Explore the vast range of titles available.

Financial Risk Forecasting is a complete introduction to practical quantitative risk management, with a focus on market risk. Derived from the authors teaching notes and years spent training practitioners in risk management techniques, it brings together the three key disciplines of finance, statistics and modeling (programming), to provide a thorough grounding in risk management techniques. Written by renowned risk expert Jon Danielsson, the book begins with an introduction to financial markets and market prices, volatility clusters, fat tails and nonlinear dependence. It then goes on to present volatility forecasting with both univatiate and multivatiate methods, discussing the various methods used by industry, with a special focus on the GARCH family of models. The evaluation of the quality of forecasts is discussed in detail. Next, the main concepts in risk and models to forecast risk are discussed, especially volatility, value-at-risk and expected shortfall. The focus is both on risk in basic assets such as stocks and foreign exchange, but also calculations of risk in bonds and options, with analytical methods such as delta-normal VaR and duration-normal VaR and Monte Carlo simulation. The book then moves on to the evaluation of risk models with methods like backtesting, followed by a discussion on stress testing. The book concludes by focussing on the forecasting of risk in very large and uncommon events with extreme value theory and considering the underlying assumptions behind almost every risk model in practical use – that risk is exogenous – and what happens when those assumptions are violated. Every method presented brings together theoretical discussion and derivation of key equations and a discussion of issues in practical implementation. Each method is implemented in both MATLAB and R, two of the most commonly used mathematical programming languages for risk forecasting with which the reader can implement the models illustrated in the book. The book includes four appendices. The first introduces basic concepts in statistics and financial time series referred to throughout the book. The second and third introduce R and MATLAB, providing a discussion of the basic implementation of the software packages. And the final looks at the concept of maximum likelihood, especially issues in implementation and testing. The book is accompanied by a website - www.financialriskforecasting.com – which features downloadable code as used in the book.

This book provides a perspective on a number of approaches to financial modelling and risk management. It examines both theoretical and practical issues. Theoretically, financial risks models are models of a real and a financial \"uncertainty\", based on both common and private information and economic theories defining the rules that financial markets comply to. Financial models are thus challenged by their definitions and by a changing financial system fueled by globalization, technology growth, complexity, regulation and the many factors that contribute to rendering financial processes to be continuously questioned and re-assessed. The underlying mathematical foundations of financial risks models provide future guidelines for risk modeling. The bookâءءs chapters provide selective insights and developments that can contribute to better understand the complexity of financial modelling and its ability to bridge financial theories and their practice.

The Basel Committee on Banking Supervision (BIS) has recently sanctioned expected shortfall (ES) as the market risk measure to be used for banking regulatory purposes, replacing the well-known value at risk (VaR). This change is motivated by the appealing theoretical properties of ES as a measure of risk and the poor properties of VaR. In particular, VaR fails to control for “tail risk.” In this transition, the major challenge faced by financial institutions is the unavailability of simple tools for evaluation of ES forecasts (i.e., backtesting ES). The main purpose of this paper is to propose such tools. Specifically, we propose backtests for ES based on cumulative violations, which are the natural analogue of the commonly used backtests for VaR. We establish the asymptotic properties of the tests, and investigate their finite sample performance through some Monte Carlo simulations. An empirical application to three major stock indexes shows that VaR is generally unresponsive to extreme events such as those experienced during the recent financial crisis, whereas ES provides a more accurate description of the risk involved. This paper was accepted by Neng Wang, finance .

