00Table-5cRisk neutral probabilities of transition over 4 periodsRating after 4 periodsCurrent RatingABCDA0.4050.2850.1780.132B0.2480.2940.2310.226C0.1630.2430.2190.375D0.0000.0000.0001.000Now that the risk neutral transition matrices have been calculated, any credit derivative may be priced.5.VALUATION OF CREDIT DERIVATIVESThe present model does not consider the credit risk associated with seller of the derivative product. Further, it does not consider the correlation between interest rate changes and credit rating migrations. In the following sections, we illustrate the pricing of two credit derivative products. 5.1A simple derivativeConsider a bond XYZ that currently has a credit rating B. Let us suppose that a credit derivative pays Rs. 100 if the rating of the bond at the end of 2 periods is C. In order to value this derivative, we need the risk-neutral probability of transition from B to C over 2 periods. From table-5a, we know that this probability is 0.176 and hence the value of the derivative is given by: Here again, the valuation of the credit derivative requires only the 2-period risk free zero rate because the pay-off from the derivative is adjusted for credit risk and is independent of the interest rate. 5.2A multi-period derivativeConsider the bond XYZ again. Now the derivative pays Rs. 100 if the credit rating of the bond changes to C during period 2 or period 3. This derivative can be decomposed into the simple derivative described above and another derivative that pays Rs. 100 in the third period if the rating of the bond is C in the third period but not in the second. For the valuation of this derivative, let us define events Ei and F as underEj : The rating of the bond changes to i at the end of 2 periods (where i = A or B)F : The rating of the bond changes to C at the end of 3 periodsThe probability that the derivative yields Rs. 100 in the third period is given by where i = A or B (6)The probabilities of transition ...
