arXiv · arXiv q-fin · 2018
In this paper we introduce an efficient fat-tail measurement framework that is based on the conditional second moments. We construct a goodness-of-fit statistic that has a direct interpretation and can be used to assess the impact of fat-tails on central data conditional dispersion. Next, we show how to use this framework to construct a powerful normality test. In particular, we compare our methodology to various pop…
Damian Jelito, Marcin Pitera
arXiv · arXiv q-fin · 2026
We show that the Markowitz portfolio is a scalar multiple of another portfolio which replaces the covariance with the second moment matrix, via simple application of the Sherman-Morrison identity. Moreover it is shown that when using conditional estimates of the first two moments, this "Sherman-Morrison-Markowitz" portfolio solves the standard unconditional portfolio optimization problems. We argue that in multi-peri…
Steven E. Pav
arXiv · arXiv q-fin · 2026
The classical mean-variance framework characterizes portfolio risk solely through return variance and the covariance matrix, implicitly assuming that all relevant sources of risk are captured by second moments. In modern financial markets, however, shocks often propagate through complex networks of interconnections, giving rise to systemic and spillover risks that variance alone does not reflect. This paper develops …
Yimeng Qiu
arXiv · arXiv q-fin · 2020
We investigate whether sophisticated volatility estimation improves the out-of-sample performance of mean-variance portfolio strategies relative to the naive 1/N strategy. The portfolio strategies rely solely upon second moments. Using a diverse group of econometric and portfolio models across multiple datasets, most models achieve higher Sharpe ratios and lower portfolio volatility that are statistically and economi…
Michael Curran, Patrick O'Sullivan, Ryan Zalla
arXiv · arXiv q-fin · 2018
We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The framework works for one or a portfolio of stocks and the Kelly fractions can be efficiently calculated.…
Tim Byrnes, Tristan Barnett
arXiv · arXiv q-fin · 2001
We study the price dynamics of stocks traded in the NASDAQ market by considering the statistical properties of an ensemble of stocks traded simultaneously. For each trading day of our database, we study the ensemble return distribution by extracting its first two central moments. According to previous results obtained for the NYSE market, we find that the second moment is a long-range correlated variable. We compare …
Fabrizio Lillo, Rosario N. Mantegna
arXiv · arXiv q-fin · 2000
We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble re…
Fabrizio Lillo, Rosario N. Mantegna
arXiv · arXiv · 2021
With the rise of computing and artificial intelligence, advanced modeling and forecasting has been applied to High Frequency markets. A crucial element of solid production modeling though relies on the investigation of data distributions and how they relate to modeling assumptions. In this work we investigate volume distributions during anomalous price events and show how their tail exponents < 2 indicate a diverging…
Jeremy D. Turiel, Tomaso Aste
arXiv · arXiv q-fin · 2026
Conditional portfolio models estimate risk relative to a chosen information set, yet rarely test whether that information removes common cross-asset dependence. When it does not, systematic risk may be treated as idiosyncratic, distorting portfolios and attainable efficient frontiers. We formulate this prior problem as screening-off for portfolio choice. A hierarchy separates causal, distributional and second-moment …
Alejandro Rodriguez Dominguez
arXiv · arXiv · 2025
This paper investigates asymptotically optimal importance sampling (IS) schemes for pricing European call options under the Heston stochastic volatility model. We focus on two distinct rare-event regimes where standard Monte Carlo methods suffer from significant variance deterioration: the limit as maturity approaches zero and the limit as the strike price tends to infinity. Leveraging the large deviation principle (…
Yun-Feng Tu, Chuan-Hsiang Han
arXiv · arXiv · 2021
We consider a 2-dimensional marked Hawkes process with increasing baseline intensity in order to model prices on electricity intraday markets. This model allows to represent different empirical facts such as increasing market activity, random jump sizes but above all microstructure noise through the signature plot. This last feature is of particular importance for practitioners and has not yet been modeled on those p…
Thomas Deschatre, Pierre Gruet
arXiv · arXiv · 2021
A reputation of high volatility accompanies the emergence of Bitcoin as a financial asset. This paper intends to nuance this reputation and clarify our understanding of Bitcoin's volatility. Using daily, weekly, and monthly closing prices and log-returns data going from September 2014 to January 2021, we find that Bitcoin is a prime example of an asset for which the two conceptions of volatility diverge. We show that…
Nassim Dehouche
arXiv · arXiv · 2019
The goal of this paper is to explore the relationship between momentum effects and liquidity in cryptocurrency markets. Portfolios based on momentum-liquidity bivariate sorts are formed and rebalanced on a varying number of cryptocurrencies through time. We find a strong momentum effect in the most liquid cryptocurrencies, which supports the theories of investor herding behavior. Moreover, we propose two profitable l…
Stjepan Begušić, Zvonko Kostanjčar
arXiv · arXiv · 2026
Loss-versus-Rebalancing (LVR) is the dominant adverse-selection cost borne by liquidity providers on automated market makers. Under geometric Brownian motion, arbitrage profit scales with the probability of a profitable block, which vanishes as the block time $Δt \to 0$; this is the standing argument for ever-shorter blocks. Modeling the reference price instead as a jump-diffusion, I show that the constant-product LV…
Nils Bundi
arXiv · arXiv · 2024
This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily addresses two gaps in the literature. The first is the lack of credit spread models founded on a stochastic basis that enables continuous modeling, as many existing models rely on fa…
Mohamed Ben Alaya, Ahmed Kebaier, Djibril Sarr
arXiv · arXiv · 2021
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers the modeling of the liability liquidity risk (or funding liquidity), the second dimension is dedicated to the modeling of the asset liquidity risk (or market liquidity), whereas the third dimension considers the management of the asset-liability liquidi…
Thierry Roncalli
arXiv · arXiv · 2021
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers the asset-liability management of the liquidity gap risk (or asset-liability…
Thierry Roncalli, Amina Cherief, Fatma Karray-Meziou, Margaux Regnault
arXiv · arXiv · 2021
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers asset-liability liquidity risk management (or asset-liability matching). The…
Thierry Roncalli, Fatma Karray-Meziou, François Pan, Margaux Regnault