The price of a financial option equals the discounted expected payoff of the option under the risk-neutral measure, and an option's Greeks are formulas that give the change in an option price with respect to parameters of interest (e.g. the price of the underlying asset). The density that reproduces the observed option price is called the risk-neutral or state price density and is used for a variety of important activities in finance, including providing an arbitrage-free tool for pricing complex and less liquid securities. The importance of understanding this density with respect to asset pricing and risk management has led to a competing number of approaches for making inference about the state price density. Unlike the option prices, Greeks can not be observed in the market and have to be calculated. As Greeks are important for measuring and managing risk as well as executing dynamic trading strategies, developing methods to calculate them efficiently and accurately is of critical importance both in theory and in practice (Broadie and Glasserman, 1996). We start by proposing a finite-dimensional model for the state price density in a Bayesian framework. This modeling approach can be viewed as a Bayesian Quadrature model, where the locations and weights of support points in the finite-dimensional representation of the risk-neutral density are random variables. This modeling approach allows a 'prior' reference distribution which can be a parametric distribution (e.g. the lognormal density) or which can be uniform and completely non-informative, and it also provides a posterior distribution of the state price density that is consistent with the observed option prices. We asses the performance of the proposed model using simulation studies based on synthetic data and then by contrasting the method with a number of competing methods using S 500 index option data. In contrast to European options, American options can be exercised anytime prior to maturity. We show how our Bayesian Quadrature approach can be extended to make inference for American options. To tackle this problem, we propose a Bayesian implied random tree model as an extension of the Bayesian Quadrature approach by building a unique binomial tree similar to Rubinstein (1994). The benefits of our approach are demonstrated via simulation study and empirical studies using S 100 index option data. Although finite-difference methods are commonly used to calculate Greeks, these estimates can often be biased and suffer from erratic behavior when the payoff function is discontinuous. We provide new and simple mathematical formulas that overcome these problems and that are applicable to a wide range of complicated options and underlying processes. Moreover, we provide an innovative Bayesian approach to calculate Greeks using observed option prices without any parametric assumptions on the underlying process, so that the proposed method avoids the model misspecification problem. We demonstrate the performance of our methods through simulation studies.

Academic research relies extensively on macroeconomic variables to forecast the U.S. equity risk premium, with relatively little attention paid to the technical indicators widely employed by practitioners. Our paper fills this gap by comparing the predictive ability of technical indicators with that of macroeconomic variables. Technical indicators display statistically and economically significant in-sample and out-of-sample predictive power, matching or exceeding that of macroeconomic variables. Furthermore, technical indicators and macroeconomic variables provide complementary information over the business cycle: technical indicators better detect the typical decline in the equity risk premium near business-cycle peaks, whereas macroeconomic variables more readily pick up the typical rise in the equity risk premium near cyclical troughs. Consistent with this behavior, we show that combining information from both technical indicators and macroeconomic variables significantly improves equity risk premium forecasts versus using either type of information alone. Overall, the substantial countercyclical fluctuations in the equity risk premium appear well captured by the combined information in technical indicators and macroeconomic variables. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1838 . This paper was accepted by Wei Jiang, finance.

We analyze the computational problem of estimating financial risk in a nested simulation. In this approach, an outer simulation is used to generate financial scenarios, and an inner simulation is used to estimate future portfolio values in each scenario. We focus on one risk measure, the probability of a large loss, and we propose a new algorithm to estimate this risk. Our algorithm sequentially allocates computational effort in the inner simulation based on marginal changes in the risk estimator in each scenario. Theoretical results are given to show that the risk estimator has a faster convergence order compared to the conventional uniform inner sampling approach. Numerical results consistent with the theory are presented. This paper was accepted by Gérard Cachon, stochastic models and simulation.

Value at Risk (VaR) forecasts can be produced from conditional autoregressive VaR models, estimated using quantile regression. Quantile modeling avoids a distributional assumption, and allows the dynamics of the quantiles to differ for each probability level. However, by focusing on a quantile, these models provide no information regarding expected shortfall (ES), which is the expectation of the exceedances beyond the quantile. We introduce a method for predicting ES corresponding to VaR forecasts produced by quantile regression models. It is well known that quantile regression is equivalent to maximum likelihood based on an asymmetric Laplace (AL) density. We allow the density's scale to be time-varying, and show that it can be used to estimate conditional ES. This enables a joint model of conditional VaR and ES to be estimated by maximizing an AL log-likelihood. Although this estimation framework uses an AL density, it does not rely on an assumption for the returns distribution. We also use the AL log-likelihood for forecast evaluation, and show that it is strictly consistent for the joint evaluation of VaR and ES. Empirical illustration is provided using stock index data. Supplementary materials for this article are available online.

We develop a Bayesian methodology for systemic risk assessment in financial networks such as the interbank market. Nodes represent participants in the network, and weighted directed edges represent liabilities. Often, for every participant, only the total liabilities and total assets within this network are observable. However, systemic risk assessment needs the individual liabilities. We propose a model for the individual liabilities, which, following a Bayesian approach, we then condition on the observed total liabilities and assets and, potentially, on certain observed individual liabilities. We construct a Gibbs sampler to generate samples from this conditional distribution. These samples can be used in stress testing, giving probabilities for the outcomes of interest. As one application we derive default probabilities of individual banks and discuss their sensitivity with respect to prior information included to model the network. An R package implementing the methodology is provided. This paper was accepted by Noah Gans, stochastic models and simulation .