Predicting credit spreads

Predictions of firm-level credit spreads based on the current spot and forward credit spreads can be significantly improved upon by using the information contained in the shape of the credit-spread curve. However, the current credit-spread curve is not a sufficient statistic for predicting future out-of-sample credit spreads; predictions can be significantly improved upon by exploiting the information contained in the shape of the riskless yield curve. In the presence of credit-spread and riskless factors, other macroeconomic, marketwide, and firm-specific risk variables do not significantly improve predictions of credit spreads. These results have important implications for credit-spreads modeling as well as for better understanding corporate capital structure and risk management policies.     

Minimum option prices under decreasing absolute risk aversion

We establish bounds on option prices in an economy where the representative investor has an unknown utility function that is constrained to belong to the family of nonincreasing absolute risk averse functions. For any distribution of terminal consumption, we identify a procedure that establishes the lower bound of option prices. We prove that the lower bound derives from a particular negative exponential utility function. We also identify lower bounds of option prices in a decreasing relative risk averse economy. For this case, we find that the lower bound is determined by a power utility function. Similar to other recent findings, for the latter case, we confirm that under lognormality of consumption, the Black Scholes price is a lower bound. The main advantage of our bounding methodology is that it can be applied to any arbitrary marginal distribution for consumption. This revised version was published online in June 2006 with corrections to the Cover Date.     

Pricing Options under Generalized GARCH and Stochastic Volatility Processes

In this paper, we develop an efficient lattice algorithm to price European and American options under discrete time GARCH processes. We show that this algorithm is easily extended to price options under generalized GARCH processes, with many of the existing stochastic volatility bivariate diffusion models appearing as limiting cases. We establish one unifying algorithm that can price options under almost all existing GARCH specifications as well as under a large family of bivariate diffusions in which volatility follows its own, perhaps correlated, process.     

Interest rate option pricing with volatility humps

This paper develops a simple model for pricing interest rate options when the volatility structure of forward rates is humped. Analytical solutions are developed for European claims and efficient algorithms exist for pricing American options. The interest rate claims are priced in the Heath-Jarrow-Morton paradigm, and hence incorporate full information on the term structure. The structure of volatilities is captured without using time varying parameters. As a result, the volatility structure is stationary. It is not possible to have all the above properties hold in a Heath Jarrow Morton model with a single state variable. It is shown that the full dynamics of the term structure is captured by a three state Markovian system. Caplet data is used to establish that the volatility hump is an important feature to capture. This revised version was published online in June 2006 with corrections to the Cover Date.     

Getting the Most Out of a Mandatory Subordinated Debt Requirement

Recent advances in asset pricing—the reduced-form approach to pricing risky debt and derivatives—are used to quantitatively evaluate several proposals for mandatory bank issue of subordinated debt. We find that credit spreads on both fixed- and floating-rate subordinated debt provide relatively clean signals of bank risk and are not unduly influenced by nonrisk factors. Fixed-rate debt with a put is unacceptable, but making the putable debt floating resolves most problems. Our approach also helps to clarify several different notions of “bank risk.”     

On pricing kernels and finite-state variable Heath Jarrow Morton models

Once a pricing kernel is established, bond prices and all other interest rate claims can be computed. Alternatively, the pricing kernel can be deduced from observed prices of bonds and selected interest rate claims. Examples of the former approach include the celebrated Cox, Ingersoll, and Ross (1985b) model and the more recent model of Constantinides (1992). Examples of the latter include the Black, Derman, and Toy (1990) model and the Heath, Jarrow, and Morton paradigm (1992) (hereafter HJM). In general, these latter models are not Markov. Fortunately, when suitable restrictions are imposed on the class of volatility structures of forward rates, then finite-state variable HJM models do emerge. This article provides a linkage between the finite-state variable HJM models, which use observables to induce a pricing kernel, and the alternative approach, which proceeds directly to price after a complete specification of a pricing kernel. Given such linkages, we are able to explicitly reveal the relationship between state-variable models, such as Cox, Ingersoll, and Ross, and the finite-state variable HJM models. In particular, our analysis identifies the unique map between the set of investor forecasts about future levels of the drift of the pricing kernel and the manner by which these forecasts are revised, to the shape of the term structure and its volatility. For an economy with square root innovations, the exact mapping is made transparent.     

Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets

This paper examines whether higher order multifactor models, with state variables linked solely to underlying LIBOR‐swap rates, are by themselves capable of explaining and hedging interest rate derivatives, or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary. Our research shows that swaptions and even swaption straddles can be well hedged with LIBOR bonds alone. We examine the potential benefits of looking outside the LIBOR market for factors that might impact swaption prices without impacting swap rates, and find them to be minor, indicating that the swaption market is well integrated with the LIBOR‐swap market.     

Pricing the Quality Option In Treasury Bond Futures1

This article develops a model for pricing the quality option embedded in the Treasury bond futures contract. Since the option value is set relative to a large family of deliverable bond prices, it is important for the theoretical bond prices to match up to the observed prices. Hence an arbitrage-based model is used where the forward rate process is initialized at its current observable value. A model for valuing the quality option in an otherwise identical forward contract is also established. This permits the quality option and marking to market costs to be separately quantified. Support is provided for the common practice of pricing Treasury bond futures contracts as forward contracts with an embedded forward quality option.     

A MULTIFACTOR MODEL OF THE QUALITY OPTION IN TREASURY FUTURES CONTRACTS

The values of quality options in Treasury futures contracts are set relative to the prices of all coupon bonds in their respective deliverable sets. As a result, any model used to value the quality option should set its price relative to the set of observed bond prices. This requirement rules out the use of most simple equilibrium models that represent all bond prices in terms of a finite number of state variables. We use the two-factor Heath-Jarrow-Morton model, which permits claims to be priced relative to observable bond prices, to investigate the potential value of the quality option in Treasury bond and note futures. We show that the quality option has significantly more value in a two-factor interest rate economy than in a single-factor economy, and that ignoring it could lead to significant mispricing.