Differentiable neural substrates for learned and described value and risk.

Studies of human decision making emerge from two dominant traditions: learning theorists [1-3] study choices in which options are evaluated on the basis of experience, whereas behavioral economists and financial decision theorists study choices in which the key decision variables are explicitly stated. Growing behavioral evidence suggests that valuation based on these different classes of information involves separable mechanisms [4-8], but the relevant neuronal substrates are unknown. This is important for understanding the all-too-common situation in which choices must be made between alternatives that involve one or another kind of information. We studied behavior and brain activity while subjects made decisions between risky financial options, in which the associated utilities were either learned or explicitly described. We show a characteristic effect in subjects' behavior when comparing information acquired from experience with that acquired from description, suggesting that these kinds of information are treated differently. This behavioral effect was reflected neurally, and we show differential sensitivity to learned and described value and risk in brain regions commonly associated with reward processing. Our data indicate that, during decision making under risk, both behavior and the neural encoding of key decision variables are strongly influenced by the manner in which value information is presented.

Modeling and forecasting value-at-risk for the Portuguese stock market

The aim of this work project is to find a model that is able to accurately forecast the daily Value-at-Risk for PSI-20 Index, independently of the market conditions, in order to expand empirical literature for the Portuguese stock market. Hence, two subsamples, representing more and less volatile periods, were modeled through unconditional and conditional volatility models (because it is what drives returns). All models were evaluated through Kupiec’s and Christoffersen’s tests, by comparing forecasts with actual results. Using an out-of-sample of 204 observations, it was found that a GARCH(1,1) is an accurate model for our purposes.

Properties of a risk measure derived from ruin theory

This paper studies a risk measure inherited from ruin theory and investigates some of its properties. Specifically, we consider a value-at-risk (VaR)-type risk measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given level. This VaR-type risk measure turns out to be equivalent to the VaR of the maximal deficit of the ruin process in infinite time. A related Tail-VaR-type risk measure is also discussed.

Stress testing a complement of value-a-risk.

Rapport de stage (maîtrise en finance mathématique et computationnelle)

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

Uma análise comparativa entre a metodologia analítica e a metodologia de simulação Monte Carlo para o cálculo do value at risk

O presente trabalho tem por objetivo descrever, avaliar comparar as metodologias analítica da simulação Monte Cario para cálculo do Value at Risk (Valor em Risco) de instituições financeiras de empresas. Para comparar as vantagens desvantagens de cada metodologia, efetuaremos comparações algébricas realizamos diversos testes empíricos com instituições hipotéticas que apresentassem diferentes níveis de alavancagem de composição em seus balanços, que operassem em diferentes mercados (consideramos os mercados de ações, de opções de compra de títulos de renda fixa prefixados).

Comparing value-at-risk methodologies

In this paper, we compare four different Value-at-Risk (V aR) methodologies through Monte Carlo experiments. Our results indicate that the method based on quantile regression with ARCH effect dominates other methods that require distributional assumption. In particular, we show that the non-robust methodologies have higher probability to predict V aRs with too many violations. We illustrate our findings with an empirical exercise in which we estimate V aR for returns of S˜ao Paulo stock exchange index, IBOVESPA, during periods of market turmoil. Our results indicate that the robust method based on quantile regression presents the least number of violations.

Value at risk : um conceito em busca de identidade : inovação ou evolução?

Análise crítica e histórica do conceito de Value at Risk, quanto à métrica e métodos utilizados na sua determinação, como instrumento na quantificação e gestão de riscos (financeiros) de mercado.

Mercado brasileiro: aplicação de análise de componentes principais no cálculo de VAR para carteiras de renda fixa

A abordagem do Value at Risk (VAR) neste trabalho será feita a partir da análise da curva de juros por componentes principais (Principal Component Analysis – PCA). Com essa técnica, os movimentos da curva de juros são decompostos em um pequeno número de fatores básicos independentes um do outro. Entre eles, um fator de deslocamento (shift), que faz com que as taxas da curva se movam na mesma direção, todas para cima ou para baixo; de inclinação (twist) que rotaciona a curva fazendo com que as taxas curtas se movam em uma direção e as longas em outra; e finalmente movimento de torção, que afeta vencimentos curtos e longos no mesmo sentido e vencimentos intermediários em sentido oposto. A combinação destes fatores produz cenários hipotéticos de curva de juros que podem ser utilizados para estimar lucros e perdas de portfolios. A maior perda entre os cenários gerados é uma maneira intuitiva e rápida de estimar o VAR. Este, tende a ser, conforme verificaremos, uma estimativa conservadora do respectivo percentual de perda utilizado. Existem artigos sobre aplicações de PCA para a curva de juros brasileira, mas desconhecemos algum que utilize PCA para construção de cenários e cálculo de VAR, como é feito no presente trabalho.Nesse trabalho, verificaremos que a primeira componente principal produz na curva um movimento de inclinação conjugado com uma ligeira inclinação, ao contrário dos resultados obtidos em curvas de juros de outros países, que apresentam deslocamentos praticamente paralelos.