International developments in accounting regulation and insurance supervision require that companies report their insurance and pension liabilities on a fair value basis. However, the standard theory of derivatives pricing cannot be applied to establish the fair value of insurance and pension liabilities. On the other hand, the standard actuarial literature only considers the pricing of pure insurance risks and ignores financial market risks, which also does not lead to a fair valuation. The purpose of the research project is to explore and elaborate on the convergence between “actuarial” and “financial” pricing methodologies to establish fair valuation for insurance and pension liabilities. In addition the research will focus on the risk management of the liabilities by a tractable and realistic hedging strategy.
2. Correlation Risk and Risk Measurement
This project focuses on extracting information about asset correlations that is embedded in the prices of basket credit derivatives, such as basket credit default swaps and collateralized debt obligations (CDOs). These basket credit derivatives have become quite popular in financial markets recently, and are typically defined on a large set of firms. The value of these instruments critically depends on the default correlation (or asset value correlation) of these firms. In fact, traders often quote prices in terms of ‘implied correlations’, using a Gaussian copula pricing model.
3. Comonotonic Risk and Asset & Liability Management
In many practical situations, projections are made for future premium income (over some time horizon) and the corresponding future payments. The value of the difference of these amounts is given by a cash flow for which the net present value is the value of the operation (often called the embedded value, or appraisal value, of the business). One then considers several scenarios for this cash flow and often uses simulations to model interest rates. Using simulation has the disadvantage that little useful information is obtained on the tail of the distribution, while in fact we would like to estimate, for instance, the 99.75% quantile. It only helps in case the tail behaviour is known in advance but this is certainly not the case for the cases we are considering.
4. Generational accounts, investment policies and the framework for supervision
The proposed research project analyzes the impact of many restrictive assumptions applied in Teulings and De Vries (2005), in particular: i) the risk free interest rate; this topic is particularly relevant, since under a risk free interest rate, the optimal amount of risk bearing before a generation enters the pension fund is unbounded; ii) the correlation between the return on human capital and on equity; the optimal share of equity in the portfolio is higher when human capital commoves with equity, iii) a utility function with adjustment cost in consumption; adjustment cost lowers the share of equity for the elderly even further, iv) jump risk in stock prices; jump risk adds a role for options. The project will generate a realistic estimates of the cost and benefits of introducing generational accounts. Furthermore, the project will elaborate on the role of precautionary savings and intergenerational buffers. Finally, the project will analyze the optimal framework for supervision of pension funds. Extensions might include the issue of how the system deals with the longevity risk, and more importantly, of idiosyncratic human capital risk. The latter issue is troubled by moral hazard problems (trade off between insurance and incentives), and has great practical implications, since it allows the joint evaluation (and potentially integration) of three types of arrangements: pension contracts, disability insurance, and the “levensloop regeling”.
