This thesis presents an empirical study on the valuation of option-embedded risky notes through CIR model and BDT model which each represents the equilibrium model and no-arbitrage model. To value those kinds of bonds, one has to consider how to value the embedded options which make the cash flows uncertain and default probabilities. In this thesis, Monte Carlo simulation and binomial interest rate tree are used to describe the random evolution of future interest rates and discount the payoff of those bonds to arrive at bonds’ value. Default probabilities are calculated based on the term structure of risk-free interest rates and risky note’s interest rates which are observed from the bond market at one day before the notes’ issue using Jarrow and Turnbull model.
The results of this study show that the prices of the short term notes (1 and 2 years) a little over-valued in both models compared to the prices when issued. In case of the long term notes (7 years), the estimated prices by the CIR model are over-valued compared to the issue prices by about one percent. On the contrary, the prices estimated by the BDT model are under-valued compared to the issue prices by about two percent. In this study, the recovery rate is assumed to be given and the default probabilities are also assumed to be independent from the risk-free interest rate process. In real world, however, default probabilities are correlated with the interest-rate level. Besides the term structure of risky notes’ interest rates which was used to produce default probabilities is not that trustable because of limited trading volume and easily affected by the market situation including liquidity risk. So further research is needed to correct these matters.
