Publications - Bent Jesper Christensen

Estimation of continuous-time linear DSGE models from discrete-time measurements

Christensen, B. J., Neri, L., Parra-Alvarez, J. C. — Thu, 01 Dec 2022 10:43:40 +0100

We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from data that are only available at discrete points in time. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, which allows avoiding discretization errors. Using the Kalman filter, we construct the exact likelihood for data sampled either as stocks or flows, and estimate frequency-invariant parameters by maximum likelihood. We address the aliasing problem arising in multivariate settings and provide conditions for precluding it, which is required for local identification of the parameters in the continuous-time economic model. We recover the unobserved structural shocks at measurement times from the reduced-form residuals in the state space representation by exploiting the underlying causal links imposed by the economic theory and the information content of the discrete-time observations. We illustrate our approach using an off-the-shelf real business cycle model. We conduct extensive Monte Carlo experiments to study the finite sample properties of the estimator based on the exact discrete-time representation, and show they are superior to those based on a naive Euler-Maruyama discretization of the economic model. Finally, we estimate the model using postwar U.S. macroeconomic data, and offer examples of applications of our approach, including historical shock decomposition at different frequencies, and estimation based on mixed-frequency data.

Optimal control of investment, premium and deductible for a non-life insurance company

Christensen, B. J., Parra-Alvarez, J. C., Serrano, R. — Mon, 01 Nov 2021 10:43:40 +0100

A risk-averse insurance company controls its reserve, modeled as a perturbed Cramér-Lundberg process, by choice of both the premium p and the deductible K offered to potential customers. The surplus is allocated to financial investment in a riskless and a basket of risky assets potentially correlating with the insurance risks and thus serving as a partial hedge against these. Assuming customers differ in riskiness, increasing p or K reduces the number of customers n(p,K) and increases the arrival rate of claims per customer λ(p,K) through adverse selection, with a combined negative effect on the aggregate arrival rate n(p,K)λ(p,K). We derive the optimal premium rate, deductible, investment strategy, and dividend payout rate (consumption by the owner-manager) maximizing expected discounted lifetime utility of intermediate consumption under the assumption of constant absolute risk aversion. Closed-form solutions are provided under specific assumptions on the distributions of size and frequency of claims.

The incremental information in the yield curve about future interest rate risk

Christensen, B. J., Kjær, M. M., Veliyev, B. — Thu, 01 Jul 2021 10:43:40 +0200

Using high-frequency intraday futures prices to measure yield volatility at selected maturities, we find that daily yield curves carry incremental information about future interest rate risk at the long end, relative to that contained in the time series of historical volatilities. Some of the information in the yield curves is not captured by standard affine models. At the short end, time series based forecasts outperform yield curve based forecasts. Both provide utility to a risk averse investor in longer term instruments, not in short, relative to a random walk. Our results point to the existence of an unspanned volatility factor.

Dynamic Global Currency Hedging

Christensen, B. J., Varneskov, R. T. — Fri, 01 Jan 2021 10:43:40 +0100

This article proposes a model for discrete-time currency hedging based on continuous-time movements in portfolio and foreign exchange rate returns. The vector of optimal currency exposures is given by the negative realized regression coefficients from a one-period conditional expectation of the intraperiod quadratic covariation matrix for portfolio and exchange rate returns. Empirical results from an extensive hedging exercise for equity investments illustrate that currency exposures exhibit important time variation, leading to substantial volatility reductions when hedging, without sacrificing returns. A risk-averse investor is willing to pay several hundred annual basis points to switch from existing hedging methods to the proposed dynamic strategies.

Measuring the impact of clean energy production on CO₂ abatement in Denmark

Christensen, B. J., Datta Gupta, N., Santucci de Magistris, P. — Fri, 01 Jan 2021 10:43:40 +0100

Using annual data from 1978 through 2016, and monthly data from January 2005 through November 2017 from Denmark, we provide a precise estimate of the upper bound on the potential impact of the adoption of wind energy on the reduction of (Formula presented.) emissions from energy production. We separate causal impacts from endogenous effects in regressions using instrumental variables including average wind speed, and from spurious effects in dynamic systems using impulse-response analysis and cointegration techniques. A one percentage point increase in the share of wind in total energy production is found to cause a reduction in (Formula presented.) emissions of the order 0.3%, based on endogeneity-corrected regression, and 0.5% over 2 years in a fractional vector error-correction model, after allowing the cumulative effects to take place. This corresponds to an upper bound estimate of 0.69 tonnes of (Formula presented.) emissions avoided per additional MWh of wind energy produced. We find that after a structural break at the time of introduction of the EU ETS and the Kyoto Protocol in 2005, the country has been on track towards meeting its long-term goals for emission reduction and green energy production, but not before.

Optimal control of investment, premium and deductible for a non-life insurance company

Christensen, B. J., Parra-Alvarez, J. C., Serrano, R. — Thu, 01 Oct 2020 10:43:40 +0200

A risk-averse insurance company controls its reserve, modelled as a perturbed Cramér-Lundberg process, by choice of both the premium p and the deductible K offered to potential customers. The surplus is allocated to financial investment in a riskless and a basket of risky assets potentially correlating with the insurance risks and thus serving as a partial hedge against these. Assuming customers differ in riskiness, increasing p or K reduces the number of customers n(p,K) and increases the arrival rate of claims per customer λ(p,K) through adverse selection, with a combined negative effect on the aggregate arrival rate n(p,K)λ(p,K). We derive the optimal premium rate, deductible, investment strategy, and dividend payout rate (consumption by the owner-manager) maximizing expected discounted life-time utility of intermediate consumption under the assumption of constant absolute risk aversion. Closed-form solutions are provided under specific assumptions on the distributions of size and frequency claims.

