Machine learning Vasicek model calibration with Gaussian processes

In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.

Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

Vasicek interest rate model

Tässä tutkielmassa estimoidaan korkomallin parametrit Maximum likelihood metodilla sekä näytetään kuinka mallintaa lyhyen koron evoluutiota ja korkokäyrän rakennetta.

Previsão da taxa de juros utilizando o modelo de Vasicek

Este trabalho estuda a previsão da taxa de juros com foco em uma estratégia de investimento. Inicialmente é feita a parametrização da taxa de juros com o modelo de Vasicek para posterior aplicação do modelo autorregressivo tanto na taxa de juros quanto nos parâmetros do Vasicek. O instrumento financeiro escolhido para verificar a eficácia da metodologia proposta foi o constant matutity swap aplicado em alguns vértices. Os resultados variaram significativamente para os diferentes horizontes de calibragem e períodos de amostragem sem um padrão de desempenho.

Previsão da estrutura a termo de taxa de juros aplicando o Filtro de Kalman ao modelo Vasicek: o caso brasileiro

Este trabalho tem o objetivo de testar a qualidade preditiva do Modelo Vasicek de dois fatores acoplado ao Filtro de Kalman. Aplicado a uma estratégia de investimento, incluímos um critério de Stop Loss nos períodos que o modelo não responde de forma satisfatória ao movimento das taxas de juros. Utilizando contratos futuros de DI disponíveis na BMFBovespa entre 01 de março de 2007 a 30 de maio de 2014, as simulações foram realizadas em diferentes momentos de mercado, verificando qual a melhor janela para obtenção dos parâmetros dos modelos, e por quanto tempo esses parâmetros estimam de maneira ótima o comportamento das taxas de juros. Os resultados foram comparados com os obtidos pelo Modelo Vetor-auto regressivo de ordem 1, e constatou-se que o Filtro de Kalman aplicado ao Modelo Vasicek de dois fatores não é o mais indicado para estudos relacionados a previsão das taxas de juros. As limitações desse modelo o restringe em conseguir estimar toda a curva de juros de uma só vez denegrindo seus resultados.

Some bounds of loss in classical semideterministic immunization

Since Samuelson, Redington and Fisher and Weil, duration and immunization are very important topics in bond portfolio analysis from both a theoretical and a practical point of view. Many results have been established, especially in semi-deterministic framework. As regards, however, the loss may be sustained, we do not think that the subject has been investigated enough, except for the results found in the wake of the theorem of Fong and Vasicek. In this paper we present some results relating to the limitation of the loss in the case of local immunization for multiple liabilities.

Machine learning Gaussian short rate

Dissertação para obtenção do Grau de Doutor em Estatística e Gestão do Risco

An atlas of human gene expression from massively parallel signature sequencing (MPSS).

We have used massively parallel signature sequencing (MPSS) to sample the transcriptomes of 32 normal human tissues to an unprecedented depth, thus documenting the patterns of expression of almost 20,000 genes with high sensitivity and specificity. The data confirm the widely held belief that differences in gene expression between cell and tissue types are largely determined by transcripts derived from a limited number of tissue-specific genes, rather than by combinations of more promiscuously expressed genes. Expression of a little more than half of all known human genes seems to account for both the common requirements and the specific functions of the tissues sampled. A classification of tissues based on patterns of gene expression largely reproduces classifications based on anatomical and biochemical properties. The unbiased sampling of the human transcriptome achieved by MPSS supports the idea that most human genes have been mapped, if not functionally characterized. This data set should prove useful for the identification of tissue-specific genes, for the study of global changes induced by pathological conditions, and for the definition of a minimal set of genes necessary for basic cell maintenance. The data are available on the Web at http://mpss.licr.org and http://sgb.lynxgen.com.

