Approximate maximum likelihood estimation for stochastic differential equations with random effects in the drift and the diffusion

Consider N independent stochastic processes \((X_i(t), t\in [0,T])\), \(i=1,\ldots , N\), defined by a stochastic differential equation with random effects where the drift term depends linearly on a random vector \(\Phi _i\) and the diffusion coefficient depends on another linear random effect \(\Psi _i\). For these effects, we consider a joint parametric distribution. We propose and study two approximate likelihoods for estimating the parameters of this joint distribution based on discrete observations of the processes on a fixed time interval. Consistent and \(\sqrt{N}\)-asymptotically Gaussian estimators are obtained when both the number of individuals and the number of observations per individual tend to infinity. The estimation methods are investigated on simulated data and show good performances.     

The new goods margin in new markets

We analyze the role of the new goods margin in the Baltic countries’ exports and imports growth during the 1995–2008 period. Using the methodology developed in Kehoe and Ruhl (2013), we define the set of least-traded goods as those that account for the lowest 10% of total exports and imports in 1995, and then trace its growth in several markets including the Baltics’ main trade partners, the European Union and Russia. We find that, on average, by 2008 least-traded goods accounted for nearly 50% of total Baltic exports to their main trade partners. Moreover, we find that increases in the share of least-traded exports coincided with the timing of the trade liberalization reforms implemented by the Baltic countries. Least-traded imports also grew at robust rates, but their growth was lower than that of exports, accounting for slightly less than a quarter of total imports, that is, about half of the exports value. Moreover, we find that the shares of least-traded imports from the EU 15 and from Russia started diverging around the time the Baltic countries joined the EU, with the EU 15 share increasing and the Russian one declining. We also find that the Baltics’ share of least-traded exports outpaced that of other economies in Central and Eastern Europe. Finally, exports of new goods from the Baltic countries suffered noticeably during the Global Financial Crisis. After the crisis ended, the restart in new goods exports growth displayed mixed patterns.     

ANFA — National Money Creation as an Existential Threat to the Currency Union?

The recent publication of the previously secret Agreement on Net Financial Assets (ANFA) directed the public’s attention to the possibility that national central banks could create money through purchases of securities on their own account. This paper provides an overview of the legal foundations for ANFA and shows the varying extent to which the member countries use these regulations. What are the interests, risks and consequences for the countries in crisis and the currency union as a whole? Is the ECB properly monitoring ANFA purchases? Could money creation via ANFA act as an explosive device for the currency union?     

Basic Income in the Finnish Context

The goal of the Finnish experiment that started this year is to try to get some evidence on how a new social policy instrument mimicking a basic income would work and what kind of behavioural consequences it would have. At this point, there are many strong arguments being made both in favour of and opposed to basic income. Unfortunately, there are not enough facts yet. The Finnish experiment hopes to change that.     

Autonomous Driving — a Challenge for the Automotive Industry

The automotive industry is one of the most important industries in Europe. This industry is responsible for 14% of total production and capital investment in the European manufacturing sector, and in Germany the share amounts to 22%. Structural change within this crucial sector is of relevance for the whole economy. Along with alternative propulsion systems such as electromobility, (semi-)autonomous vehicles are one of the big trends in the automotive industry. For established providers, the possibility of disruptive change poses a threat to existing markets, while a gradual introduction of new technologies also increases competition. Nevertheless, with their strong market position in the premium segment and especially their relevant research activities, European and especially German automotive manufacturers are well placed to successfully master the coming challenges in the automotive market.     

The role of measurability in game-theoretic probability

This paper argues that the requirement of measurability (imposed on trading strategies) is indispensable in continuous-time game-theoretic probability. The necessity of the requirement of measurability in measure theory is demonstrated by results such as the Banach–Tarski paradox and is inherited by measure-theoretic probability. The situation in game-theoretic probability turns out to be somewhat similar in that dropping the requirement of measurability allows a trader in a financial security with a non-trivial price path to become infinitely rich while risking only one monetary unit.     

Model uncertainty,recalibration, and the emergence of delta–vega hedging

We study option pricing and hedging with uncertainty about a Black–Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta–vega hedging is asymptotically optimal in the limit for small uncertainty aversion. The corresponding indifference price corrections are determined by the disparity between the vegas, gammas, vannas and volgas of the non-traded and the liquidly traded options.     

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

In a market with stochastic investment opportunities, we study an optimal consumption–investment problem for an agent with recursive utility of Epstein–Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The superdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein–Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein–Zin aggregator is neither Lipschitz nor jointly concave in all its variables.     

Hedging with small uncertainty aversion

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their “distance” to a reference local volatility model. In the limit for small uncertainty aversion, this leads to explicit formulas for prices and hedging strategies in terms of the security’s cash gamma.     

Arbitrage-free pricing of multi-person game claims in discrete time

We introduce a class of financial contracts involving several parties by extending the notion of a two-person game option to a contract in which an arbitrary number of parties is involved and each of them is allowed to make a wide array of decisions at any time, not restricted to simply exercising the option. The collection of decisions by all parties then determines the contract’s termination date as well as the terminal payoff for each party. We provide sufficient conditions under which a discrete-time multi-person game option has a unique arbitrage-free price, which is additive with respect to any partition of the contract. Our results are illustrated by the detailed study of a particular multi-person contract with puttable tranches.