A Corrected Value-at-Risk Predictor

In this note it is argued that the estimation error in Value-at-Risk predictors gives rise to underestimation of portfolio risk. We propose a simple correction and find in an empirical illustration that it is economically relevant.Estimation Error; Finance; Garch; Prediction; Risk Management

Effects of Explanatory Variables in Count Data Moving Average Models

This note gives dynamic effects of discrete and continuous explanatory variables for count data or integer-valued moving average models. An illustration based on a model for the number of transactions in a stock is included.INMA model; Marginal effect; Intra-day; Financial data

Value at Risk for Large Portfolios

We argue that the practise of valuing the portfolio is important for the calculation of the V aR. In particular, the seller (buyer) of an asset does not face horizontal demand (supply) curves. We propose a partially new approach for incorporating this fact in the V aR and in an empirical illustration we compare it to a competing approach. We find substantial differences.Demand; Supply; Liquidity Risk; Limit Order Book; Bank; Sweden

On risk prediction

This thesis comprises four papers concerning risk prediction. Paper [I] suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks. Using daily data 2000-2006 for the Baltic state stock exchanges and that of Moscow we nd recursive structures with Riga directly depending in returns on Tallinn and Vilnius, and Tallinn on Vilnius. For volatilities both Riga and Vilnius depend on Tallinn. In addition, we find evidence of asymmetric effects of shocks arising in Moscow and in the Baltic states on both returns and volatilities. Paper [II] argues that the estimation error in Value at Risk predictors gives rise to underestimation of portfolio risk. A simple correction is proposed and in an empirical illustration it is found to be economically relevant. Paper [III] studies some approximation approaches to computing the Value at Risk and the Expected Shortfall for multiple period asset returns. Based on the result of a simulation experiment we conclude that among the approaches studied the one based on assuming a skewed t distribution for the multiple period returns and that based on simulations were the best. We also found that the uncertainty due to the estimation error can be quite accurately estimated employing the delta method. In an empirical illustration we computed five day Value at Risk’s for the S&P 500 index. The approaches performed about equally well. Paper [IV] argues that the practise used in the valuation of the portfolio is important for the calculation of the Value at Risk. In particular, when liquidating a large portfolio the seller may not face horizontal demand curves. We propose a partially new approach for incorporating this fact in the Value at Risk and in an empirical illustration we compare it to a competing approach. We find substantial differences.Finance; Time series; GARCH; Estimation error; Asymmetry; Supply and demand

Identi�cation of jumps in �financial price series

The paper outlines and tests, by means of Monte-Carlo simulations, a simple strategy of using existing non-parametric tests for jumps at the daily frequency to identify jumps at higher sampling frequencies. The suggested strategy allow for identi�cation of the number of jumps and jump times during a day, as well as, the size and direction (negative or positive) of the jumps. The method is of importance in order to facilitate detailed empirical studies concerning, for example, causes for jumps in fi�nancial price series at �ner levels than the daily. The Monte Carlo study reveals that the strategy works reasonably well, particular for lower jump intensities. An application of the studied strategy on the Handelsbanken stock is provided

Identi�cation of jumps in �financial price series

The paper outlines and tests, by means of Monte-Carlo simulations, a simple strategy of using existing non-parametric tests for jumps at the daily frequency to identify jumps at higher sampling frequencies. The suggested strategy allow for identi�cation of the number of jumps and jump times during a day, as well as, the size and direction (negative or positive) of the jumps. The method is of importance in order to facilitate detailed empirical studies concerning, for example, causes for jumps in fi�nancial price series at �ner levels than the daily. The Monte Carlo study reveals that the strategy works reasonably well, particular for lower jump intensities. An application of the studied strategy on the Handelsbanken stock is provided

On Risk Prediction

This thesis comprises four papers concerning risk prediction. Paper [I] suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks. Using daily data 2000-2006 for the Baltic state stock exchanges and that of Moscow we find recursive structures with Riga directly depending in returns on Tallinn and Vilnius, and Tallinn on Vilnius. For volatilities both Riga and Vilnius depend on Tallinn. In addition, we find evidence of asymmetric effects of shocks arising in Moscow and in the Baltic states on both returns and volatilities. Paper [II] argues that the estimation error in Value at Risk predictors gives rise to underestimation of portfolio risk. A simple correction is proposed and in an empirical illustration it is found to be economically relevant. Paper [III] studies some approximation approaches to computing the Value at Risk and the Expected Shortfall for multiple period asset re- turns. Based on the result of a simulation experiment we conclude that among the approaches studied the one based on assuming a skewed t dis- tribution for the multiple period returns and that based on simulations were the best. We also found that the uncertainty due to the estimation error can be quite accurately estimated employing the delta method. In an empirical illustration we computed five day Value at Risk's for the S&P 500 index. The approaches performed about equally well. Paper [IV] argues that the practise used in the valuation of the port- folio is important for the calculation of the Value at Risk. In particular, when liquidating a large portfolio the seller may not face horizontal de- mandcurves. We propose a partially new approach for incorporating this fact in the Value at Risk and in an empirical illustration we compare it to a competing approach. We find substantial differences

Identi�cation of jumps in �financial price series

The paper outlines and tests, by means of Monte-Carlo simulations, a simple strategy of using existing non-parametric tests for jumps at the daily frequency to identify jumps at higher sampling frequencies. The suggested strategy allow for identi�cation of the number of jumps and jump times during a day, as well as, the size and direction (negative or positive) of the jumps. The method is of importance in order to facilitate detailed empirical studies concerning, for example, causes for jumps in fi�nancial price series at �ner levels than the daily. The Monte Carlo study reveals that the strategy works reasonably well, particular for lower jump intensities. An application of the studied strategy on the Handelsbanken stock is provided.Financial econometrics, jumps, realized variance, bipower variation, stock price

Identification of jumps in financial price series

The paper outlines and tests, by means of Monte-Carlo simulations, a simple strategy of using existing non-parametric tests for jumps at the daily frequency to identify jumps at higher sampling frequencies. The suggested strategy allow for identification of the number of jumps and jump times during a day, as well as, the size and direction (negative or positive) of the jumps. The method is of importance in order to facilitate detailed empirical studies concerning, for example, causes for jumps in financial price series at finer levels than the daily. The Monte Carlo study reveals that the strategy works reasonably well, particular for lower jump intensities. An application of the studied strategy on the Handelsbanken stock is provided.Financial econometrics; jumps; realized variance; bipower variation; stock price