Abstracts

Hiroumi Misaki (University of Tsukuba)

Title: The SIML Estimation of Integrated Volatility and Covariance

Estimating the volatility and covariance of financial asset prices is an issue of considerable importance in financial econometrics research. The separating information maximum likelihood (SIML) method has been proposed for estimating the integrated volatility and covariance from high frequency data contaminated by market microstructure noise. We examine usefulness of the SIML method as follows. (i) We test the method with both quote and transaction prices to investigate its robustness against noise. (ii) We test the efficiency of hedging by comparing the performances of simple portfolios constructed based on estimated hedging ratios. (iii) We compare the accuracy of several estimation methods using a number of computer simulations. We conclude that the SIML method is suitable for practical applications.

Giulia Livieri (Scuola Normale Superiore di Pisa)

Title: Asymptotic results for the Fourier estimator of the integrated quarticity

In this paper we prove a central limit theorem for the Fourier quarticity estimator. We obtain a new consistency result and we show that the estimator reaches the parametric rate 1/2. The optimal variance is obtained, with a suitable choice of the number of frequencies employed to compute the Fourier coefficients of the volatility, while the limiting distribution has a bias. As a by-product, thanks to the Fourier methodology, we obtain consistent estimators of any even power of the volatility function and an estimator of the spot quarticity. We assess the finite sample performance of the Fourier quarticity estimator in a numerically exercise with different market micro-structure frictions. The paper is here

Dan Crisan (Imperial College, London)

Title: Modelling multi-period carbon markets using singular forward backward SDEs

I will introduce a model the evolution of emissions and the price of emissions allowances in a carbon market such as the European Union Emissions Trading System (EU ETSP). The model accounts for multiple trading periods (and phases) and multiple times at which compliance can occur. At the end of each trading period, the participating firms must surrender allowances for the emissions made during that period, but any excess allowances can be used for compliance in the following periods. We show that the multi-period allowance pricing problem is well-posed for various mechanisms linking the trading periods (such as banking, borrowing and withdrawals). The results are based on the analysis of a forward-backward stochastic differential equation with the following special characteristics: i. the forward and backward components are coupled, ii. the final condition is singular and iii. the forward component of the model is degenerate. I will also introduce an infinite period model, that is, a model for carbon market with a sequence of compliance times and no end date. I will show that, under appropriate conditions, the value function for the multi-period pricing problem converges, as the number of periods increases, to a value function for this infinite period model. This is joint work with Jean-Francois Chassagneux (Paris Diderot) and Hinesh Chotai (Citybank).

Francesco Cordoni (Scuola Normale Superiore di Pisa)

Title: Identification of Overdetermined and Noisy Structural VAR Models: The Collapsing-ICA Approach

When the number of observed macroeconomic variables is larger than the number of structural shocks driving the economy, the associated structural VAR system is said to be overdetermined. We propose an identification method for overdetermined structural VAR models contaminated by noise by combining a collapsing procedure with the Independent Component Analysis. We discuss the consistency of the proposed combined procedure and examine its finite sample properties with Monte Carlo simulations. The empirical application of the proposed scheme on U.S. data allows to identify the low dimensional system of structural shocks driving the U.S. economy. Working paper available at https://ssrn.com/abstract=3415426

Kazuhiro Yoshikawa (Hirosaki University)

Title: Linear independence over countable sets and its applications to probability theory

In this talk, we consider one generalization of linear independence over the rationals. We can prove the existence of the real numbers with linear independence over the rationals, using the difference in cardinality between real numbers and rational numbers. It is a key of our generalization, which makes it easy to treat multidimensional discrete distributions. For example, we can obtain infinite divisibilities of the joint distribution of discrete valued random variables from the distributions of their linear combinations. As another example, we also consider linear unimodality for discrete distributions.

Stefano Marmi (Scuola Normale Superiore di Pisa)

Title: Coupling the Yoccoz–Birkeland population model with price dynamics: chaotic livestock commodities market cycles

We propose a new model for the time evolution of livestock commodities which exhibits endogenous deterministic stochastic behaviour. The model is based on the Yoccoz-Birkeland integral equation, a model first developed for studying the time-evolution of single species with high average fertility, short mating season and density dependent reproduction rates. Joint work with Sylvain ARLOT (Orsay) and Duccio PAPINI (Udine). Article published on Nonlinearity 32 (2019) 2564–2592