Financial modelling applied to long-horizon savings and pension products.
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his thesis studies financial models applied to valuation and risk measurement applicable to products in the life and pension area. Stock market theory and option pricing are described as a theoretical background. Mathematical models for simulation and pricing of financial instruments shows the history of financial mathematics and is the backbone of interest rate models and derivatives. Popular one-factor interest rate models and more complex models such as the Heath Jarrow Morton and LIBOR market model is derived. This is then linked up to products in the life and pension area, where defined benefit pension and guaranteed level long-term savings causes insurance companies to take on market risk. This risk is evaluated using the LIBOR market model and it is shown how two popular measurements for risk, Value-at-Risk and Expected Shortfall, behaves under different market conditions. Upcoming solvency and capital requirements from the norwegian securities commision, Kredittilsynet, use stresstests as a substitute for Value-at-Risk. With use of the LIBOR market model, the stresstest estimate is compared against Value-at-Risk. The analyzis indicates that the risk estimate used by Kredittilsynet is to low.