- Methods to determine the market-consistent price of pension and insurance contracts
We used an indifference price approach to develop a consistent pricing framework, and relate it to the pricing rule-of-thumb that practitioners use: Best estimate plus a market value margin. The best estimate corresponds to the expected discounted value of the claims. The market value margin can be interpreted as a safety load, which usually depends on the expected risk-aversion coefficient. Under general assumptions, we developed an approximate pricing framework for life insurance liabilities using utility indifference. The resulting pricing rule is clearly linked to the best estimate plus a market value margin rule-of-thumb. - Results on optimal regulation and the interaction between insurers and the regulator
This project analyses how to choose regulatory intervention levels in order to control the shortfall probability of an insurance company. Whenever the impact of regulatory authorities' rules on the fair value of company's liabilities and assets is non-negligible, then a “fixed volatility rule” for the regulatory intervention levels of the insurance company follows a dynamic investment strategy. The project also analyses the interaction between the regulatory rule and the insurance company's risk management. - Analytical Approximation of Embedded Options
Life insurance products have profit sharing features in combination with guarantees. In practice, these kinds of options are mostly valued by Monte Carlo simulations. However, for risk management calculations and reporting processes, such calculations are very time-consuming. In our paper analytical approximations are derived for these kinds of options. The analytical approximation for options with direct payment is almost exact while the approximation for compounding options is also satisfactory.
Sub project 2: Correlation Risk and Risk Measurement
- Results on option-pricing anomalies
This project contributes to the literature on explaining why such put options are substantially more expensive than the most standard models suggest. Jump- and volatility risk are the important drivers of these deviations. The project studies international integration of markets for this risk. For each market separately, we provide evidence that volatility and jump risk are priced risk factors. We found little evidence of global unconditional pricing of risk. In investigating the presence of time-variation in the cross-market relationships, we found evidence that option markets have become increasingly interrelated. The benefits of diversifying jump- and volatility risk internationally are substantial, but declining over our sample, in line with the hypothesis of increased but imperfect integration of world markets for jump- and volatility risk. - The impact of adding housing futures to an investor’s optimal portfolio-choice problem
The portfolio implications and welfare improvements of the housing futures are small. This is mainly due to the large remaining idiosyncratic house price risk, which cannot be hedged using futures written on a city-level house price index. - The risk and return of private equity funds
We found a high market beta for venture capital funds and a low beta for buyout firms. The risk-adjusted returns of the average private equity fund are reported to be surprisingly low. The paper also sheds on previous findings that larger and more experienced funds have higher returns, by showing that this is mainly caused by higher risk exposures of those funds, and not by abnormal performance.
Sub project 3: Comonotonic Risk and Asset & Liability Management
- Optimal dividends and ALM under unhedgeable risk
In this paper we develop a framework for optimal investment decisions for insurance companies under unhedgeable risk. The perspective that we choose is from an insurance company that tries to maximise the stream of dividends paid to its shareholders. The policy instruments that the company has are the dividend policy and the investment policy. The insurance company can continue to pay dividends until bankruptcy, and hence the time of bankruptcy is also endogenously controlled by the dividend and investment policies. Using stochastic control theory, we derive simultaneously the optimal investment policy and the optimal dividend policy, taking the insurance risks to be given. - Spectral decomposition of optimal asset-liability management
This paper concerns optimal asset-liability management when the assets and the liabilities are modeled by means of correlated geometric Brownian motions as suggested in Gerber and Shiu (2003). In a first part, we apply singular stochastic control techniques to derive a free boundary equation for the optimal value creation as a growth of liabilities or as dividend payment to shareholders. We provide analytical solutions to the HJB optimality equation in a rather general context. In a second part, we study the convergence of the cash flows to the optimal value creation using spectral methods. For particular cases, we also provide a series expansion for the probabilities of bankruptcy in finite time.
Sub project 4: Generational accounts, investment policies and the framework for supervision
- Generational accounting, solidarity and pension losses
The stock market collapse led to political tensions between generations due to the fuzzy definition of the property rights over the pension funds’ wealth. The problem is best resolved by the introduction of generational accounts. Modern consumption and portfolio theory shows that the younger generations should have the higher equity exposure due to their human capital. Stock market losses should be distributed smoothly over lifetime consumption by adjusting both current contributions and future entitlements. We present expressions for the substantial welfare losses involved in various practically relevant deviations from the optimal system.
Update January 21, 2009