Giulia Livieri

• Scuola Normale Superiore

We develop a model based on mean-field games of competitive firms producing similar goods according to a standard AK model with a depreciation rate of capital generating pollution as a byproduct. Our analysis focuses on the widely-used cap-and-trade pollution regulation. Under this regulation, firms have the flexibility to respond by implementing p...

We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak convergence of the unique stationary measure to the invariant measure of the map, and show that the average L...

We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak convergence of the unique stationary measure to the invariant measure of the map, and show that the average L...

We propose a Markovian model to understand how Italy's public sphere behaves on the green energy transition theme. The paper uses the example of solar photovoltaics as a point of reference. The adoption decision is assumed to be sequentially influenced by the network communication of each person or family and the payback period of the investment. W...

The degree of uncertainty associated with the value of a company plays a relevant role in valuation analysis. We propose an original and robust methodology for company market valuation, which replaces the traditional point estimate of the conventional Discounted Cash Flow model with a probability distribution of fair values that convey information...

We study the asymptotic normality of two feasible estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected estimator reaches the optimal rate n1/4, while the estimator without bias-correction has a slower convergence rate...

We study a random version of the population-market model proposed by Arlot, Marmi, and Papini in Arlot et al. (2019). The latter model is based on the Yoccoz–Birkeland integral equation and describes a time evolution of livestock commodities prices which exhibits endogenous deterministic, stochastic behavior. We introduce a stochastic component ins...

We study a random version of the population-market model proposed by Arlot, Marmi and Papini in Arlot et al. (2019). The latter model is based on the Yoccoz-Birkeland integral equation and describes a time evolution of livestock commodities prices which exhibits endogenous deterministic stochastic behaviour. We introduce a stochastic component insp...

We study the asymptotic organization among many optimizing individuals interacting in a suitable “moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player games. This proof depends upon the derivation of a law of large numbers for the empirical processes in the limit...

We study the asymptotic normality of two estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected estimator reaches the optimal rate 1/4, while the estimator without bias-correction has a slower convergence rate and a sma...

The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum ana...

Market liquidity is a latent and dynamic variable. We propose a dynamical linear price impact model at high frequency in which the price impact coefficient is a product of a daily, a diurnal, and an auto-regressive stochastic intraday component. We estimate the model using a Kalman filter on order book data for stocks traded on the NASDAQ in 2016....

We consider a model of a simple financial system consisting of a leveraged investor that invests in a risky asset and manages risk by using Value-at-Risk (VaR). The VaR is estimated by using past data via an adaptive expectation scheme. We show that the leverage dynamics can be described by a dynamical system of slow-fast type associated with a uni...

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player games. This proof depends upon the derivation of a law of large numbers for the empirical processes in the limit...

We provide general conditions under which a class of discrete-time volatility models driven by the score of the conditional density converges in distribution to a stochastic differential equation as the interval between observations goes to zero. We show that the form of the diffusion limit depends on: (i) the link function, (ii) the conditional se...

We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative scheme that produces an optimal control in terms of a Skorokhod reflection at a (state-dependent) surface tha...

This paper proposes a nonparametric theory for statistical inferences on zero returns of high-frequency asset prices. Using an infill asymptotic design, we derive limit theorems for the percentage of zero returns observed on a finite time interval and for other related quantities. Within this framework, we develop two nonparametric tests. First, we...

The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the free-energy...

In this study we provide an analytical characterization of the impact of zero returns on the popular realized covariance estimator of Barndorff-Nielsen and Shephard [Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica, 2004, 72(3), 885–925]. In our framework...

We investigate the effects of (domestic and international) financial cyclical factors on the US business cycle over the period 1890–2013 using an augmented stochastic version of the neoclassical growth model. In our setting, financial factors enter as determinants of the total factor productivity cyclical pattern. By means of static and dynamic est...

In this paper, we prove a central limit theorem for an estimator of the integrated quarticity based on Fourier analysis, strictly related to the one proposed in Mancino and Sanfelici (Quant Finance 12: 607–622, 2012). Also, a consistency result is derived. We show that the estimator reaches the parametric rate \(\rho (n)^{1/2}\), where \(\rho (n)\)...

We provide general conditions under which a class of discrete-time volatility models driven by the score of the conditional density converges in distribution to a stochastic differential equation as the interval between observations goes to zero. We show that the form of the diffusion limit depends only on the link function and on the conditional s...

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this...

Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer [7] and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting through a mean-field, leave the game as soon as their private states hit some given boundary. In this paper, we p...

Asset transaction prices sampled at high frequency are much staler than one might expect in the sense that they frequently lack new updates showing zero returns. In this paper, we propose a theoretical framework for formalizing this phenomenon. It hinges on the existence of a latent continuous-time stochastic process $p_t$ valued in the open interv...

In this paper we prove a central limit theorem for the Fourier quarticity estimator proposed in Mancino and Sanfelici (2012). In particular, we obtain a new consistency result and we show that the estimator reaches the parametric rate ρ(n) 1/2 , where ρ(n) is the discretization mesh and n the number of points of such a discretization. The optimal v...

We propose a stochastic Solow growth model where a cyclical component is added to the total factor productivity process. Theoretically, an important feature of the model is that its main equation takes a state space representation where key parameters can be estimated via an unobserved component approach without involving capital stock measures. In...

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of our approach is that – in a similar spirit to the Brow...

It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This result has been established using high frequency volatility estimations from historical price data. We revisit th...

It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This result has been established using high frequency volatility estimations from historical price data. We revisit th...

A simple mean-variance portfolio optimization problem in continuous time is solved using the mean field approach. In this approach, the original optimal control problem, which is time inconsistent, is viewed as the McKean-Vlasov limit of a family of controlled many-component weakly interacting systems. The prelimit problems are solved by dynamic pr...

Motivated by the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both the observed returns and realized measures to the latent conditional variance. The first contribution of the paper is to provide an anal...

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of our approach is that -- in a similar spirit to the Bro...

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of our approach is that -- in a similar spirit to the Bro...