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Active Working Papers

Noise Regularization for Conditional Density Estimation, (joint work with Jonas Rothfuss, Fabio Ferreira, Simon Boehm, Simon Walther, Tamim Asfour, Andreas Krause), Jul 2019


Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network based CDE models can suffer from severe over-fitting when trained with the maximum likelihood objective. Due to the inherent structure of such models, classical regularization approaches in the parameter space are rendered ineffective. To address this issue, we develop a model-agnostic noise regularization method for CDE that adds random perturbations to the data during training. We demonstrate that the proposed approach corresponds to a smoothness regularization and prove its asymptotic consistency. In our experiments, noise regularization significantly and consistently outperforms other regularization methods across seven data sets and three CDE models. The effectiveness of noise regularization makes neural network based CDE the preferable method over previous non- and semi-parametric approaches, even when training data is scarce.


Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks, (joint work with Jonas Rothfuss, Fabio Ferreira, Simon Walther), Mar 2019


Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable x and a dependent variable y by modeling their conditional probability p(y|x). The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic.


Forward-looking P, (joint work with Simon Walther), Aug 2019


We present a forward-looking estimator for the time-varying physical return distribution with minimal prior assumptions about the shape of the distribution and no exogenous assumptions about the economy or preferences. Our estimator, which is based on a neural network, derives its forecasts from option-implied measures and predicts the conditional mean and volatility of returns such that profitable trading strategies can be derived. In contrast to backward-looking estimators and alternative forward-looking parametric and non-parametric approaches, its distribution forecasts cannot be rejected in statistical tests and it features lower prediction errors and higher conditional log likelihood values than the alternatives.


On the Pricing of Short- and Long-Duration Dividends: A Quadratic Macro-Factor Model, (joint work with Stephan Florig, Sven Schoemer), Sep 2018


Abstract: This is the first arbitrage-free macro-factor asset pricing model that jointly prices U.S. equity, dividend strips and Treasury bonds as a function of the economy and monetary policy. Our model generalizes popular state-of-the-art term structure models and allows us to extract new insights on how short- and long-duration dividends and their discount rates respond to changes in the economy and in monetary policy. This paper is a response to the survey on the term structure of returns of Binsbergen and Kojien [2017] who conclude that the literature lacks a macro-factor model that jointly prices equity yields, Treasury yields and the dividend yield.


A Model-Free Term Structure of U.S. Dividend Premiums, (joint work with Stephan Florig, Christian Wuchte), Aug 2018


Abstract: We construct a model-free infinite maturity term structure of dividend risk premiums. Applying the method to 2004 - 2017 U.S. data reveals that the U.S. term structure of dividend risk premiums has been hump-shaped on average: zero for instantaneous dividends, increasing for dividends that arrive within the upcoming 13 months and downward sloping thereafter. The model-free dividend risk premiums carry predictive information for future dividend growth and returns on equity and dividends. Buying the next year of S&P 500 dividends whenever the one-year dividend risk premium is positive has earned twice the Sharpe ratio of the index after transaction costs.


Option-Implied Information: What's the Vol Surface Got to Do With It?, (joint work with Simon Walther), Jun 2018


We find that option-implied information such as forward-looking variance, skewness and the variance risk premium are sensitive to the way the volatility surface is constructed. For some state-of-the-art volatility surfaces, the differences are economically surprisingly large and lead to systematic biases, especially for out-of-the-money put options. To overcome this problem we propose a volatility surface that is built with a one-dimensional kernel regression. We assess its statistical accuracy relative to existing state-of-the-art parametric, semi- and non-parametric volatility surfaces by means of leave-one-out cross-validation. Based on 14 years of end-of-day and intraday S&P 500 and Euro Stoxx 50 option data we conclude that the proposed one-dimensional kernel regression represents option market information more accurately than existing approaches of the literature.