Targeting predictors in random forest regression

Borup, D., Christensen, B. J., Mühlbach, N. N., Nielsen, M. S. — Fri, 01 May 2020 10:43:40 +0200

Random forest regression (RF) is an extremely popular tool for the analysis of high-dimensional data. Nonetheless, its benefits may be lessened in sparse settings, due to weak predictors, and a pre-estimation dimension reduction (targeting) step is required. We show that proper targeting controls the probability of placing splits along strong predictors, thus providing an important complement to RF’s feature sampling. This is supported by simulations using representative finite samples. Moreover, we quantify the immediate gain from targeting in terms of increased strength of individual trees. Macroeconomic and financial applications show that the bias-variance tradeoff implied by targeting, due to increased correlation among trees in the forest, is balanced at a medium degree of targeting, selecting the best 10–30% of commonly applied predictors. Improvements in predictive accuracy of targeted RF relative to ordinary RF are considerable, up to 12–13%, occurring both in recessions and expansions, particularly at long horizons.

Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market

Asmussen, S., Christensen, B. J., Thøgersen, J. — Mon, 01 Jul 2019 10:43:40 +0200

Two insurance companies I ₁ ,I ₂ with reserves R ₁ (t),R ₂ (t) compete for customers, such that in a suitable stochastic differential game the smaller company I ₂ with R ₂ (0)1 (0) aims at minimizing R ₁ (t)−R ₂ (t) by using the premium p ₂ as control and the larger I ₁ at maximizing by using p ₁ . The dependence of reserves on premia is derived by modelling the customer's problem explicitly, accounting for market frictions V, reflecting differences in cost of search and switching, information acquisition and processing, or preferences. Assuming V to be random across customers, the optimal simultaneous choice p ₁ ^∗ ,p ₂ ^∗ of premiums is derived and shown to provide a Nash equilibrium for beta distributed V. The analysis is based on the diffusion approximation to a standard Cramér–Lundberg risk process extended to allow investment in a risk-free asset.

Stackelberg equilibrium premium strategies for push-pull competition in a non-life insurance market with product differentiation

Asmussen, S., Christensen, B. J., Thøgersen, J. — Wed, 01 May 2019 10:43:40 +0200

Two insurance companies I1, 1 I2 with reserves R1(t), R2(t) compete for customers, such that in a suitable differential game the smaller company I2 with R2(0) < R1(0) aims at minimizing R1(t) 􀀀 R2(t) by using the premium p2 as control and the larger I1 at maximizing by using p1. Deductibles K1, K2 are fixed but may be different. If K1 > K2 and I2 is the leader choosing its premium first, conditions for Stackelberg equilibrium are established. For gamma distributed rates of claim arrivals, explicit equilibrium premiums are obtained, and shown to depend on the running reserve difference. The analysis is based on the diffusion approximation to a standard Cramér-Lundberg risk process extended to allow investment in a risk-free asset.

Assessing predictive accuracy in panel data models with long-range dependence

Borup, D., Christensen, B. J., Ergemen, Y. E. — Thu, 28 Mar 2019 10:43:40 +0100

This paper proposes tests of the null hypothesis that model-based forecasts
are uninformative in panels, allowing for individual and interactive fixed effects
that control for cross-sectional dependence, endogenous predictors, and
both short-range and long-range dependence. We consider a Diebold-Mariano
style test based on comparison of the model-based forecast and a nested nopredictability benchmark, an encompassing style test of the same null, and a
test of pooled uninformativeness in the entire panel. A simulation study shows
that the encompassing style test is reasonably sized in finite samples, whereas
the Diebold-Mariano style test is oversized. Both tests have non-trivial local
power. The methods are applied to the predictive relation between economic
policy uncertainty and future stock market volatility in a multi-country analysis.

An asset pricing approach to testing general term structure models

Christensen, B. J., van der Wel, M. — Tue, 01 Jan 2019 10:43:40 +0100

We develop a new empirical approach to term structure analysis that allows testing for time-varying risk premiums and arbitrage opportunities in models with both unobservable factors and factors identied as the innovations to observed macroeconomic variables. Factors may play double roles as both covariance-generating common shocks driving yields and determinants of market prices of risk in cross-sectional pricing. The evidence favors time-varying risk prices signicantly related to the second Stock-Watson principal component of macroeconomic variables and to changes in the
industrial production index. Our preferred specication includes these two observable and two unobservable factors, with the no-arbitrage condition imposed.

