Contact person. Bert de Bock
Thesis 1. Dynamic Replicating Portfolio Models
Abstract. Savings accounts represent a large part of the funding of a bank. The bank wants to use this money for investments, but this is associated with a risk. The clients can freely deposit or withdraw money at any time they choose to and therefore, a savings account does not have a predetermined maturity. Assumptions regarding the maturity must be made and a savings account is therefore modeled by a portfolio that consists of fixed-income securities that mimics the cash flows of the account. There are multiple ways to create such a replicating portfolio model. During my internship, I created a dynamic model which forecasts the unknown risk factors, such as the market rates, the client rate and the volume, and provides the user with a dynamic investment rule, which states how to invest the available money for every time step. The model has also been tested on actual data and the results are compared with the results of a static model. In a static model the investment rule is constant in time. This means that maturing money is always reinvested in the same maturity and available money is always allocated according to the same percentages.
Thesis 2. One-Way Trading With Transaction Costs
Abstract. In the one-way trading problem a trader initially has all his capital invested in shares. He wishes to sell all his shares on the stock market to maximize his final cash. Vovk showed that there are certain trading strategies that will guarantee some final amount of cash, depending on the maximum observed price. He also characterized the best possible guarantees and their corresponding strategies. In reality a trader has to pay a fee to a broker for every transaction. When transaction costs are added to the one-way trading model, Vovks strategies can result in very large losses. We adjusted the strategies such that they trade more economically. We showed they perform almost as good as Vovks strategies for the transaction cost free model.
Thesis 3. On the optimal investment policy for a dormant pension fund with fixed liabilities
Abstract. In recent years, due to the aftermath of the credit crisis and the euro crisis, interest rates have hit record lows. Low interest rates increase the costs or discounted value of pension plans and pension funds. Historically and in recent years stocks, on average, had higher yields than bonds. The question that arises is if it is possible to have a pension plan, which utilises risky assets such as stocks, with lower costs and still is considered to be safe enough.
Thesis 4. Calculating a Dutch Pension Fund’s Capital Requirement for Longevity Risk
Abstract. Longevity risk is the risk arising from uncertainty in the prediction of future mortality. This risk must be faced by pension funds. The legislation for Dutch pension funds prescribes that the pension funds need to keep in reserve a certain level of capital for this risk. De Nederlandsche Bank (DNB) suggests a method for calculating this capital requirement. Problems with this method are that it is generalized, not transparent and it does not make use of recent insights in mortality. Therefore, in this thesis an alternative method is developed, that provides a better insight in the current risk. This alternative method is a Monte Carlo method, using a stochastic mortality model. The stochastic model used is recently published and is calibrated on the most recent data. Finally, the capital requirement is calculated using both methods. It turns out that the resulting capital requirement from the alternative method is less than half of the capital requirement calculated using the method suggested by DNB.
Thesis 5. Macro-Level and Micro-Level Claims Reserving for Non-Life Insurances
Abstract. Insurance companies need to hold capital aside to meet future liabilities associated with events that are covered by existing contracts. The process of estimating the reserves is called claims reserving. Macro-level reserving models are already used for decades by insurance companies. This is because they are widely applicable and easy to use. With the introduction of Solvency II, a regulatory framework for insurances, insurance undertakings are encouraged to explore more advanced reserving models. The main goal of this thesis is to investigate whether the claims reserving process for non-life insurances can be improved. In the macro-level models, a lot of useful information that is often available remains unused. This leads to introducing a micro-level reserving model, which can take into account much more detailed information than the macro-level models. For this thesis, a macro-level model and a basic micro-level model are implemented. Where the macro-level model only gives projections of the aggregated payment amounts, the micro-level model allows for examining the projections for every single claim. Because of this, every component of the micro-level model can be tested and adjusted individually (reporting delay, claim development, payment distributions). Based on the results of the out-of-sample tests, it can not be concluded that one model performs better than the other. For this, the models should also be tested on other data sets. With further research, adjustments can be made such that the micro-level model is suitable for application in practice. Based on the findings in this thesis, insurance companies could improve the possibilities for applications of micro-level reserving models by preparing their data and the registration of it. Therefore, more awareness should be created at insurance and reinsurance companies about the micro-level model and the required data quality.
Thesis 6. An investment strategy for pension funds, with the focus on the purchasing power of the pension entitlements
Abstract. Currently, more than 50% of the participants of a pension fund have a pension funds that has a funding deficit. Those pension funds are not allowed by law to index the pension benefits of their participants to the inflation. This results in a decrease in purchasing power of the pension entitlements. In this talk we first look at the historical performance of stocks and bonds. Based on these results we will introduce an investment strategy for pension funds that should better preserve the purchasing power of its participants. This strategy will be applied on a model pension fund and compared with a common investment strategy of pension funds.