Optimal Transport Filtering with Particle Reweighing in Finance

We show the application of an optimal transportation approach to estimate stochastic volatility process by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct the flow to a rarely visited areas of the state space by using a particle method (a mutation and a reweighing mechanism). We demonstrate the efficiency of our approach on a simple example of the European option price under the Stein-Stein stochastic volatility model for which a closed form formula is available. Both homotopy and reweighted homotopy methods show a lower variance, root-mean squared errors and a bias compared to other filtering schemes recently developed in the signal-processing literature, including particle filter techniques

On the Super-Additivity and Estimation Biases of Quantile Contributions

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions

The Precautionary Principle (with Application to the Genetic Modification of Organisms)

We present a non-naive version of the Precautionary (PP) that allows us to avoid paranoia and paralysis by confining precaution to specific domains and problems. PP is intended to deal with uncertainty and risk in cases where the absence of evidence and the incompleteness of scientific knowledge carries profound implications and in the presence of risks of "black swans", unforeseen and unforeseable events of extreme consequence. We formalize PP, placing it within the statistical and probabilistic structure of ruin problems, in which a system is at risk of total failure, and in place of risk we use a formal fragility based approach. We make a central distinction between 1) thin and fat tails, 2) Local and systemic risks and place PP in the joint Fat Tails and systemic cases. We discuss the implications for GMOs (compared to Nuclear energy) and show that GMOs represent a public risk of global harm (while harm from nuclear energy is comparatively limited and better characterized). PP should be used to prescribe severe limits on GMOs

Background risk and quantum calculus

Abstract Infinitesimal calculus is heavily used in decision making analysis. This paper demonstrates that the application of quantum calculus in analysing preferences choice directly introduces background risk and its effects on risk-aversion, subjective probabilities and moment preferences. Quantum calculus provides another approach to the mathematical treatment of decision making, namely analysis of utility preferences

Bank regulation, risk and return : evidence from the credit and sovereign debt crisis

In this paper, we analyze whether regulation reduced risk during the credit crisis and the sovereign debt crisis for a cross section of global banks. In this regard, we examine distance to default (Laeven and Levine, 2008), systemic risk (Acharya et al., 2010), idiosyncratic risk, and systematic risk. We employ World Bank survey data on regulations to test our conjectures. We find that regulatory restrictions, official supervisory power, capital stringency, along with private monitoring can explain bank risk in both crises. Additionally, we find that deposit insurance schemes enhance moral hazard, as this encouraged banks to take on more risk and perform poorly during the sovereign debt crisis. Finally, official supervision and private monitoring explains the returns during both crisis periods

Systemic Risk Indicators Based on Nonlinear PolyModel

The global financial market has become extremely interconnected as it demonstrates strong nonlinear contagion in times of crisis. As a result, it is necessary to measure financial systemic risk in a comprehensive and nonlinear approach. By establishing a large set of risk factors as the main bones of the financial market network and applying nonlinear factor analysis in the form of so-called PolyModel, this paper proposes two systemic risk indicators that can prognosticate the advent and trace the development of financial crises. Through financial network analysis, theoretical simulation, empirical data analysis and final validation, we argue that the indicators suggested in this paper are proved to be very effective in forecasting and tracing the financial crises from 1998 to 2017. The economic benefit of the indicator is evidenced by the enhancement of a protective put/covered call strategy on major stock markets

An empirical approach to financial crisis indicators based on random matrices

International audienceThe aim of this work is to build a class of financial crisis indicators based on the spectral properties of the dynamics of market data. After choosing an appropriate size for a rolling window, the historical market data inside this rolling window are seen every trading day as a random matrix from which a correlation matrix is obtained. Our goal is to study the correlations between the assets that constitute this market and look for reproducible patterns that are indicative of an impending financial crisis. A weighting of the assets in the market is then introduced and is proportional to the daily traded volumes. This manipulation is realized in order to give more importance to the most liquid assets. Our financial crisis indicators are based on the spectral radius of this weighted correlation matrix. The idea behind this type of financial crisis indicators is that large eigenvalues are a sign of dynamic instability. The out-of-sample predictive power of the financial crisis indicators in this framework is then demonstrated, in particular by using them as decision-making tools in a protective put strategy