Introduction to globalization

Christensen, B. J., Kowalczyk, C. — Sun, 01 Jan 2017 10:43:40 +0100

Globalization implies the continuing expansion and intensification of economic, political, social, cultural and judicial relations across borders. It is furthered by reductions in transportation and communication costs, the rise of new information technologies, such as the internet, and liberalizations in the markets for goods, services, labor, capital, and technology. Although it also occurs within existing legal structures, globalization in many cases involves political decisions about deregulation, free trade, and the integration of markets. It changes the life styles and living conditions for people around the world, presenting new opportunities to some, but risks and threats to others. Individuals, firms, governments, and transnational organizations that are lifted out of the framework of the nation state, like the World Bank, United Nations, the European Union, and multinational firms all face challenges of how to respond to globalization. The present volume provides important information to private and public decision makers who are choosing strategies for production, investment, and public policy in the increasingly globalized society.

Business on globalization-A panel

Knudstorp, J. V., Maskus, K., Teece, D., Christensen, B. J. — Sun, 01 Jan 2017 10:43:40 +0100

This chapter is based on a transcription of the panel '‘Business on Globalization,'’ moderated by Bent Jesper Christensen, Aarhus University, on November 10, 2011, at the Aarhus University conference Globalization: Strategies and Effects, Hotel Koldingfjord, Denmark. Introductory remarks by Jørgen Vig Knudstorp are in Sect. 1, remarks on globalization, trade, power, culture, digitalization, demography, and planet issues in Sect. 2, on free trade, complexity, cycles, and inequality in Sect. 3, and on operating models, location decisions, and marketing in Sect. 4. Questions by panelists Keith Maskus and David Teece are in Sect. 5, along with replies by Jørgen Vig Knudstorp.

End-of-Life Medical Spending In Last Twelve Months of Life is Lower than Previously Reported

French, E. ., Aragon, M., Mccauley, J. ., et al. — Sun, 01 Jan 2017 10:43:40 +0100

Globalization

Sun, 01 Jan 2017 10:43:40 +0100

Medium Band Least Squares Estimation of Fractional Cointegration in the Presence of Low-Frequency Contamination

Christensen, B. J., Varneskov, R. T. — Sat, 01 Apr 2017 10:43:40 +0200

This paper introduces a new estimator of the fractional cointegrating vector between stationary long memory processes that is robust to low-frequency contamination such as random level shifts, outliers, Markov switching means, and certain deterministic trends. In particular, the proposed medium band least squares (MBLS) estimator uses sample-size-dependent trimming of frequencies in the vicinity of the origin to account for such contamination. Consistency and asymptotic normality of the MBLS estimator are established, a feasible inference procedure is proposed, and rigorous tools for assessing the cointegration strength and testing MBLS against the existing narrow band least squares estimator are developed. Finally, the asymptotic framework for the MBLS estimator is used to provide new perspectives on volatility factors in an empirical application to long-span realized variance series for S&P 500 equities. (C) 2016 Elsevier B.V. All rights reserved.

Medical Spending in Denmark

Christensen, B. J., Gørtz, M., Kallestrup-Lamb, M. — Mon, 21 Nov 2016 10:43:40 +0100

Using full population longitudinal data from merged administrative registers
for Denmark, we document that medical spending is highly concentrated in the
population, and persistent through time at the individual level. In
addition, we provide overviews of institutional details of the Danish health
care system, aggregate trends in health care expenditures, and the relevant
register data. Nearly two thirds of expenditures are on hospitals and one
fifth on long-term care, with the remainder roughly equally split between
primary care and prescription drugs. Health expenditures are higher for men
than for women from age 61 to 78, and otherwise higher for women. Between
ages 50 and 80, hospital expenditures more than triple for men while more
than doubling for women, and total health expenditures quadruple for men
while tripling for women. The top 1 per cent of all spenders account for nearly one-quarter of total spending in a given year, and averaging over three years
only reduces this fraction to one-fifth. The top 20 per cent of spenders in a given year are more likely to remain in that category two years later than not. The poorest fifth of the population aged 25 and above is responsible for more than twice as much spending on health as the richest, and this reverse social gradient is even stronger for long-term care and is stronger among men than among women, especially in hospital expenses. Expenditures in the year (over the three years) before death are nearly 12 times (respectively nine times) higher than average, but nevertheless are only 11 per cent (respectively a quarter) of lifetime spending. Out-of-pocket expenses on prescription drugs only amount to 3 per cent of total health expenditures and are less concentrated than these.

Estimating dynamic equilibrium models using mixed frequency macro and financial data

Christensen, B. J., Posch, O., Van Der Wel, M. — Thu, 01 Sep 2016 10:43:40 +0200

We provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency, along with macro series at standard lower frequency. Our formulation of the macro-finance model in continuous time conveniently accounts for the difference in observation frequency. We suggest the use of martingale estimating functions (MEF) to infer the structural parameters of the model directly through a nonlinear scheme. This method is compared to regression-based methods and the generalized method of moments (GMM). We illustrate our approaches by estimating various versions of the AK-Vasicek model with mean-reverting interest rates. We provide asymptotic theory and Monte Carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of US macro and financial data.

