Mixtures of Tails in Clustered Automobile Collision Claims

Knowledge of the tail shape of claim distributions provides important actuarial information. This paper discusses how two techniques commonly used in assessing the most appropriate underlying distribution can be usefully combined. The maximum likelihood approach is theoretically appealing since it is preferable to many other estimators in the sense of best asymptotic normality. Likelihood based tests are, however, not always capable of discriminating among non-nested classes of distributions. Extremal value theory offers an attractive tool to overcome this problem. A much larger set of distribution classes is nested by their tail parameter. This paper shows that both estimation strategies can be usefully combined when the data generating process is characterized by strong clustering in time and size. We find that the extreme value theory is a useful starting point in detecting the appropriate distribution class. Once that has been achieved, the likelihood-based EM-algorithm is proposed to capture the clustering phenomena. Clustering is particularly pervasive in actuarial data. An empirical application to a four-year data set of Dutch automobile collision claims is therefore used to illustrate the approach

Tailing the Bid-Asking Spread

This paper discusses an application of a rather novel technique for the estimation of the tails of return distributions for financial assets. This extreme value approach proves to be particularly useful when assessing characteristics of high frequency (tick-by-tick) transaction data. Tail parameter estimates allow derivation of probabilities of large price changes. These probabilities improve optimal setting of bid-ask spreads based on the order processing component of the bid-ask spread. Estimates for optimal levels are compared to 'observed' bid-ask spreads. The latter, which are estimates in itself, are based on recently developed methods in the literature

A Threshold Error Correction Model for Intraday Futures and Index Returns

Index-futures arbitragers only enter into the market if the deviation from the arbitrage relation is large enough to compensate for transaction costs and associated interest rate and dividend risks. We estimate the band around the theoretical futures price within which arbitrage is not profitable for most arbitragers, using a threshold autoregression model. Combining these thresholds with an error correction model, we can make a distinction between the effects of arbitragers and infrequent trading on index and futures returns

A Threshold Error Correction Model for Intraday Futures and Index Returns

Index-futures arbitragers only enter into the market if the deviation from the arbitrage relation is large enough to compensate for transaction costs and associated interest rate and dividend risks. We estimate the band around the theoretical futures price within which arbitrage is not profitable for most arbitragers, using a threshold autoregression model. Combining these thresholds with an error correction model, we can make a distinction between the effects of arbitragers and infrequent trading on index and futures returns

Mixtures of Tails in Clustered Automobile Collision Claims

Knowledge of the tail shape of claim distributions provides important actuarial information. This paper discusses how two techniques commonly used in assessing the most appropriate underlying distribution can be usefully combined. The maximum likelihood approach is theoretically appealing since it is preferable to many other estimators in the sense of best asymptotic normality. Likelihood based tests are, however, not always capable of discriminating among non-nested classes of distributions. Extremal value theory offers an attractive tool to overcome this problem. A much larger set of distribution classes is nested by their tail parameter. This paper shows that both estimation strategies can be usefully combined when the data generating process is characterized by strong clustering in time and size. We find that the extreme value theory is a useful starting point in detecting the appropriate distribution class. Once that has been achieved, the likelihood-based EM-algorithm is proposed to capture the clustering phenomena. Clustering is particularly pervasive in actuarial data. An empirical application to a four-year data set of Dutch automobile collision claims is therefore used to illustrate the approach