Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I

We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability properties of such discretization. This method should provide, in particular, useful and concrete informations on how good is any numerical scheme used to integrate a given integrable PDE. The procedure, illustrated on a fairly general 10-parameter family of discretizations of the nonlinear Schroedinger equation, consists of the following three steps: i) the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in epsilon, following the Degasperis - Manakov - Santini procedure; ii) the application, to such expansion, of the Degasperis - Procesi (DP) integrability test, to test the asymptotic integrability properties of the discrete system and its ``distance'' from its continuous limit; iii) the use of the main output of the DP test to construct infinitely many approximate symmetries and constants of motion of the discrete system, through novel and simple formulas.Comment: 34 pages, no figur

What do asset prices have to say about risk appetite and uncertainty?

Implied volatility indices should have information about risk parameters, once they are cleansed of the influence of normal volatility dynamics and macro-economic uncertainty. Building on intuition from the dynamic asset pricing literature, we uncover unobserved risk aversion and fundamental uncertainty from the observed time series of the VIX and the credit spreads while controlling for realized volatility, expectations about the macroeconomic outlook, and interest rates. We apply this methodology to monthly data from both Germany and the US. We find that implied volatilities contain a substantial amount of information regarding risk aversion whereas credit spreads have a lot to say about both risk aversion and uncertainty. Moreover, there is a significant comovement in the German and US risk aversion. JEL Classification:Credit Spread, Economic uncertainty, risk aversion, Time variation in risk and return, Volatility dynamics

The Maastricht Convergence Criteria and Optimal Monetary Policy for the EMU Accession Countries.

The EMU accession countries are obliged to fulfill the Maastricht convergence criteria prior to entering the EMU. This paper uses a DSGE model of a two-sector small open economy, to address the following question: How do the Maastricht convergence criteria modify optimal monetary policy in an economy facing domestic and external shocks? First, we derive the micro founded loss function that represents the objective function of the optimal monetary policy not constrained to satisfy the criteria. We find that the optimal monetary policy should not only target inflation rates in the domestic sectors and aggregate output fluctuations but also domestic and international terms of trade. Second, we show how the loss function changes when the monetary policy is constrained to satisfy the Maastricht criteria. The loss function of such a constrained policy is characterized by additional elements penalizing fluctuations of the CPI inflation rate, the nominal interest rate and the nominal exchange rate around the new targets which are potentially different from the steady state of the unconstrained optimal monetary policy. Under the chosen parameterization, the unconstrained optimal monetary policy violates two criteria: concerning the CPI inflation rate and the nominal interest rate. The constrained optimal policy results in targeting the CPI inflation rate and the nominal interest rate that are 0.7% lower (in annual terms) than the CPI inflation rate and the nominal interest rate in the countries taken as a reference. The welfare costs associated with these constraints need to be offset against credibility gains and other benefits related to the compliance with the Maastricht criteria that are not modelled. JEL Classification: F41, E52, E58, E61EMU accession countries, Maastricht convergence criteria, optimal monetary policy

Avoiding Rotated Bitboards with Direct Lookup

This paper describes an approach for obtaining direct access to the attacked squares of sliding pieces without resorting to rotated bitboards. The technique involves creating four hash tables using the built in hash arrays from an interpreted, high level language. The rank, file, and diagonal occupancy are first isolated by masking the desired portion of the board. The attacked squares are then directly retrieved from the hash tables. Maintaining incrementally updated rotated bitboards becomes unnecessary as does all the updating, mapping and shifting required to access the attacked squares. Finally, rotated bitboard move generation speed is compared with that of the direct hash table lookup method.Comment: 7 pages, 1 figure, 4 listings; replaced test positions, fixed typo

Assessing the benefits of international portfolio diversification in bonds and stocks.

This paper considers a stylized asset pricing model where the returns from exchange rates, stocks and bonds are linked by basic risk-arbitrage relationships. Employing GMM estimation and monthly data for 18 economies and the US (treated as the domestic country), we identify through a simple test the countries whose assets strongly comove with US assets and the countries whose assets might other larger diversification benefits. We also show that the strengthening of the comovement of returns across countries is neither a gradual process nor a global phenomenon, reinforcing the case for international diversification. However, our results suggest that fund managers are better other constructing portfolios selecting assets from a subset of countries than relying on either fully inter-nationally diversified or purely domestic portfolios. JEL Classification: F31, G10asset pricing, Exchange Rates, international parity conditions, market integration, stochastic discount factor

Mutation Clusters from Cancer Exome

We apply our statistically deterministic machine learning/clustering algorithm *K-means (recently developed in https://ssrn.com/abstract=2908286) to 10,656 published exome samples for 32 cancer types. A majority of cancer types exhibit mutation clustering structure. Our results are in-sample stable. They are also out-of-sample stable when applied to 1,389 published genome samples across 14 cancer types. In contrast, we find in- and out-of-sample instabilities in cancer signatures extracted from exome samples via nonnegative matrix factorization (NMF), a computationally costly and non-deterministic method. Extracting stable mutation structures from exome data could have important implications for speed and cost, which are critical for early-stage cancer diagnostics such as novel blood-test methods currently in development.Comment: 84 page

Estimate solar contribution to the global surface warming using the ACRIM TSI satellite composite

We study, by using a wavelet decomposition methodology, the solar signature on global surface temperature data using the ACRIM total solar irradiance satellite composite by Willson and Mordvinov. These data present a +0.047%/decade trend between minima during solar cycles 21-23 (1980-2002). We estimate that the ACRIM upward trend might have minimally contributed $\sim$10-30% of the global surface temperature warming over the period 1980-2002

Epstein-Zin preferences and their use in macro-finance models: implications for optimal monetary policy

Epstein-Zin preferences have attracted significant attention within the macro-finance literature based on DSGE models as they allow to substantially increase risk aversion, and consequently generate non-trivial risk premia, without compromising the ability of standard models to achieve satisfactory macroeconomic data coherence. Such appealing features certainly hold for structural modelling frameworks where monetary policy is set according to Taylor-type rules or seeks to minimize an ad hoc loss function under commitment. However, Epstein-Zin preferences may have significant quantitative implications for both asset pricing and macroeconomic allocation under a welfare-based monetary policy conduct. Against this background, the paper focuses on the impact of such preferences on the Ramsey approach to monetary policy within a medium-scale model based on Smets and Wouters (2007) including a wide range of nominal and real frictions that have proven to be relevant for quantitative business cycle analysis. After setting an empirical benchmark that generates a mean value of 100 bp for the ten-year term premium, we show that Epstein-Zin preferences significantly affect the macroeconomic outcome when optimal policy is considered. The level and the dynamic pattern of risk premia are also markedly altered. We show that the effect of Epstein-Zin preferences is extremely sensitive to the presence of real rigidities in the form of quasi-kinked demands. We also analyse how this effect can be linked to a combined e¤ect of capital accumulation and wage rigidities. JEL Classification: E44, E52, E61, G12macroeconometric equivalence, non time-separable preferences, optimal monetary policy, term premium