Retirement and Health in the Nordic Welfare State

Gupta, N. D., Christensen, B. J. — Thu, 01 Jan 2015 10:43:40 +0100

Dynamic Global Currency Hedging

Christensen, B. J., Varneskov, R. T. — Tue, 19 Jan 2016 10:43:40 +0100

This paper proposes a model for discrete-time hedging based on continuous-time movements in portfolio and foreign currency exchange rate returns. In particular, the vector of optimal currency exposures is shown to be given by the negative realized regression coefficients from a one-period conditional expectation of the intra-period quadratic covariation matrix for portfolio and foreign exchange rate returns. These are labelled the realized currency betas. The model, hence, facilitates dynamic hedging strategies that depend exclusively on the dynamic evolution of the ex-post quadratic covariation matrix. These hedging strategies are suggested implemented using modern, yet simple, non-parametric techniques to accurately measure and dynamically model historical quadratic covariation matrices. The empirical results from an extensive hedging exercise for equity investments illustrate that the realized currency betas exhibit important time variation, leading to substantial economic, as well as statistically significant, volatility reductions from the proposed hedging strategies, compared to existing benchmarks, without sacrificing returns. As a result, a risk-averse investor is shown to be willing to pay several hundred basis points to switch from existing hedging methods to the proposed realized currency beta approach. Interestingly, the empirical analysis strongly suggests that the superior performance of the latter during the most recent global financial crisis of 2008 is, at least partially, funded by carry traders.

Medium Band Least Squares Estimation of Fractional Cointegration in the Presence of Low-Frequency Contamination

Christensen, B. J., Varneskov, R. T. — Mon, 01 Jun 2015 10:43:40 +0200

This paper introduces a new estimator of the fractional cointegrating vector between stationary long memory processes that is robust to low-frequency contamination such as level shifts, i.e., structural changes in the means of the series, and deterministic trends. In particular, the proposed medium band least squares (MBLS) estimator uses sample dependent trimming of frequencies in the vicinity of the origin to account for such contamination. Consistency and asymptotic normality of the MBLS estimator are established, a feasible inference procedure is proposed, and rigorous tools for assessing the cointegration strength and testing MBLS against the existing narrow band least squares estimator are developed. Finally, the asymptotic framework for the MBLS estimator is used to provide new perspectives on volatility factors in an empirical application to long-span realized variance series for S&P 500 equities.

The impact of financial crises on the risk-return tradeoff and the leverage effect

Christensen, B. J., Nielsen, M. Ø., Zhu, J. — Thu, 01 Jan 2015 10:43:40 +0100

We investigate the impact of financial crises on two fundamental features of stock returns, namely, the risk-return tradeoff and the leverage effect. We apply the fractionally integrated exponential GARCH-in-mean (FIEGARCH-M) model for daily stock return data, which includes both features and allows the co-existence of long memory in volatility and short memory in returns. We extend this model to allow the financial parameters governing the volatility-in-mean effect and the leverage effect to change during financial crises. An application to the daily U.S. stock index return series from 1926 through 2010 shows that both financial effects increase significantly during crises. Strikingly, the risk-return tradeoff is significantly positive only during financial crises, and insignificant during non-crisis periods. The leverage effect is negative throughout, but increases significantly by about 50% in magnitude during financial crises. No such changes are observed during NBER recessions, so in this sense financial crises are special. Applications to a number of major developed and emerging international stock markets confirm the increase in the leverage effect, whereas the international evidence on the risk-return tradeoff is mixed.

The SR Approach: A New Estimation Method for Non-Linear and Non-Gaussian Dynamic Term Structure Models

Andreasen, M. M., Christensen, B. J. — Thu, 01 Jan 2015 10:43:40 +0100

Portfolio size as funktion of the premium: modeling and optimization

Asmussen, S., Christensen, B. J., Taksar, M. I. — Tue, 01 Jan 2013 10:43:40 +0100

An insurance company has a large number N of potential customers characterized by i.i.d. r.v.'s A1,…,AN giving the arrival rates of claims. Customers are risk averse, and a customer accepts an offered premium p according to his A-value. The modeling further involves a discount rate d>r of customers, where r is the risk-free interest rate. Based on calculations of the customers' present values of the alternative strategies of insuring and not insuring, the portfolio size n(p) is derived, and also the rate of claims from the insured customers is given. Further, the value of p which is optimal for minimizing the ruin probability is derived in a diffusion approximation to the Cramér-Lundberg risk process with an added liability rate L of the company. The solution involves the Lambert W function. Similar discussion is given for extensions involving customers having only partial information on their A and stochastic discount rates.

A unified framework for testing in the linear regression model under unknown order of fractional integration

Christensen, B. J., Kruse, R., Sibbertsen, P. — Mon, 28 Oct 2013 10:43:40 +0100

We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional integration. We propose a Lagrange Multiplier-type test whose limiting distribution is independent of the order of integration of the errors. Different testing scenarios for the case of deterministic and stochastic regressors are considered. Simulations demonstrate that the proposed test works well for a variety of different cases, thereby emphasizing its generality.

Portfolio size as function of the premium

Asmussen, S., Christensen, B. J., Taksar, M. — Tue, 01 Jan 2013 10:43:40 +0100

An insurance company has a large number N of potential customers characterized by i.i.d. r.v.'s A₁,...,A_N giving the arrival rates of claims. Customers are risk averse, and a customer accepts an offered premium p according to his A-value. The modelling further involves a discount rate d>r of customers, where r is the risk-free interest rate. Based on calculations of the customers' present values of the alternative strategies of insuring and not insuring, the portfolio size is derived, and also the rate of claims from the insured customers is given. Furthermore, the value of p which is optimal for minimizing the ruin probability is derived in a diffusion approximation to the Cramér-Lundberg risk process with an added liability rate L of the company. The solution involves the Lambert W function. Similar discussion is given for extensions involving customers having only partial information on their A and stochastic discount rates.

