In this thesis, we consider two issues related with financial risks. The first one is default risk of a firm and the other one is income loss of a family from death event of breadwinner.
A firm will be suffering from loss if default of issuer of a fixed income security occur. To transfer risk of default of a fixed income, a firm can enter into a contract, called CDS(Credit Default Swap). For an exact evaluation of credit derivatives such as CDS or BDS(Basket Default Swap), concrete analysis of default probability and default correlation should be preceded. Empirical researches said that mean rate of asset return and volatility of asset return change over time, i.e. across business cycle. Therefore, we derive default probability and default correlation under regime-switching market environment. We adopt a two-state Markov-chain to incorporate business cycle into our model. Using numerical results, we can explain various relationship between default probability, default correlation, and market condition. As an application of our model, we price CDS and BDS under regime-switching market environment and arrived some useful implications.
The second theme is on life insurance. A family will be suffering from loss if death event of the breadwinner occur. Life insurance purchase can be considered in the context of family portfolio. Using dynamic programming principle, we derive a HJB(Hamilton-Jacobi-Bellman) equation. Being considered as control variables, consumption, investment in risky assets and life insurance purchase can be obtained as feedback forms of the value function. In addition, we relax restriction on interest rates, i.e., we differentiate borrowing rate from deposit rate. With analytic solutions, we obtain some implications.