the negative relation between default risk and interest rates. Results suggest that the duration measure must be adjusted for the effects of default risk and stochastic interest rates to achieve an effective bond portfolio immunization.     

Testing Term Structure Estimation Methods: Evidence from the UK STRIPS Market

Prices and yields of UK government zero‐coupon bonds are used to test alternative yield curve estimation models. Zero‐coupon bonds permit a more pure comparison, as the models are providing only the interpolation service and also not making estimation feasible. It is found that better yield curves estimates are obtained by fitting to the yield curve directly rather than fitting first to the discount function. A simple procedure to set the smoothness of the fitted curves is developed, and a positive relationship between over‐smoothness and the fitting error is identified. A cubic spline function fitted directly to the yield curve provides the best overall balance of fitting error and smoothness, both along the yield curve and within local maturity regions.     

A Duration Model For Defaultable Bonds

I extend recent theoretical work on duration and derive an improved model for the risk‐adjusted duration of corporate bonds. My ex‐ante risk‐adjusted duration is the sum of the bond's Fisher‐Weil duration and the duration of the potential expected delay in recovery caused by the default option. My main conclusion is that failing to adjust duration for default is costly for high‐yield bonds, especially those with a shorter time to maturity. For investment‐grade bonds, this cost is trivial for all maturities.     

The delivery option in credit default swaps

Under standard assumptions the reduced-form credit risk model is not capable of accurately pricing the two fundamental credit risk instruments – bonds and credit default swaps (CDS) – simultaneously. Using a data set of euro-denominated corporate bonds and CDS our paper quantifies this mispricing by calibrating such a model to bond data, and subsequently using it to price CDS, resulting in model CDS spreads up to 50% lower on average than observed in the market. An extended model is presented which includes the delivery option implicit in CDS contracts emerging since a basket of bonds is deliverable in default. By using a constant recovery rate standard models assume equal recoveries for all bonds and hence zero value for the delivery option. Contradicting this common assumption, case studies of Chapter 11 filings presented in the paper show that corporate bonds do not necessarily trade at equal levels following default. Our extension models the implied expected recovery rate of the cheapest-to-deliver bond and, applied to data, largely eliminates the mispricing. Calibrated recovery values lie between 8% and 47% for different obligors, exhibiting strong variation among rating classes and industries. A cross-sectional analysis reveals that the implied recovery parameter depends on proxies for the delivery option, primarily the number of available bonds and bond pricing errors. No evidence is found for a direct influence of the bid-ask spread, notional amount, coupon, or rating used as proxies for bond market liquidity.     

Bond pricing with a surface of zero coupon yields

We present a new method for consistent cross‐sectional pricing of all traded bonds in the fixed income market. By applying thin plate regression splines ( Wood, 2003 ) to bootstrapped zero coupon bond yields ( Hagan and West, 2006 ), the method decomposes traded yields into a risk‐free component plus premia for credit and liquidity risks, where the decomposition is consistent with the market valuations and underlying cash flows of the bonds. We apply the framework to end of quarter yield data from 2008 to 2011 on Australian dollar denominated semi‐government, supranational and agency (SSA) bonds, and find that the surface provides an excellent fit to the underlying zero coupon yield curves. Further, the decomposition of selected yield time series and cross‐sections demonstrates how credit premia increased for Australian SSA bonds through the Global Financial Crisis (GFC), but were counterbalanced by liquidity discounts as investors sought safe haven securities.     

CREDIT SPREADS AND THE ZERO‐COUPON TREASURY SPOT CURVE

We examine the relation between credit spreads on industrial bonds and the underlying Treasury term structure. We use zero‐coupon spot rates to eliminate the coupon bias and to allow for a consistent study both within and across the different credit ratings. Our results indicate that the level and slope of the Treasury term structure are negatively correlated with changes in the credit spread on investment‐grade corporate bonds. We also find that the relation between credit spreads and the Treasury term structure is relatively stable through time. This is good news for value‐at‐risk calculations, as this suggests that the correlations among assets of different credit classes are stable; therefore use of historic correlations to model spread relations can be valid.     

Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models

This paper demonstrates how to value American interest rate options under the jump-extended constant-elasticity-of-variance (CEV) models. We consider both exponential jumps (see Duffie et al., 2000) and lognormal jumps (see Johannes, 2004) in the short rate process. We show how to superimpose recombining multinomial jump trees on the diffusion trees, creating mixed jump-diffusion trees for the CEV models of short rate extended with exponential and lognormal jumps. Our simulations for the special case of jump-extended Cox, Ingersoll, and Ross (CIR) square root model show a significant computational advantage over the Longstaff and Schwartz’s (2001) least-squares regression method (LSM) for pricing American options on zero-coupon bonds.     

Stochastic durations,the convexity effect,and the impact of interest rate changes

This article shows that the equilibrium models of bond pricing do not preclude arbitrage opportunities caused by convexity. Consequently, stochastic durations derived from these models are limited in their ability to act as interest rate risk measures. The research of the present article makes use of an intertemporal utility maximization framework to determine the conditions under which duration is an adequate interest rate risk measure. Additionally, we show that zero coupon bonds satisfy those equilibrium conditions, whereas coupon bonds or bond portfolios do not as a result of the convexity effect. The results are supported by empirical evidence, which confirms the influence of convexity on the deviation of coupon bond returns from equilibrium.     