The impact of financial crises on the risk-return tradeoff and the leverage effect

Christensen, B. J., Nielsen, M. Ø., Zhu, J. — Sun, 01 Jan 2012 10:43:40 +0100

We investigate the impact of financial crises on two fundamental features of stock returns, namely, the risk-return tradeoff and the leverage effect. We apply the fractionally integrated exponential GARCH-in-mean (FIEGARCH-M) model for daily stock return data, which includes both features and allows the co-existence of long memory in volatility and short memory in returns. We extend this model to allow the financial parameters governing the volatility-in-mean effect and the leverage effect to change during financial crises. An application to the daily U.S. stock index return series from 1926 through 2010 shows that both …financial effects increase significantly during crises. Strikingly, the risk-return tradeoff is significantly positive only during financial crises, and insignificant during non-crisis periods. The leverage effect is negative throughout, but increases significantly by about 50% in magnitude during …financial crises. No such changes are observed during NBER recessions, so in this sense …financial crises are special. Applications to a number of major developed and emerging international stock markets confirm the increase in the leverage effect, whereas the international evidence on the risk-return tradeoff is mixed.

The Impact of Health Changes on Labor Supply: Evidence from Merged Data on Individual Objective Medical Diagnosis Codes and Early Retirement Behavior

Christensen, B. J., Kallestrup-Lamb, M. — Sun, 01 Jan 2012 10:43:40 +0100

The justification bias in the estimated impact of health shocks on retirement is mitigated by using objective health measures from a large, register-based longitudinal data set including medical diagnosis codes, along with labor market status, financial, and socio-economic variables. The duration until retirement is modeled using single and competing risk specifications, observed and unobserved heterogeneity, and flexible baseline hazards. Wealth is used as a proxy for elapsed duration to mitigate the potential selection bias stemming from conditioning on initial participation. The competing risk specification distinguishes complete multi-period routes to retirement, such as unemployment followed by early retirement. A result on comparison of coefficients across all states is offered. The empirical results indicate a strong impact of health changes on retirement, and hence a large potential for public policy measures intended to retain older workers longer in the labor force. Disability responds more to health shocks than early retirement, especially to diseases of the circulatory, respiratory, and musculoskeletal systems, as well as mental and behavioral disorders. Some unemployment spells followed by early retirement appear voluntary, and spurred by life style diseases.

Estimating Dynamic Equilibrium Models using Macro and Financial Data

Christensen, B. J., Posch, O., van der Wel, M. — Sat, 01 Jan 2011 10:43:40 +0100

We show that including financial market data at daily frequency, along with macro series at standard lower frequency, facilitates statistical inference on structural parameters in dynamic equilibrium models. Our continuous-time formulation conveniently accounts for the difference in observation frequency. We suggest two approaches for the estimation of structural parameters. The first is a simple regression-based procedure for estimation of the reduced-form parameters of the model, combined with a minimum-distance method for identifying the structural parameters. The second approach uses martingale estimating functions to estimate the structural parameters directly through a non-linear optimization scheme. We illustrate both approaches by estimating the stochastic AK model with mean-reverting spot interest rates. We also provide Monte Carlo evidence on the small sample behavior of the estimators and estimate the model using 20 years of U.S. macro and financial data.

Latent Integrated Stochastic Volatility, Realized Volatility, and Implied Volatility: A State Space Approach

Bach, C., Christensen, B. J. — Sun, 14 Feb 2010 10:43:40 +0100

We include simultaneously both realized volatility measures based on high-frequency asset returns and implied volatilities backed out of individual traded at the money option prices in a state space approach to the analysis of true underlying volatility. We model integrated volatility as a latent fi…rst order Markov process and show that our model is closely related to the CEV and Barndorff-Nielsen & Shephard (2001) models for local volatility. We show that if measurement noise in the observable volatility proxies is not accounted for, then the estimated autoregressive parameter in the latent process is downward biased. Implied volatility performs better than any of the alternative realized measures when forecasting future integrated volatility. The results are largely similar across the stock market (S&P 500), bond market (30-year U.S. T-bond), and foreign currency exchange market ($/£ ).

Semiparametric Inference in a GARCH-in-Mean Model

Christensen, B. J., Dahl, C. M., Iglesias, E. . — Sun, 01 Jan 2012 10:43:40 +0100

Periodicity, Non-stationarity, and Forecasting of Economic and Financial Time Series: Editors' Introduction

Bollerslev, T., Christensen, B. J., Haldrup, N., Lunde, A. — Sat, 01 Jan 2011 10:43:40 +0100

The Impact of Health Changes on Labor Supply: Evidence from Merged Data on Individual Objective Medical Diagnosis Codes and Early Retirement Behavior