The Euro Crisis and the 24h Pre-ECB Announcement Return, (joint work with Elmar Jakobs, Lukas May and Julius Landwehr), Aug 2017


Abstract: We document economically and statistically large 24h pre-ECB announcement returns in European equity. For selected industries, such as the European banking sector, the respective annual premium (2010 – 2015) was 12% (Sharpe ratio of 1.6); at a time when the annual return of the European banking sector was on average flat (lost decade). Our statistical tests point into the direction that in times of abnormally high fear of a eurozone break-up, investors anticipated the ECB to announce monetary policy measures that support the euro and hence the market value of equity across selected industries and countries increased in anticipation of the announcement. In that sense, we conclude that the 24h pre-ECB announcement premium is the result of a 'monetary policy put’.


Monetary Policy During Liquidity Dry-Ups, (joint work with Marliese Uhrig-Homburg and Stefan Fiesel), Dec 2016 


Abstract: We provide new international evidence for a monetary policy liquidity transmission channel in the United States, United Kingdom, and the Eurozone. The central banks of these countries are, with a different degree, able to soften the economic downward spiral after an unexpected arrival of a financial market illiquidity shock. In order to uncover this transmission channel, we rely on a nonlinear and international economic set-up to distinguish between times of liquidity crisis and non-crisis and to account for common (global) and country specific (local) shocks. We also find that out of these central banks, the Federal Reserve has an especially influential transmission channel with strong and beneficial spillover effects to the United Kingdom and the Eurozone economy.




Refereed Papers

Inflation Ambiguity and the Term Structure of U.S. Government Bonds. Journal of Monetary Economics 60, no. 2 (March 2013): 295-309.

Abstract: Variations in trend inflation are the main driver for variations in the nominal yield curve. According to empirical data, investors observe a set of empirical models that could all have generated the time-series for trend inflation. This set has been large and volatile during the 1970s and early 1980s and small during the 1990s. I show that log utility together with model uncertainty about trend inflation can explain the term premium in U.S. Government bonds. The equilibrium has two inflation premiums, an inflation risk premium and an inflation ambiguity premium.



Conference Contributions

Nominal Bonds, Real Bonds, and Equity (joint work with Andrew Ang); American Finance Assocation 2014.


Abstract: We decompose the term structure of expected equity returns into (1) the real short rate, (2) a premium for holding real long-term bonds, or the real duration premium, the excess returns of nominal long-term bonds over real bonds which reflects (3) expected inflation and (4) inflation risk, and (5) a real cashflow risk premium, which is the excess return of equity over nominal bonds. The shape of the nominal and real bond yield curves are upward sloping due to increasing duration and inflation risk premiums. The term structures of expected equity returns and equity risk premiums, in contrast, are downward sloping due to the decreasing effect of short-term expected inflation, or trend inflation, across horizons. Around 70% of the variation of expected equity returns at the 10-year horizon is due to variation in the output gap and trend inflation.


Economic Policy Uncertainty and Asset Price Volatility;  NBER Asset Pricing Meetings 2010, European Finance Assocation 2011.


Abstract: We document that fear about misspecified economic and central bank policies explain 45% of variations in bond option implied volatilities and interest rate volatilities. We endogenize this empirical pattern with a parsimonious equilibrium asset pricing model. In equilibrium, volatility is endogenously driven by fear of not knowing the data generating process that drives future economic and future central bank policies. An increase in either of these two uncertainties steepens the yield curve and increases the volatility in asset and option markets. A structural estimation of the equilibrium model explains the upward sloping term structures of interest rates, bond volatility, and option volatility, with only four in real-time observable economic and central bank related risk and uncertainty factors. The study ends with highlighting an inverse relationship between interest rates and volatility disparity from fundamentals during the policy hiking period of 2004-2007 and during QE1.



How does the Bond Market Perceive Government Interventions?; Western Finance Assocation 2011, NBER Asset Pricing Meetings 2011


Abstract: The ongoing threat of the U.S. public sector sliding over the 'fiscal cliff' urges financial economists to better understand the foundations for how government spending affects the real economy and financial markets. This paper is the first study to document that uncertainty about future government spending is a first-order risk factor in the bond market, leading to rising real and nominal interest rates, a steeper term spread, an increase in bond market volatility and bond premia. We study an equilibrium asset pricing model with a forward-looking representative agent and a forward-looking government to shed light on these empirical facts.