Execution Risk

Transaction costs in trading involve both risk and return. The return is associated with the cost of immediate execution and the risk is a result of price movements during a more gradual trading. The paper shows that the trade-off between risk and return in optimal execution should reflect the same risk preferences as in ordinary investment. The paper develops models of the joint optimization of positions and trades, and shows conditions under which optimal execution does not depend upon the other holdings in the portfolio. Optimal execution however may involve trades in assets other than those listed in the order; these can hedge the trading risks. The implications of the model for trading with reversals and continuations are developed. The model implies a natural measure of liquidity risk

Risk and Volatility: Econometric Models and Financial Practice

The advantage of knowing about risks is that we can change our behavior to avoid them. Of course, it is easily observed that to avoid all risks would be impossible; it might entail no flying, no driving, no walking, eating and drinking only healthy foods and never being touched by sunshine. Even a bath could be dangerous. I could not receive this prize if I sought to avoid all risks. There are some risks we choose to take because the benefits from taking them exceed the possible costs. Optimal behavior takes risks that are worthwhile. This is the central paradigm of finance; we must take risks to achieve rewards but not all risks are equally rewarded. Both the risks and the rewards are in the future, so it is the expectation of loss that is balanced against the expectation of reward. Thus we optimize our behavior, and in particular our portfolio, to maximize rewards and minimize risks.time series;

Value at risk models in finance

The main objective of this paper is to survey and evaluate the performance of the most popular univariate VaR methodologies, paying particular attention to their underlying assumptions and to their logical flaws. In the process, we show that the Historical Simulation method and its variants can be considered as special cases of the CAViaR framework developed by Engle and Manganelli (1999). We also provide two original methodological contributions. The first one introduces the extreme value theory into the CAViaR model. The second one concerns the estimation of the expected shortfall (the expected loss, given that the return exceeded the VaR) using a regression technique. The performance of the models surveyed in the paper is evaluated using a Monte Carlo simulation. We generate data using GARCH processes with different distributions and compare the estimated quantiles to the true ones. The results show that CAViaR models perform best with heavy-tailed DGP. JEL Classification: C22, G22CAViaR, extreme value theory, Value at Risk

Hedging Options in a GARCH Environment: Testing the Term Structure of Stochastic Volatility Models

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P 500 index volatility. Volatility models are compared by their ability to hedge options positions sensitive to the term structure of volatility. Overall, the most effective hedge is a Black-Scholes (BS) delta-gamma hedge, while the BS delta-vega hedge is the least effective. The most successful volatility hedge is GARCH components delta-gamma, suggesting that the GARCH components estimate of the term structure of volatility is most accurate. The success of the BS delta-gamma hedge may be due to mispricing in the options market over the sample period.

Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH

In this paper, we develop the theoretical and empirical properties of a new class of multi-variate GARCH models capable of estimating large time-varying covariance matrices, Dynamic Conditional Correlation Multivariate GARCH. We show that the problem of multivariate conditional variance estimation can be simplified by estimating univariate GARCH models for each asset, and then, using transformed residuals resulting from the first stage, estimating a conditional correlation estimator. The standard errors for the first stage parameters remain consistent, and only the standard errors for the correlation parameters need be modified. We use the model to estimate the conditional covariance of up to 100 assets using S&P 500 Sector Indices and Dow Jones Industrial Average stocks, and conduct specification tests of the estimator using an industry standard benchmark for volatility models. This new estimator demonstrates very strong performance especially considering ease of implementation of the estimator.

DYNAMIC CONDITIONAL CORRELATION - A SIMPLE CLASS OF MULTIVARIATE GARCH MODELS

Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations and provide sensible empirical results

DYNAMIC CONDITIONAL CORRELATION : A SIMPLE CLASS OF MULTIVARIATE GARCH MODELS

Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations and provide sensible empirical results