Christensen, B. J., Kallestrup-Lamb, M. — Fri, 01 Jan 2010 10:43:40 +0100

People quit the labor force for many different reasons, voluntarily or not, through various arrangements such as unemployment benefits, disability benefits or specially designed early retirement schemes. This paper complements the existing literature by considering a large, register-based sample including objective medical diagnosis codes. We estimate detailed hazard models of duration until retirement, controlling for unobserved heterogeneity and nonparametric baseline hazards, as well as observed heterogeneity through time-varying explanatory variables. These include diagnosis codes, along with a host of demographic, labor market and financial regressors. The panel structure of the data allows following individuals year by year from the age of 50 and precisely measure changes in objectively measured health and other regressors, as well as labor market status. We consider 12 broad, mutually exclusive and exhaustive categories of health diagnoses defined by aggregation across ICD codes. The use of objective medical diagnosis codes should eliminate the justification bias due to self-reports of health, and the large sample size obtained by using register rather than survey data should mitigate the e¤ect of any remaining mismeasurement of true work incapacity. Together, these improvements should help distinguish empirically important effects of health and economic variables on retirement. We distinguish a number of alternative exit routes, in particular, disability, early retirement, unemployment, and others (including out of the labor force and welfare). We estimate both single risk models, lumping all retirement states, and competing risk specifications, including all separate exit routes. Throughout, females are included in the estimations, and we present separate results by gender. We find sizeable differences in retirement behavior across marital status, gender, labor market attachment, occupation, income, and in particular health. We find that the disability retirement exit route that requires specific medical criteria to be met is different from the early retirement route. The latter shares similarities with private pension schemes in a number of countries, including the U.S., where benefits are tied to previous wages, and employers also contribute to this retirement scheme. These differences are pronounced within labor market attachment, income, and in particular health. Furthermore, unemployment followed by early retirement is different from unemployment followed by other programs regarding marital status, gender, income, and health. These comparisons hinge on the competing risk framework. Finally, even when using objective medical diagnosis measures we still find significant effects from health on retirement. Thus, not all health impact on retirement reported in earlier literature was due to justification bias.

Level Shifts in Volatility and the Implied-Realized Volatility Relation

Christensen, B. J., de Magistris, P. S. — Fri, 01 Jan 2010 10:43:40 +0100

We propose a simple model in which realized stock market return volatility and implied volatility backed out of option prices are subject to common level shifts corresponding to movements between bull and bear markets. The model is estimated using the Kalman filter in a generalization to the multivariate case of the univariate level shift technique by Lu and Perron (2008). An application to the S&P500 index and a simulation experiment show that the recently documented empirical properties of strong persistence in volatility and forecastability of future realized volatility from current implied volatility, which have been interpreted as long memory (or fractional integration) in volatility and fractional cointegration between implied and realized volatility, are accounted for by occasional common level shifts.

The Risk-Return Tradeoff and Leverage Effect in a Stochastic Volatility-in-Mean Model

Christensen, B. J., Posedel, P. — Fri, 01 Jan 2010 10:43:40 +0100

We study the risk premium and leverage effect in the S&P500 market using the stochastic
volatility-in-mean model of Barndor¤-Nielsen & Shephard (2001). The Merton (1973, 1980)
equilibrium asset pricing condition linking the conditional mean and conditional variance of
discrete time returns is reinterpreted in terms of the continuous time model. Tests are per-
formed on the risk-return relation, the leverage effect, and the overidentifying zero intercept
restriction in the Merton condition. Results are compared across alternative volatility proxies,
in particular, realized volatility from high-frequency (5-minute) returns, implied Black-Scholes
volatility backed out from observed option prices, model-free implied volatility (VIX), and
staggered bipower variation. Our results are consistent with a positive risk-return relation and
a significant leverage effect, whereas an additional overidentifying zero intercept condition is
rejected. We also show that these inferences are sensitive to the exact timing of the chosen
volatility proxy. Robustness of the conclusions is verified in bootstrap experiments.

An Asset Pricing Approach to Testing General Term Structure Models including Heath-Jarrow-Morton Specifications and Affine Subclasses

Christensen, B. J., van der Wel, M. — Fri, 01 Jan 2010 10:43:40 +0100

We develop a new empirical approach to term structure analysis that allows testing
for time-varying risk premia and for the absence of arbitrage opportunities based on
the drift restriction within the Heath, Jarrow and Morton (1992) framework. As in the
equity case, a zero intercept condition is tested, but in addition to the standard bilinear
term in factor loadings and market prices of risk, the relevant mean restriction in the
term structure case involves an additional nonlinear (quadratic) term in factor loadings.
We estimate our general model using likelihood-based dynamic factor model techniques
for a variety of volatility factors, and implement the relevant likelihood ratio tests. Our
factor model estimates are similar across a general state space implementation and
an alternative robust two-step principal components approach. The evidence favors
time-varying market prices of risk. Most of the risk premium is associated with the
slope factor, and individual risk prices depend on own past values, factor realizations,
and past values of other risk prices, and are significantly related to the output gap,
consumption, and the equity risk price. The absence of arbitrage opportunities is
strongly rejected with one or two factors in the model, but not with three or more
factors.

The SR Approach: a new Estimation Method for Non-Linear and Non-Gaussian Dynamic Term Structure Models

Andreasen, M. M., Christensen, B. J. — Fri, 01 Jan 2010 10:43:40 +0100

This paper suggests a new and easy approach to estimate linear and non-linear dynamic term
structure models with latent factors. We impose no distributional assumptions on the factors and
they may therefore be non-Gaussian. The novelty of our approach is to use many observables (yields
or bonds prices) in the cross-section dimension. An important bene…t of using many observables
in each time period is that the latent factors can be estimated quite accurately using standard
regressions, and that parameters can be estimated by standard moment matching methods.

Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model

Christensen, B. J., Nielsen, M. Ø., Zhu, J. — Fri, 01 Jan 2010 10:43:40 +0100

Udgivelsesdato: June

The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock, and Bond Markets

Busch, T., Christensen, B. J., Nielsen, M. Ø. — Sat, 01 Jan 2011 10:43:40 +0100

Economic Modeling and Inference

Christensen, B. J., Kiefer, N. M. — Thu, 01 Jan 2009 10:43:40 +0100

Optimal inference in dynamic models with conditional moment restrictions

Christensen, B. J., Sørensen, M. — Tue, 01 Jan 2008 10:43:40 +0100

By an application of the theory of optimal estimating function, optimal in-
struments for dynamic models with conditional moment restrictions are derived.
The general efficiency bound is provided, along with estimators attaining the
bound. It is demonstrated that the optimal estimators are always at least as ef-
ficient as the traditional optimal generalized method of moments estimator, and
usually more efficient. The form of our optimal instruments resembles that from
Newey (1990), but involves conditioning on the history of the stochastic pro-
cess. In the special case of i.i.d. observations, our optimal estimator reduces to
Newey's. Specification and hypothesis testing in our framework are introduced.
We derive the theory of optimal instruments and the associated asymptotic dis-
tribution theory for general cases including non-martingale estimating functions
and general history dependence. Examples involving time-varying conditional
volatility and stochastic volatility are offered.

Semiparametric Inference in a GARCH-in-Mean Model

Christensen, B. J., Dahl, C. M., Iglesias, E. M. — Tue, 01 Jan 2008 10:43:40 +0100

A new semiparametric estimator for an empirical asset pricing model with general nonpara-
metric risk-return tradeoff and a GARCH process for the underlying volatility is introduced.
The estimator does not rely on any initial parametric estimator of the conditional mean func-
tion, and this feature facilitates the derivation of asymptotic theory under possible nonlinearity
of unspecified form of the risk-return tradeoff. Besides the nonlinear GARCH-in-mean effect,
our specification accommodates exogenous regressors that are typically used as conditioning
variables entering linearly in the mean equation, such as the dividend yield. Using the profile
likelihood approach, we show that our estimator under stated conditions is consistent, asymp-
totically normal, and efficient, i.e. it achieves the semiparametric lower bound. A sampling
experiment provides evidence on finite sample properties as well as comparisons with the fully
parametric approach and the iterative semiparametric approach using a parametric initial esti-
mate proposed by Conrad and Mammen (2008). An empirical application to the daily S&P 500
stock market returns suggests that the linear relation between conditional expected return and
conditional variance of returns from the literature is misspecified, and this could be the reason
for the disagreement on the sign of the relation.

The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock and Bond Markets

Christensen, B. J. — Mon, 01 Jan 2007 10:43:40 +0100

We study the forecasting of future realized volatility in the stock, bond, and foreign exchange markets, as well as the continuous sample path and jump components of this, from variables in the information set, including implied volatility backed out from option prices. Recent nonparametric statistical techniques are used to separate realized volatility into its continuous and jump components, thus enhancing forecasting performance as shown by Andersen et al. (2005). We generalize the heterogeneous autoregressive (HAR) model to include implied volatility as an additional regressor, and to the separate forecasting of the realized components. We also introduce a new vector HAR (VecHAR) model for the resulting simultaneous system, controlling for possible endogeneity issues in the forecasting equations. We show that implied volatility contains incremental information about future volatility relative to both continuous and jump components of past realized volatility. Perhaps surprisingly, the jump component of realized return volatility is, to some extent, predictable, and options appear to be calibrated to incorporate information about future jumps.

The Effect of Long Memory in Volatility on Stock Market Fluctuations

Christensen, B. J., Nielsen, M. Ø. — Mon, 01 Jan 2007 10:43:40 +0100

Recent empirical evidence demonstrates the presence of an important long memory component in realized asset return volatility. We specify and estimate multivariate models for the joint dynamics of stock returns and volatility that allow for long memory in volatility without imposing this property on returns. Asset pricing theory imposes testable cross-equation restrictions on the system that are not rejected in our preferred specifications, which include a strong financial leverage effect. We show that the impact of volatility shocks on stock prices is small and short-lived, in spite of a positive risk-return trade-off and long memory in volatility.

Market Power in Power Markets: Evidence from Forward Prices of Electricity

Christensen, B. J., Jensen, T. E., Mølgaard, R. — Mon, 01 Jan 2007 10:43:40 +0100

We examine the forward market for electricity for indications of misuse of market power, using a unique data set on OTC price indications posted by Elsam A/S, the dominant producer in Western Denmark, which is one of the price areas under the Nordic power exchange Nord Pool. The Danish Competition Council (the regulatory government agency) has ruled that Elsam has used its dominant position to obtain excessive spot prices over a period from July 2003 through December 2006. We show that significant forward premia exist, and that they are related both to spot market volatility and misuse of market power in the spot market, indicating that misuse of market power in the forward market accompanied that which took place in the spot market, according to this ruling. This is consistent with the hypothesis that Elsam used the forward market to disguise its spot market manipulation. The findings are consistent across forward premium regressions and structural forward pricing models.

Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model

Christensen, B. J., Nielsen, M. Ø., Zhu, J. — Mon, 01 Jan 2007 10:43:40 +0100

We extend the fractionally integrated exponential GARCH (FIEGARCH) model for
daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen
(1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory
property of volatility carries over to returns, we consider a filtered FIEGARCH-in-mean
(FIEGARCH-M) effect in the return equation. The filtering of the volatility-in-mean
component thus allows the co-existence of long memory in volatility and short memory in
returns. We present an application to the S&P 500 index which documents the empirical
relevance of our model

The Effect of Long Memory in Volatility on Stock Market Fluctuations

Christensen, B. J., Nielsen, M. Ø. — Mon, 01 Jan 2007 10:43:40 +0100

Recent empirical evidence demonstrates the presence of an important long memory
component in realized asset return volatility. We specify and estimate multivariate models
for the joint dynamics of stock returns and volatility that allow for long memory in volatility
without imposing this property on returns. Asset pricing theory imposes testable cross-
equation restrictions on the system that are not rejected in our preferred specifications,
which include a strong financial leverage effect. We show that the impact of volatility
shocks on stock prices is small and short-lived, in spite of a positive risk-return trade-off
and long memory in volatility.

Panel Data and Structural Labour Market Models

Bunzel, H., Christensen, B. J. — Sat, 01 Jan 2000 10:43:40 +0100

The Implied-Realized Volatility Relation Revisited

Christensen, B. J., Hansen, C. S. — Thu, 01 Jan 1998 10:43:40 +0100

The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock, and Bond Markets

Christensen, B. J., Busch, T., Nielsen, M. Ø. — Sun, 01 Jan 2006 10:43:40 +0100

Publications - Bent Jesper Christensen

Estimation of continuous-time linear DSGE models from discrete-time measurements

Optimal control of investment, premium and deductible for a non-life insurance company

The incremental information in the yield curve about future interest rate risk

Dynamic Global Currency Hedging

Measuring the impact of clean energy production on CO2 abatement in Denmark

Optimal control of investment, premium and deductible for a non-life insurance company

Targeting predictors in random forest regression

Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market

Stackelberg equilibrium premium strategies for push-pull competition in a non-life insurance market with product differentiation

Assessing predictive accuracy in panel data models with long-range dependence

An asset pricing approach to testing general term structure models

Introduction to globalization

Business on globalization-A panel

End-of-Life Medical Spending In Last Twelve Months of Life is Lower than Previously Reported

Globalization

Medium Band Least Squares Estimation of Fractional Cointegration in the Presence of Low-Frequency Contamination

Medical Spending in Denmark

Estimating dynamic equilibrium models using mixed frequency macro and financial data

Retirement and Health in the Nordic Welfare State

Dynamic Global Currency Hedging

Medium Band Least Squares Estimation of Fractional Cointegration in the Presence of Low-Frequency Contamination

The impact of financial crises on the risk-return tradeoff and the leverage effect

The SR Approach: A New Estimation Method for Non-Linear and Non-Gaussian Dynamic Term Structure Models

Portfolio size as funktion of the premium: modeling and optimization

A unified framework for testing in the linear regression model under unknown order of fractional integration

Portfolio size as function of the premium

The impact of financial crises on the risk-return tradeoff and the leverage effect

The Impact of Health Changes on Labor Supply: Evidence from Merged Data on Individual Objective Medical Diagnosis Codes and Early Retirement Behavior

Estimating Dynamic Equilibrium Models using Macro and Financial Data

Latent Integrated Stochastic Volatility, Realized Volatility, and Implied Volatility: A State Space Approach

Semiparametric Inference in a GARCH-in-Mean Model

Periodicity, Non-stationarity, and Forecasting of Economic and Financial Time Series: Editors' Introduction

The Impact of Health Changes on Labor Supply: Evidence from Merged Data on Individual Objective Medical Diagnosis Codes and Early Retirement Behavior

Level Shifts in Volatility and the Implied-Realized Volatility Relation

The Risk-Return Tradeoff and Leverage Effect in a Stochastic Volatility-in-Mean Model

An Asset Pricing Approach to Testing General Term Structure Models including Heath-Jarrow-Morton Specifications and Affine Subclasses

The SR Approach: a new Estimation Method for Non-Linear and Non-Gaussian Dynamic Term Structure Models

Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model

The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock, and Bond Markets

Economic Modeling and Inference

Optimal inference in dynamic models with conditional moment restrictions

Semiparametric Inference in a GARCH-in-Mean Model

The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock and Bond Markets

The Effect of Long Memory in Volatility on Stock Market Fluctuations

Market Power in Power Markets: Evidence from Forward Prices of Electricity

Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model

The Effect of Long Memory in Volatility on Stock Market Fluctuations

Panel Data and Structural Labour Market Models

The Implied-Realized Volatility Relation Revisited

The Role of Implied Volatility in Forecasting Future Realized Volatility and Jumps in Foreign Exchange, Stock, and Bond Markets

Measuring the impact of clean energy production on CO₂ abatement in Denmark