Backtesting Stochastic Mortality Models

Abstract

This study sets out a backtesting framework applicable to the multiperiod-ahead forecasts from stochastic mortality models and uses it to evaluate the forecasting performance of six different stochastic mortality models applied to English & Welsh male mortality data. The models considered are the following: Lee-Carter’s 1992 one-factor model; a version of Renshaw-Haberman’s 2006 extension of the Lee-Carter model to allow for a cohort effect; the age-period-cohort model, which is a simplified version of Renshaw-Haberman; Cairns, Blake, and Dowd’s 2006 two-factor model; and two generalized versions of the last named with an added cohort effect. For the data set used herein, the results from applying this methodology suggest that the models perform adequately by most backtests and that prediction intervals that incorporate parameter uncertainty are wider than those that do not. We also find little difference between the performances of five of the models, but the remaining model shows considerable forecast instability.     

Patterns of Aging-Related Changes on the Way to 100

Abstract

The objective of this paper is to investigate dynamic properties of age trajectories of physiological indices and their effects on mortality risk and longevity using longitudinal data on more than 5,000 individuals collected in biennial examinations of the Framingham Heart Study (FHS) original cohort during about 50 subsequent years of follow-up. We first performed empirical analyses of the FHS longitudinal data. We evaluated average age trajectories of indices describing physiological states for different groups of individuals and established their connections with mortality risk. These indices include body mass index, diastolic blood pressure, pulse pressure, pulse rate, level of blood glucose, hematocrit, and serum cholesterol. To be able to investigate dynamic mechanisms responsible for changes in the aging human organisms using available longitudinal data, we further developed a stochastic process model of human mortality and aging, by including in it the notions of “physiological norms,” “allostatic adaptation and allostatic load,” “stress resistance,” and other characteristics associated with the internal process of aging and the effects of external disturbances. In this model, the persistent deviation of physiological indices from their normal values contributes to an increase in morbidity and mortality risks. We used the stochastic process model in the statistical analyses of longitudinal FHS data. We found that different indices have different average age patterns and different dynamic properties. We also found that age trajectories of long-lived individuals differ from those of the shorter-lived members of the FHS original cohort for both sexes. Using methods of statistical modeling, we evaluated “normal” age trajectories of physiological indices and the dynamic effects of allostatic adaptation. The model allows for evaluating average patterns of aging-related decline in stress resistance. This effect is captured by the narrowing of the U-shaped mortality risk (considered a function of physiological state) with age. We showed that individual indices and their rates of change with age, as well as other measures of individual variability, manifested during the life course are important contributors to mortality risks. The advantages and limitations of the approach are discussed.     

Stability of international stock market relationships across month of the year and different holding intervals

Potential benefits from international diversification depend upon the stability in stock market relationships. Using monthly data of 11 international stock markets, this paper examines the stability in stock market relationships across month of the year and across different holding intervals. Empirical results show that the correlation structure is more stable than the covariance structure. While empirical evidence supports the hypothesis that the correlation structure is very stable across different holding intervals, the empirical support for the stability in correlation structure across month of the year is much weaker.     

Liquidity and market makers: a pseudo-experimental analysis with ultrahigh frequency data

An analysis is given of the effect of market makers on liquidity using a transaction-level database. For this purpose, the focus is on a financial market where a change in regulations created explicitly the category of market maker in 1997 and that date is used to construct a pseudo-experiment. In contrast with other studies that use ultrahigh frequency data, the days to be analysed are selected using a statistical procedure to match observations before and after the change in regulation. The propensity score is used to perform the matching. After choosing the days, an estimate of an ordered probit model is made to explain the intraday behaviour of price changes. The coefficient estimates from the ordered probit model are used to calculate a measure of liquidity based on the steepness of the response function of price changes to volume. The results show that liquidity, measured in this way, has not been affected by the introduction of the market makers.     

Liquidity determination in an order-driven market

We exploit full order level information from an electronic FX broking system to provide a comprehensive account of the determination of its liquidity. We not only look at bid-ask spreads and trading volumes, but also study the determination of order entry rates and depth measures derived from the entire limit order book. We find strong predictability in the arrival of liquidity supply/demand events. Further, in times of low (high) liquidity, liquidity supply (demand) events are more common. In times of high trading activity and volatility, the ratio of limit to market order arrivals is high but order book spreads and depth deteriorate. These results are consistent with market order traders having better information than limit order traders.     

The effect of the establishment of an organized exchange on weak form efficiency: the case of Istanbul Gold Exchange

Evidence is presented from IGE (the Istanbul Gold Exchange) that an institutional regulation such as the establishment of an organized exchange is an important component of informational efficiency that should not be disregarded in the process of financial liberlization.     

A framework to measure integrated risk

A framework underlying various models that measure the credit risk of a portfolio is extended in this paper to allow the integration of credit risk with a range of market risks using Monte Carlo simulation. A structural model is proposed that allows interest rates to be stochastic and provides closed-form expressions for the market value of a firm's equity and its probability of default. This model is embedded within the integrated framework and the general approach illustrated by measuring the risk of a foreign exchange forward when there is a significant probability of default by the counterparty. For this example moving from a market risk calculation to an integrated risk calculation reduces the expected future value of the instrument by an amount that could not be calculated using the common pre-settlement exposure technique for estimating the credit risk of a derivative.