| dc.description.abstract | Abstract
A CB Asset SWAP is now very popular in the market and it involves the IRS. In the pricing process, there does not exist a proper credit spread for the credit premium. We show in the paper a way to forecast the credit spread with the use of a Markov chain.
When issuing a corporate bond, one can determine the default premium according to the default probability; hence, we could say that the premium mainly comes from default risk. In the evaluation and stripping process of a CB, one should use the corporate interest rate to price the CB. In this way, the relationship between the risk and the premium will be reasonable.
This paper applies the Markov chain to predict the default probability among different ratings and from with the default probability we can estimate a credit spread. We also use the Monte Carlo simulation and the Vasicek model to evaluate CB prices. Longstuff and Schwartz modify the Monte Carlo approach with a least-square method to evaluate the American option price. We apply a modified method to evaluate the CB price, and from this, we are able to evaluate the call on a CB. We strip the CB into a call on the CB and a pure corporate bond and then sell it to an option investor and a fixed-income investor.
With historical data like transition matrix coming from S&P or Moody’s, we are able to estimate a CB’s the default probability and according to the default, we can evaluate all kinds of credit derivatives.
Moreover, we also analyze the effect of options which are embed in CBs. The options are the issuer’s call option and the reset right and conversion right. We also analyze the sensitivity of the recovery rate and find that the issuer’s call option has a negative impact on the a CB’s value, and the effect is decreasing as the rating falls. The reset right has a positive effect on a CB’s value and its derivatives, with the effect increasing as the rating decreases. The recovery rate has a positive effect on a CB’s value, whereby for a lower rated, it is more sensitive for the recovery rate. We also show the relationship between default probability and default-risk premium in section 4. | en_US |