Jesper Lund

An Empirical Investigation of Continuous-Time Equity Return Models

This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of time-varying intensity. We find that any reasonably descriptive continuous-time model for equity-index returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equity-index returns and the stylized features of the corresponding options market prices.

Estimating continuous-time stochastic volatility models of the short-term interest rate

Abstract We obtain consistent parameter estimates of continuous-time stochastic volatility diffusions for the U.S. risk-free short-term interest rate, sampled weekly over 1954–1995, using the Efficient Method of Moments procedure of Gallant and Tauchen. The preferred model displays mean reversion and incorporates ‘level effects’ and stochastic volatility in the diffusion function. Extensive diagnostics indicate that the Cox-Ingersoll-Ross model with an added stochastic volatility factor provides a good characterization of the short rate process. Further, they suggest that recently proposed GARCH models fail to approximate the discrete-time short rate dynamics, while ‘Level-EGARCH’ models perform reasonably well.

GMM and present value tests of the C-CAPM: evidence from the Danish, German, Swedish and UK stock markets

Abstract In this paper we test the consumption oriented capital asset pricing model with constant relative risk aversion using long time series data from four European stock markets. Two different methodologies are applied: Hansens GMM method and the VAR approach proposed by Campbell and Shiller. Overall the statistical tests are unable to reject the C-CAPM, and the dividend-price ratio generally predicts future dividend growth in the direction implied by the model. However, the estimates of the relative risk aversion parameter are mostly implausible and imprecise, and the dividend-price ratio tends to predict future consumption growth in the wrong direction. Hence, discount rates are time-varying in a way that is inconsistent with the C-CAPM/CRRA specification.

A Model for Studying the Effect of EMU on European Yield Curves

In January 1999, the European monetary union (EMU) was formally launched with 11 member countries. However, before May 1998 there was considerable uncertainty about who would join EMU, and whether the project would start on time. When a monetary union is formed, exchange rates between the member countries are irrevocably fixed, and yield spreads stemming from exchange-rate risk are eliminated. As a direct consequence, EMU affected the prices of long-term bonds well before 1999, but quantifying this effect can be difficult when there is uncertainty about the monetary union. We address these issues and develop a bond-pricing model which explicitly takes into account that a country may join a monetary union at a future, unspecified date. The empirical results show that a narrow EMU, consisting of Germany, France and the Benelux countries, has been priced with almost 100% probability throughout the period 1995—1998, whereas, on average, the implied probability of joining EMU has been somewhat lower for the other EU countries. However, in the period leading up to May 1998, the estimated probabilities have increased considerably for the countries that joined EMU in January 1999. JEL classification codes: G12, G13, F36.

Common stochastic trends in international stock prices and dividends: an example of testing overidentifying restrictions on multiple cointegration vectors

Based on a cointegrated VAR model, a joint test of the within-country and crosscountry low-frequency implications of the present value model of stock prices is derived and applied to postwar annual stock market data from four European countries. Following Johansen (1995) and Johansen and Juselius (1994) the test is formulated as a test of overidentifying restrictions on multiple cointegration vectors. The analysis is similar in spirit to the analysis carried out by Kasa (1992). However, whereas Kasa analyses prices and dividends in two separate VAR models and does not test restrictions implied by the present value model on the cointegration vectors, we perform the analysis within one comprehensive VAR model and test the full set of within-country and cross-country implications by a single likelihood ratio test. The empirical results indicate the presence of common trends among dividends in the four countries; how many is, however, difficult to judge. Furthermore, the results of the tests of the overidentifying restrictions are not clearcut. If dividends share one or two common trends the restrictions are not rejected at standard significance levels. However, if dividends share three common trends, the restrictions are strongly rejected.