Valuation and hedging of participating life-insurance policies under management discretion

The valuation and hedging of participating life insurance policies, also known as with-profits policies, is considered. Such policies can be seen as European path-dependent contingent claims whose underlying security is the investment portfolio of the insurance company that sold the policy. The fair valuation of these policies is studied under the assumption that the insurance company has the right to modify the investment strategy of the underlying portfolio at any time. Furthermore, it is assumed that the issuer of the policy does not setup a separate portfolio to hedge the risk associated with the policy. Instead, the issuer will use its discretion about the investment strategy of the underlying portfolio to hedge shortfall risks. In that sense, the insurer’s investment portfolio serves simultaneously as the underlying security and as the hedge portfolio. This means that the hedging problem can not be separated from the valuation problem. We investigate the relationship between risk-neutral valuation and hedging of these policies in complete and incomplete financial markets.     

The effect of management discretion on hedging and fair valuation of participating policies with maturity guarantees

In this paper we consider how an insurer should invest in order to hedge the maturity guarantees inherent in participating policies. Many papers have considered the case where the guarantee is increased each year according to the performance of an exogenously given reference portfolio subject to some guaranteed rate. However, in this paper we will consider the more realistic case whereby the reference portfolio is replaced by the insurer’s own investments which are controlled completely at the discretion of the insurer’s management. Hence in our case any change in the insurer’s investment strategy leads to a change in the underlying value process of the participating contract. We use a binomial tree model to show how this risk can be hedged, and hence calculate the fair value of the contract at the outset.     

Semiparametric Bootstrap Approach to Hypothesis Tests and Confidence Intervals for the Hurst Coefficient

A major application of rescaled adjusted range analysis (R–S analysis) is to the study of price fluctuations in financial markets. There, the value of the Hurst constant, H, in a time series may be interpreted as an indicator of the irregularity of the price of a commodity, currency or similar quantity. Interval estimation and hypothesis testing for H are central to comparative quantitative analysis. In this paper we propose a new bootstrap, or Monte Carlo, approach to such problems. Traditional bootstrap methods in this context are based on fitting a process chosen from a wide but relatively conventional range of discrete time series models, including autoregressions, moving averages, autoregressive moving averages and many more. By way of contrast we suggest simulation using a single type of continuous-time process, with its fractal dimension. We provide theoretical justification for this method, and explore its numerical properties and statistical performance by application to real data on commodity prices and exchange rates. This revised version was published online in June 2006 with corrections to the Cover Date.     

Web Quantlets for Time Series Analysis

New and advanced methods for nonlinear time series analysis are in general not available in standard software packages. Their implementation requires substantial time, computing power as well as programming skills. In time series analysis such a scenario is given by a recently suggested nonparametric lag selection procedure for univariate nonlinear autoregressive models which is based on the Corrected Asymptotic Final Prediction Error. In this paper we suggest a worldwide Web based specific client/server architecture that provides empirical researchers with fast access to new methods and powerful computing environments without knowing the statistical computing language and the server location. This architecture is implemented using the XploRe Quantlet technology and illustrated for nonparametric lag selection. Access to the Quantlet computing service can be obtained via standard WWW browsers or a Java client. The XploRe Quantlet service can be helpful in constructing research books and interactive teaching environments as the electronic version of this paper, available from http://ise.wiwi.hu-berlin.de/rolf/webquant.pdf, demonstrates.