The Second T.N. Thiele Symposium on Financial Econometrics

Abstracts:


Yacine Ait-Sahalia (Princeton):

Closed form likelihood expansions for multivariate diffusions

This paper provides closed-form expansions for the transition density and likelihood function of arbitrary multivariate diffusions. The expansions are based on a Hermite series, whose coefficients are calculated explicitly by exploiting the special structure afforded by the diffusion hypothesis. Because the transition function for most diffusion models is not known explicitly, the expansions of this paper can help make maximum-likelihood a practical estimation method for discretely sampled multivariate diffusions. Examples of interest in financial econometrics are included.


Casper G. de Vries (Rotterdam):

Auctions with Numerous Bidders

Extreme value theory and statistics have been usefully applied in finance regarding questions of value-at-risk and systemic risk. In this study we venture into a novel application. Vickrey in the Journal of Finance published the first serious paper on auctions back in the early 1960s. Auctions are frequently used in financial economics, like at an IPO or in a treasury auction. Most of the theory is concerned with auctions in which a small number of bidders is present. This paper studies auctions in which the number of potential bidders is large, such as in internet auctions or during an IPO. With numerous bidders, quantities like the expected revenue are computationally intractable. Moreover, little is known about the distribution of valuations. In our approach, the expected revenue to the auctioneer and the expected maximum valuation are found without assuming a particular distribution function for the bidders' valuations. We use statistical extreme value theory to derive an estimator for the auctioneer's expected revenue from a single auction, circumventing the need for pooling. The theory is applied to data from internet auctions.


Greg Duffee (Berkeley):

Do forecasts of stock returns also forecast covariances?

I construct forecasts of aggregate stock returns with standard variables, then use the forecasts to predict covariances between stock returns and real variables such as consumption and GDP growth. The results are strong and surprising. Return forecasts contain substantial information about covariances, but the sign of the relation is opposite that predicted in standard asset-pricing models. When expected returns are high, covariances are near zero; when expected returns are low, covariances are positive and large. These results have important implications for asset pricing and our understanding of the joint dynamics of stock prices and business cycles.


Joost Driessen (Amsterdam):

Is Default Event Risk Priced in Corporate Bonds?

We identify and estimate the sources of risk that cause corporate bonds to earn an excess return over default-free bonds. In particular, we estimate the risk premium associated with a default event. Default is modelled using a jump process with stochastic intensity. For a large set of firms, we model the default intensity of each firm as a function of common and firm-specific factors. In the model, corporate bond excess returns can be due to risk premia on factors driving the intensities and due to a risk premium on the default jump risk. The model is estimated using data on corporate bond prices for 104 US firms and historical default rate data. We find significant risk premia on the factors that drive intensities. However, these risk premia cannot fully explain the size of corporate bond excess returns. Next, we estimate the size of the default jump risk premium, correcting for possible tax and liquidity effects. The estimates show that this event risk premium is a significant and economically important determinant of excess corporate bond returns.

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Tom Engsted (Aarhus):

The comovement of US and UK stock markets

US and UK stock returns are highly positively correlated over the period 1918-1999. Using VAR-based variance decompositions, we investigate the nature of this comovement. Excess return innovations are decomposed into news about future dividends, real interest rates, and excess returns. We find that the latter news component is the most important in explaining stock return volatility in both the US and the UK and that stock return news is highly correlated across countries. This is evidence against Beltratti and Shiller's (1993) finding that the comovement of US and UK stock markets can be explained in terms of a simple present value model. We interpret the comovement as indicating that equity premia in the two countries are hit by common real shocks. The work presented is joint with Carsten Tanggaard (Aarhus).

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Patrick Houweling (Rotterdam):

An Empirical Comparison of Default Swap Pricing Models

In this paper we compare market prices of credit default swaps with model prices. A default swap protects its buyer from losses caused by the occurrence of a default event to a corporate or sovereign debt issuer. In exchanged for this default protection, the buyer pays a periodic premium to the protection seller. The no-arbitrage value of the default swap premium can be derived by applying a reduced form credit risk model. We estimate a reduced form model with a constant recovery rate and a polynomial hazard rate function. For comparison, we also implement a method often applied by market practitioners that uses a bond's credit spread as a direct estimate of the default swap premium. We find that the reduced form model outperforms the direct method. Moreover, we shed light on the choice of the default-free term structure of interest rates. We find that swap and repo curves significantly outperform the government curve as proxy for default-free interest rates for investment grade issuers, but that their performance is similar for speculative grade issuers. As such, this is one of the first papers to empirically confirm that financial markets no longer see Treasury bonds as the default-free benchmark. We also pay attention to the choice of the recovery rate. We show that not only bond spreads, but also default swap premiums are relatively insensitive to changes in the recovery rate as long as the integrated hazard function is scaled accordingly.

