Abstract
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.
Highlights
A bond is probably the most traditional and important investment instrument with regard to the volume and liquidity of the transactions
If an analogical option is in the hands of a bondholder we speak about embedded put option
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
Summary
A bond is probably the most traditional and important investment instrument with regard to the volume and liquidity of the transactions. Issuers frequently have the right to buy back a certain amount of the debt or to repay all the instrument on certain points of time before maturity (Bermuda Style Option in this case). Sometimes there is set a certain protection period for an investor, after the issuance In this case, we speak about the call option (callable bond) and the issuer pays for the option – the bond is cheaper for an investor. If an analogical option is in the hands of a bondholder we speak about embedded put option. This option can be of considerable value. The issuer might even have the right to pay back a bond at any time, i.e., the bond contains an American Style Prepayment Option
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