This study presents a procedure for valuing KoMoCo MBS (mortgage-backed securities) 2003-2, using a bivariate binomial option pricing technique. By forcing the two underlying state variables (the real estate value and the spot rate of interest) to undergo transformations, bivariate binomial trees are created, and using reversing transformation, the house value and the interest rate can be computed at each node. Working backward through the trees, the bond without option, prepayment option, and default option are evaluated.
As the Korean housing market moves dramatically and the mortgage loan-to-house value (LTV) grows up to 70%, the default option should be considered with the prepayment option when valuing MBS.
The borrower’s position is the value of the house less the value of the mortgage, and since the borrower holds options to maximize his position, the value of the mortgage will be the smallest possible value given the three scenarios; prepayment, default, and continuation.
When the prepayment option and the default option are evaluated separately, there is no big difference between MBS which is evaluated with the option to prepay and MBS with the option to prepay and default, as the value of the default option is small because of low LTV. But when the prepayment option and default option are evaluated simultaneously, the value of MBS with the option to prepay and default is much less than the value of MBS with the option to prepay.
For the flexibility of the model, transaction costs and borrower’s income are introduced. The values of the options decrease as the transaction costs increase. But the borrower’s income has little effect on the default option.
