Behaviour of bond's embedded option with regard to credit rating

In this financial engineering research, we study the behaviour of an option premium of a call/put option which is embedded in a typical fixed coupon bond with finite maturity. The contribution of the research is the conclusion about the dynamics of premium changes; represented by direction and sensitivity; with respect to the changes in credit rating and also risk-free interest rate development. The aim of the research is also to clearly demonstrate this theoretically complicated topic to the financial practitioners using a practical example. We are about to consider a 3-dimensional process where the dimensions are: time, rating development process and risk-free interest rate development. We use Standard & Poor's rating transition matrix to create rating tree and Hull-White model for modelling of risk-free interest rate development. We add embedded call/put option to the bond structure and assume the call/put option to be exercised in case of interest rates decline/rise or rating worsening/improvement. For valuation, we use the risk-neutral concept. Using a numerical solution on the 3-dimensional tree (implemented in MATLAB), we avoid problems that appear while analytical solving of partial differential equations.