Multi-Factor Interest Rate Models and Portfolio Management within Life Insurance Companies in Low-Rate Environments
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In this Master's thesis we study the equity market and the two multi-factor interest rate models Heath-Jarrow-Morton model (HJM) and the LIBOR market model (LMM) on the Norwegian, European and US interest rate market. These models are used to analyze a floor and to investigate the management of paid-up policy portfolios kept by life insurance companies. The main concerns are the current low-rate environment experienced in the financial markets today, and their exposure to negative interest rates. The two interest rate models are calibrated to the market using volatility factors. The HJM uses principal component analysis to find the volatility factors, while the LMM uses Exponentially Weighted Moving Average. The paid-up policy portfolios are then analyzed using Value at Risk and Expected Shortfall. We find that the probability of negative rates is clearly present in the HJM-framework, while it is zero in LMM because of the log-normal assumption. Further, we also see that the probability of negative rates are larger in the European market, compared to the Norwegian and US market. This in turn leads to significantly higher floor prices in the European market. The prices calculated with HJM and LMM deviates the most near the current spot rate, with HJM always giving higher floor prices than LMM. In the end we see that the European paid-up policy portfolios give less gain to the insurance companies compared to the Norwegian and US portfolios. The simulation also shows that a higher gain demand requires a larger share in the equity markets. This result is in line with the general yield hunting strategies observed in the market today.