Forward-neutral valuation relationships for options on zero coupon bonds

This paper extends the literature on Risk-Neutral Valuation Relationships (RNVRs) to derive valuation formulae for options on zero coupon bonds when interest rates are stochastic. We develop Forward-Neutral Valuation Relationships (FNVRs) for the transformed-bounded random walk class. Our transformed-bounded random walk family of forward bond price processes implies that (i) the prices of the zero coupon bonds are bounded below at zero and above at one, and (ii) negative continuously compounded interest rates are ruled out. FNVRs are frameworks for option pricing, where the forward prices of the options are martingales independent of the market prices of risk. We illustrate the generality and flexibility of our approach with models that yield several new closed-form solutions for call and put options on discount bonds.     

The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models

This paper analyzes the role of jumps in continuous‐time short rate models. I first develop a test to detect jump‐induced misspecification and, using Treasury bill rates, find evidence for the presence of jumps. Second, I specify and estimate a nonparametric jump‐diffusion model. Results indicate that jumps play an important statistical role. Estimates of jump times and sizes indicate that unexpected news about the macroeconomy generates the jumps. Finally, I investigate the pricing implications of jumps. Jumps generally have a minor impact on yields, but they are important for pricing interest rate options.     

SERIAL ISSUE EVIDENCE FOR THE RELATION BETWEEN THE RISK STRUCTURE AND MATURITY: A DECOMPOSITION METHODOLOGY

The risk structure of the interest rates literature shows that coupon effects can cause changes in yield spreads as maturity lengthens. These effects make it difficult to empirically isolate the default risk component of the spread for coupon-paying bonds. Attempts to calculate zero-coupon risk structures suffer from the relative scarcity of zero-coupon corporate bonds. We show that yield spreads for coupon-paying bonds that are identical except for default risk decompose into a relative duration component, a premium discount coupon component, and a default component. We present closed-form solutions for measuring the first two components so that the default risk portions can be isolated as residuals. We further present an empirical application of the decomposition metrics for sixteen exchange-traded serial issues and nonparametrically examine the relation between the default premia and maturity. We find various maturity relations.     

Lévy jump risk: Evidence from options and returns

Using index options and returns from 1996 to 2009, I estimate discrete-time models where asset returns follow a Brownian increment and a Lévy jump. Time variations in these models are generated with an affine GARCH, which facilitates the empirical implementation. I find that the risk premium implied by infinite-activity jumps contributes to more than half of the total equity premium and dominates that of the Brownian increments suggesting that it is more representative of the risks present in the economy. Overall, my findings suggest that infinite-activity jumps, instead of the Brownian increments, should be the default modeling choice in asset pricing models.     

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

Public Pension Promises: How Big Are They and What Are They Worth?

We calculate the present value of state employee pension liabilities using discount rates that reflect the risk of the payments from a taxpayer perspective. If benefits have the same default and recovery characteristics as state general obligation debt, the national total of promised liabilities based on current salary and service is $3.20 trillion. If pensions have higher priority than state debt, the value of liabilities is much larger. Using zero‐coupon Treasury yields, which are default‐free but contain other priced risks, promised liabilities are $4.43 trillion. Liabilities are even larger under broader concepts that account for salary growth and future service.     

How much of the corporate bond spread is due to personal taxes?

Existing term structure models of defaultable bonds have often underestimated corporate bond spreads. A potential problem is that investors’ taxes are ignored in these models. We propose a pricing model that accounts for stochastic default probability and differential tax treatments for discount and premium bonds. By estimating parameters directly from bond data, we obtain significantly positive estimates for the income tax rate of a marginal corporate bond investor after 1986. This contrasts sharply with the previous finding that the implied tax rates for Treasury bonds are close to zero. Results show that taxes explain a substantial portion of corporate bond spreads.     

Quadratic term structure models in discrete time

This paper extends the results on quadratic term structure models in continuous time to the discrete time setting. The continuous time setting can be seen as a special case of the discrete time one. Discrete time quadratic models have advantages over their continuous time counterparts as well as over discrete time affine models. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors, time-dependent parameters, regime changes and “jumps” in the underlying factors. In particular regime changes and “jumps” cannot so easily be accommodated in continuous time quadratic models. Pricing bond options requires simple integration and model estimation does not require a restrictive choice of the market price of risk.     

Actuarial pricing of deposit insurance

Using a pricing formula for options on coupon bonds (Jamshidian [1989], El Karoui and Rochet [1990]) we are able to compute the actuarial pricing of deposit insurance for a commercial bank. Our formula takes into account the maturity structure of the bank's balance sheet, as well as market parameters such as the term structure of interest rates and the volatilities of zero coupon bonds. The relation with asset liability management methods is explored.     

Does Fair Value Accounting Exacerbate the Procyclicality of Bank Lending?

This study investigates whether fair value accounting contributes to the procyclicality of bank lending. Using banks’ approval/denial decisions on residential mortgage applications to capture banks’ supply of credit, I find no evidence that fair value accounting has procyclical effects on bank lending over the past two business cycles. I further identify two reasons for this result. First, the main accounting item distinguishing fair value accounting from historical cost accounting—unrealized gains and losses on available‐for‐sale securities—does not affect lending decisions. Second, unrealized gains and losses on available‐for‐sale securities are not procyclical, as the risk‐free interest rate rises during some expansionary periods, resulting in unrealized losses, while the risk‐free interest rate (and sometimes the default spread) falls during some recessionary periods, resulting in unrealized gains.