Pricing of a balance sheet option limited by a minimum solvency boundary

Abstract: Pension companies are required by law to remain above a certain solvency level. The main purpose of this thesis is to determine the cost of remaining above a lower solvency level for different pension companies. This will be modelled by an option with a balance sheet as the underlying asset. The balance sheet is assumed to consist of bonds, stocks, liabilities and own funds. Both liabilities and bonds are modelled using forward rates. Data used in this thesis is historical stock prices and forward rates. Several potential models for stock and forward rate processes are considered. Examples of models considered are Bates model, Libor market model and a discrete model based on normal log-normal mixture random variables which have different properties and distributions. The discrete normal log-normal mixture model is concluded to be the model best suited for stocks and bonds, i.e. the assets, and for liabilities. The price of the balance sheet option is determined using quasi-Monte Carlo simulations. The price is determined in relation to the initial value of the own funds for different portfolios with different initial solvency levels and different lower solvency bounds. The price as a function of the lower solvency bound seems to be an exponential function and varies depending on portfolio, initial solvency level and lower solvency bound. The price converges with sufficient accuracy. It is concluded that the model proves that remaining above a lower solvency level results in a significant cost for the pension company. A further improvement suggested is to validate the constructed model with other models.