Deep hedging

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We discuss how standard reinforcement learning methods can be applied to non-linear reward structures, i.e. in our case convex risk measures. As a general contribution to the use of deep learning for stochastic processes, we also show in Section 4 that the set of constrained trading strategies used by our algorithm is large enough to ε-approximate any optimal solution. Our algorithm can be implemented efficiently even in high-dimensional situations using modern machine learning tools. Its structure does not depend on specific market dynamics, and generalizes across hedging instruments including the use of liquid derivatives. Its computational performance is largely invariant in the size of the portfolio as it depends mainly on the number of hedging instruments available. We illustrate our approach by an experiment on the S&P500 index and by showing the effect on hedging under transaction costs in a synthetic market driven by the Heston model, where we outperform the standard ‘complete-market’ solution.     

Search costs and efficiency: Do unemployed workers search enough?

Many labor market policies affect the marginal benefits and costs of job search. The impact and desirability of such policies depend on the distribution of search costs. In this paper, we provide an equilibrium framework for identifying the distribution of search costs and we apply it to the Dutch labor market. In our model, the wage distribution, job search intensities, and firm entry are simultaneously determined in market equilibrium. Given the distribution of search intensities (which we directly observe), we calibrate the search cost distribution and the flow value of non-market time; these values are then used to derive the socially optimal firm entry rates and distribution of job search intensities. From a social point of view, some unemployed workers search too little due to a hold-up problem, while other unemployed workers search too much due to coordination frictions and rent-seeking behavior. Our results indicate that jointly increasing unemployment benefits and the sanctions for unemployed workers who do not search at all can be welfare-improving.     

Accounting for age in marital search decisions

Spouse quality, measured by educational attainment, varies significantly with the age at which an individual marries, peaking in the mid-twenties then declining through the early-forties. Interestingly, this decline is much sharper for women than men, meaning women increasingly marry less educated men as they age. Moreover, quality has worsened for educated women over several decades, while it has improved for men. Using a non-stationary sequential search model, we identify and quantify the search frictions that generate these age-dependent marriage outcomes. We find that single-life utility is typically the dominant friction, though college women in the 1950 and 1970 cohorts are affected even more by deteriorating suitor quality. Regardless of educational status, individual choice (as opposed to pure luck) is pivotal in explaining marriage market outcomes earlier in life.     

Bargaining frictions, labor income taxation, and economic performance

This paper is an attempt to explain differences in economic performance between a subset of OECD countries. We classify countries in terms of their degree of rigidity in the labor market, and use a matching model with labor/leisure choice, bargaining frictions, and labor income taxation to capture these rigidity differences. Added flexibility improves economic performance in different ways depending on whether income taxation is high or low. Feeding income taxation rates estimated from the countries at hand, we find that the model is able to replicate the observed rigidity levels. The model is also shown to reproduce well cross-country differences in non-employment population ratios and the share of part-time jobs. In the absence of rigidity differences, taxation shows little promise to replicate cross-country differences, as it has insufficient quantitative effects on production and productivity. However, the interaction of rigidity and income taxation is crucial in explaining the empirical patterns of the non-employment rate and of the share of part-time jobs.     

What (really) accounts for the fall in hours after a technology shock?

The paper asks how state of the art DSGE models that account for the conditional response of hours following a positive neutral technology shock compare in a marginal likelihood race. To that end we construct and estimate several competing small-scale DSGE models that extend the standard real business cycle model. In particular, we identify from the literature six different hypotheses that generate the empirically observed decline in hours worked after a positive technology shock. These models alternatively exhibit (i) sticky prices; (ii) firm entry and exit with time to build; (iii) habit in consumption and costly adjustment of investment; (iv) persistence in the permanent technology shocks; (v) labor market friction with procyclical hiring costs; and (vi) Leontief production function with labor-saving technology shocks. In terms of model posterior probabilities, impulse responses, and autocorrelations, the model favored is the one that exhibits habit formation in consumption and investment adjustment costs. A robustness test shows that the sticky price model becomes as competitive as the habit formation and costly adjustment of investment model when sticky wages are included.     

Bayesian Evaluation of DSGE Models with Financial Frictions

We evaluate two most popular approaches to implementing financial frictions into DSGE models: the Bernanke, Gertler, and Gilchrist ( 1999 ) setup, where frictions affect the price of loans, and the Kiyotaki and Moore ( 1997 ) model, where they concern the quantity of loans. We take both models to the data and check how well they fit it on several margins. Overall, comparing the models favors the Bernanke, Gertler, and Gilchrist framework. However, even this model does not make a clear improvement over the New Keynesian benchmark in terms of marginal likelihood and similarity of impulse responses to those obtained from a VAR.     

Costly external finance and labor market dynamics

We study the role of agency frictions and costly external finance in cyclical labor market dynamics, with a focus on how credit-market frictions may amplify aggregate TFP shocks. The main result is that aggregate TFP shocks lead to large fluctuations of labor market quantities if the model is calibrated to the empirically observed countercyclicality of the finance premium. A financial accelerator mechanism thus amplifies labor market fluctuations by rendering rigidity in real wage dynamics. In contrast, if the finance premium is procyclical, which the model can be parameterized to accommodate, amplification is absent, and labor-market fluctuations display the Shimer (2005) puzzle.     

Optimal dividend policy with random interest rates

Several recent papers have studied the impact of macroeconomic shocks on the financial policies of firms. However, they only consider the case where these macroeconomic shocks affect the profitability of firms but not the financial markets conditions. We study the polar case where the profitability of firms is stationary, but interest rates and issuance costs are governed by an exogenous Markov chain. We characterize the optimal dividend policy and show that these two macroeconomic factors have opposing effects: all things being equal, firms distribute more dividends when interest rates are high and less when issuing costs are high.     

Duration of bankruptcy proceedings and monetary policy effectiveness

A common assumption in well-known costly-state-verification frameworks is that when a borrower defaults, creditors receive a payoff immediately (after incurring bankruptcy costs). While this assumption enhances tractability, it is unrealistic given the considerable delays in the actual practice of bankruptcy. In this paper, I identify the duration of bankruptcy proceedings as an additional source of friction in financial markets and investigate the relationship between this friction and the effectiveness of monetary policy by using U.S. state-level data. Consistent with the commonly-observed positive relationship between the degree of standard financial frictions and the amplitude of macroeconomic responses, I find that U.S. monetary policy is most effective in states with longer bankruptcy proceedings.     

Financial sophistication and the distribution of the welfare cost of inflation

The welfare cost of anticipated inflation is quantified in a calibrated model of the U.S. economy that exhibits tractable equilibrium dispersion in wealth and earnings. Inflation does not generate large losses in societal welfare, yet its impact varies noticeably across segments of society depending also on the financial sophistication of the economy. If money is the only asset, then inflation mostly hurts the wealthier and more productive agents, while those poorer and less productive may even benefit from inflation. The converse holds in a more sophisticated financial environment where agents can insure against consumption risk with assets other than money.