The Monetary policy rules in EU-15: before and after the euro

The objective of this paper is to identify empirically the logic behind short-term interest rates setting

The Monetary policy rules in Europe: heterogeneity and common patters

The objective of this study is the empirical identification of the monetary policy rules pursued in individual countries of EU before and after the launch of European Monetary Union. In particular, we have employed an estimation of the augmented version of the Taylor rule (TR) for 25 countries of the EU in two periods (1992-1998, 1999-2006). While uniequational estimation methods have been used to identify the policy rules of individual central banks, for the rule of the European Central Bank has been employed a dynamic panel setting. We have found that most central banks really followed some interest rate rule but its form was usually different from the original TR (proposing that domestic interest rate responds only to domestic inflation rate and output gap). Crucial features of policy rules in many countries have been the presence of interest rate smoothing as well as response to foreign interest rate. Any response to domestic macroeconomic variables have been missing in the rules of countries with inflexible exchange rate regimes and the rules consisted in mimicking of the foreign interest rates. While we have found response to long-term interest rates and exchange rate in rules of some countries, the importance of monetary growth and asset prices has been generally negligible. The Taylor principle (the response of interest rates to domestic inflation rate must be more than unity as a necessary condition for achieving the price stability) has been confirmed only in large economies and economies troubled with unsustainable inflation rates. Finally, the deviation of the actual interest rate from the rule-implied target rate can be interpreted as policy shocks (these deviation often coincided with actual turbulent periods).

The Monetary policy rules and the inflation process in open emerging

This paper has three objectives. First, it aims at revealing the logic of interest rate setting pursued by monetary authorities of 12 new EU members. Using estimation of an augmented Taylor rule, we find that this setting was not always consistent with the official monetary policy. Second, we seek to shed light on the inflation process of these countries. To this end, we carry out an estimation of an open economy Philips curve (PC). Our main finding is that inflation rates were not only driven by backward persistency but also held a forward-looking component. Finally, we assess the viability of existing monetary arrangements for price stability. The analysis of the conditional inflation variance obtained from GARCH estimation of PC is used for this purpose. We conclude that inflation targeting is preferable to an exchange rate peg because it allowed decreasing the inflation rate and anchored its volatility.

Inflation dynamics and the New Keynesian Phillips curve in EU-4

The paper seeks to shed light on inflation dynamics of four new EU member states: the Czech Republic, Hungary, Poland and Slovakia. To this end, the New Keynesian Phillips curve augmented for open economies is estimated and additional statistical tests applied. We find the following. (1) The claim of New Keynesians that the real marginal cost is the main inflation-forcing variable is fragile. (2) Inflation seems to be driven by external factors. (3) Although inflation holds a forward-looking component, the backward-looking component is substantial. An intuitive explanation for higher inflation persistence may be rather adaptive than rational price setting of local firms.

How does monetary policy change? evidence on inflation targeting countries

We examine the evolution of monetary policy rules in a group of inflation targeting countries (Australia, Canada, New Zealand, Sweden and the United Kingdom) applying moment- based estimator at time-varying parameter model with endogenous regressors. Using this novel flexible framework, our main findings are threefold. First, monetary policy rules change gradually pointing to the importance of applying time-varying estimation framework. Second, the interest rate smoothing parameter is much lower that what previous time-invariant estimates of policy rules typically report. External factors matter for all countries, albeit the importance of exchange rate diminishes after the adoption of inflation targeting. Third, the response of interest rates on inflation is particularly strong during the periods, when central bankers want to break the record of high inflation such as in the U.K. or in Australia at the beginning of 1980s. Contrary to common wisdom, the response becomes less aggressive after the adoption of inflation targeting suggesting the positive effect of this regime on anchoring inflation expectations. This result is supported by our finding that inflation persistence as well as policy neutral rate typically decreased after the adoption of inflation targeting.

Is monetary policy in new members states asymmetric?

Estimated Taylor rules became popular as a description of monetary policy conduct. There are numerous reasons why real monetary policy can be asymmetric and estimated Taylor rule nonlinear. This paper tests whether monetary policy can be described as asymmetric in three new European Union (EU) members (the Czech Republic, Hungary and Poland), which apply an inflation targeting regime. Two different empirical frameworks are

Monetary policy rules and financial stress: does financial instability matter for monetary

We examine whether and how main central banks responded to episodes of financial stress over the last three decades. We employ a new methodology for monetary policy rules estimation, which allows for time-varying response coefficients as well as corrects for endogeneity. This flexible framework applied to the U.S., U.K., Australia, Canada and Sweden together with a new financial stress dataset developed by the International Monetary Fund allows not only testing whether the central banks responded to financial stress but also detects the periods and type of stress that were the most worrying for monetary authorities and to quantify the intensity of policy response. Our findings suggest that central banks often change policy