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Catherine Laredo (Paris):

Likelihood and related methods for stochastic volatility models

In this lecture, we investigate likelihood and related processes for Stochastic Volatility Models, which are discretely observed with fixed sampling interval. Links between Stochastic Volatility and Hidden Markov Models are first given. Indeed, Stochastic Volatility Models are Hidden Markov Models whose hidden chain has a non compact state space. We present some properties of the exact likelihood and develop a new contrast approach for these models. This contrast is based on the conditional likelihood method, often used for ARCH-type models. We prove the strong consistency of the conditional likelihood estimators under appropriate conditions. As an illustration, the method is applied to the Kalman filter, for which this contrast and the exact likelihood lead to asymptotically equivalent estimators. Then, it is applied to mean-reverting stochastic volatility models.


Jesper Lund (Copenhagen):

Revisiting the Shape of the Yield Curve: The Effect of Interest Rate Volatility

This paper examines the relationship between interest-rate volatility and the shape of the yield curve. The yield curve is parsimoniously described by its level, slope, and curvature. The level, the slope and the curvature are analyzed within a trivariate heteroskedastic model, where the conditional short-rate volatility is included in the mean specification. The slope and the curvature depend positively and significantly on the short-rate volatility. The effect of the interest rate volatility is more pronounced for the curvature than for the slope. Differences between subperiods are explored, as are differences across the maturity spectrum. The work presented is joint with Charlotte Christiansen (Aarhus).


Anders Rahbek (Copenhagen):

The Autoregressive Conditional Root Model

In this paper we develop a multivariate time series model which allows long-term disequilibriums to have epochs of non-stationarity, giving the impression that long term relationships between economic variables have temporarily broken down, before they endogenously collapse back towards their long term relationship. The autoregressive root process is shown to be ergodic and covariance stationary under some rather general conditions. We study how this model can be estimated and tested, developing appropriate asymptotic theory for this task. Finally we discuss modelling real exchange rates. The work presented is joint with Neil Shepard (University of Oxford).


Joel Reneby (Stockholm):

The Valuation of Corporate Liabilities: Theory and Test

We develop a structural bond pricing approach and implement it on time series of 143 US industrial bonds. In contrast to earlier findings, we find that our model produces unbiased estimates of credit spreads. We also obtain less variable pricing errors than previous studies and show that our model is able to explain a significant portion of changes in yield spreads out of sample; the performance is competitive with that reported for more flexible reduced form models. Our model's errors are analyzed by regressing them on a set of bond specific, firm specific and economy wide variables. We feel that we have shown that two common criticisms of the structural approach to bond pricing - systematic biases and prohibitive implementation difficulties - can be overcome. The work presented is joint with Jan Ericsson (McGill).


Neil Shephard (Oxford):

Jumps and power variation

This paper reports an asymptotic analysis of realised power variation, that is sums of powers of absolute high frequency returns, in some cases where there is both stochastic volatility and jumps. Our analysis will be based on a fixed interval of time (e.g. a trading day or a calendar month), with our asymptotic theory allowing the number of high frequency returns during this period to go to infinity. We will see that realised power variation is less effected by jumps when the power of the absolute returns is low - indeed in the case where we add jumps to the SV process then the asymptotic distribution of realised power variation is unaffected by the jumps when the power is less than one. This provides theoretical evidence that empirical work based on low powers of absolute returns may be more robust than that based on realised variances and that the range of realised power variations has additional information in it than the familiar realised variance. The work presented is joint with Ole E. Barndorff-Nielsen (University of Aarhus).


Catalin Starica (Gothenburg):

A non-stationary multivariate model for financial returns

A simple non-stationary model for multivariate returns is proposed. Unlike most of the multivariate econometric models for financial returns, this model supposes the volatility to be exogenous. The vector of returns is assumed to follow an AR(1) process whose innovations are independent and have a slowly changing unconditional covariance structure. The methodological frame is that of non-parametric regression with non-random equidistant design points, where the regression function is the evolving unconditional covariance. Special attention is payed to the accurate description of the tails of the innovations. As an application the model is fit to a multivariate data set of returns on three different financial instruments: a foreign exchange rate, an index and an interest rate. The 1-day ahead multivariate distributional forecast performance is evaluated.
Key Words: Sample autocorrelation, long range dependence, non-parametric regression, Nadaraya-Watson kernel estimator, distributional forecast, heavy tails.