Scott Joslin

Why Gaussian macro-finance term structure models are (nearly) unconstrained factor-VARs

This paper explores the impact of simultaneously enforcing the no-arbitrage structure of a Gaussian macro-finance term structure model (MTSM) and accommodating measurement errors on bond yield through filtering on the maximum likelihood estimates of the model-implied conditional distributions of the macro risk factors and bond yields. For the typical yield curves and macro variables studied in this literature, the estimated joint distribution within a canonical MTSM is nearly identical to the estimate from an economic-model-free factor vector-autoregression (factor-VAR), even when measurement errors are large. It follows that a canonical MTSM does not offer any new insights into economic questions regarding the historical distribution of the macro risk factors and yields, over and above what is learned from a factor-VAR. In particular, the discipline of a canonical MTSM is empirically inconsequential for analyses of impulse response functions of bond yields and macro factors or empirical studies of term premiums. These results are rotation-invariant and, therefore, apply to many of the specifications of risk factors in the literature. In deriving these results we develop a new canonical form for MTSMs that is particularly revealing about the nature of the over-identifying restrictions implied by MTSMs relative to yield-based factor models.

Can Unspanned Stochastic Volatility Models Explain the Cross Section of Bond Volatilities

In fixed income markets, volatility is unspanned if volatility risk cannot be hedged with bonds. We first show that all affine term structure models with state space ℝ+M×ℝN−M can be drift normalized and show when the standard variance normalization can be obtained. Using this normalization, we find conditions for a wide class of affine term structure models to exhibit unspanned stochastic volatility (USV). We show that the USV conditions restrict both the mean reversions of risk factors and the cross section of conditional yield volatilities. The restrictions imply that previously studied affine USV models are unlikely to be able to generate the observed cross section of yield volatilities. However, more general USV models can match the cross section of bond volatilities. This paper was accepted by Wei Xiong, finance.

Demand for Crash Insurance, Intermediary Constraints, and Risk Premia in Financial Markets

We model the market for economic disaster insurance to examine the dynamic relation between the net demand by public investors and the disaster risk premium. In the model, when the probability of disasters rises, dealers become more constrained and averse to disaster risk, which reduces their risk sharing capacity, causing the equilibrium net public demand for disaster insurance to fall and the disaster risk premium to rise at the same time. Consistent with the model predictions, we nd that public demand for deep out-of-the-money put options on the market index has strong predictive power for future stock returns. Large net public buying of OTM puts is associated with low future returns, with an R 2 of 19% for the predictability regression of future 3-month returns. This predictive power of option demand is distinct from that of the standard predictive variables in the literature, is particularly strong during the recent nancial crisis, and it weakens as one moves to at-the-money and in-the-money options. We also provide evidence that low net public demand for disaster insurance is linked to deleveraging for security brokers and dealers.We propose a new measure of financial intermediary constraints based on how the intermediaries manage their tail risk exposures. Using a unique dataset for the trading activities in the market of deep out-of-the-money S&P 500 put options, we identify periods when the variations in the net amount of trading between financial intermediaries and public investors are likely to be mainly driven by shocks to intermediary constraints. We then infer tightness of intermediary constraints from the quantities of option trading during such periods. We show that a tightening of intermediary constraint according to our measure is associated with increasing option expensiveness, higher risk premia for a wide range of financial assets, deterioration in funding liquidity, and deleveraging of broker-dealers.

An equivalence result for VC classes of sets

Let R and θ be infinite sets and let A # R × θ. We show that the class of projections of A onto R is a Vapnik–Chervonenkis (VC) class of sets if and only if the class of projections of A onto θ is a VC class. We illustrate the result in the context of semiparametric estimation of a transformation model. In this application, the VC property is hard to establish for the projection class of interest but easy to establish for the other projection class.

Interest rate volatility, the yield curve, and the macroeconomy

This paper provides theory and evidence that a low-dimensional term structure model can simultaneously price bonds and related options. It shows that a component of volatility risk largely unrelated to the shape of the yield curve is a determinant of expected excess returns for holding long maturity bonds. It also finds evidence for this return relationship both in the model and directly in the data through regression analysis. The paper also identifies a link between corporate earnings performance and interest rate volatility, providing a channel driving interest rate volatility. The structure of risk in the model that gives rise to these features of volatility is distinct from that inherent in recent models with unspanned stochastic volatility.