Modelling and management of mortality risk: a review

In the first part of the paper, we consider the wide range of extrapolative stochastic mortality models that have been proposed over the last 15–20 years. A number of models that we consider are framed in discrete time and place emphasis on the statistical aspects of modelling and forecasting. We discuss how these models can be evaluated, compared and contrasted. We also discuss a discrete-time market model that facilitates valuation of mortality-linked contracts with embedded options. We then review several approaches to modelling mortality in continuous time. These models tend to be simpler in nature, but make it possible to examine the potential for dynamic hedging of mortality risk. Finally, we review a range of financial instruments (traded and over-the-counter) that could be used to hedge mortality risk. Some of these, such as mortality swaps, already exist, while others anticipate future developments in the market.     

Modelling conditional heteroscedasticity and jumps in Australian short-term interest rates

The present paper explores a class of jump–diffusion models for the Australian short‐term interest rate. The proposed general model incorporates linear mean‐reverting drift, time‐varying volatility in the form of LEVELS (sensitivity of the volatility to the levels of the short‐rates) and generalized autoregressive conditional heteroscedasticity (GARCH), as well as jumps, to match the salient features of the short‐rate dynamics. Maximum likelihood estimation reveals that pure diffusion models that ignore the jump factor are mis‐specified in the sense that they imply a spuriously high speed of mean‐reversion in the level of short‐rate changes as well as a spuriously high degree of persistence in volatility. Once the jump factor is incorporated, the jump models that can also capture the GARCH‐induced volatility produce reasonable estimates of the speed of mean reversion. The introduction of the jump factor also yields reasonable estimates of the GARCH parameters. Overall, the LEVELS–GARCH–JUMP model fits the data best.     

A Simple Measure for Examining the Proxy Problem of the Short-Rate

The behavior of a finite-maturity yield used as a proxy for the short-rate can deviate substantially from that of the short-rate, which causes estimation biases of model parameters and pricing errors of interest-rate claims. This study proposes a simple measure that visualizes this deviation based on an analytical approximation of the term structure of interest rates. The computation of the measure is almost as easy as that of an affine model, so the adequacy of proxy can be readily checked even for short-rate models that do not admit closed-forms of bond prices.     

The interest rate effects of government bond purchases away from the lower bound

I analyze the recent experience of unconventional monetary policy in Sweden to study the interest rate transmission mechanisms of government bond purchases when interest rates are away from the lower bound. Using dynamic term structure models and event study regressions I find that government bond purchases have important portfolio balance and signaling effects. The signaling channel operates mainly by lowering short-rate expectations in the intermediate segment of the yield curve, while the portfolio balance channel is effective in lowering longer maturity term premia. In addition, I find that target interest rate policy and government bond purchases operate in different segments of the yield curve. This suggests that a combination of the two policies can be used to lower interest rates across the whole maturity spectrum, making monetary policy more expansionary.