bond coupon interest due to both junior and senior bonds = USD

问题如下：

A manager from the structured credit risk desk at a bank is presenting to a group of newly hired risk analysts on calculating cash flows in a securitization structure. The manager illustrates the procedure with the existing collateral pool of loans and the corresponding liabilities, all with a maturity of 5 years, using the following information:

The manager makes additional observations as follows:

• The loans in the collateral pool pay a fixed spread of 2.2% over the swap curve

• There were no defaults in year 1

• The value of the overcollateralization account at the end of year 1 was EUR 0

What is the value of the overcollateralization account at the end of year 2 if there are 8 defaults in year 2?

选项：

A.EUR 600,000 B.EUR 1,056,000 C.EUR 2,544,000 D.EUR 3,600,000

解释：

C is correct: The value of the overcollateralization account (OC) at end of year 2 (OC2) includes the compounded year-1 value of the OC (OC1), the recovered principal amount at the end of year 2 (R2) and is computed as follows:

OC2 = (1 + swap rate)*OC1 + R2.

Since there is no default in year 1, consider

Min[(0.035 + 0.022)*100*1,000,000 - 6,300,000; 1,500,000] = -600,000

As that is negative, the overcollateralization account is entirely depleted at the end of year 1.

For year 2,

First:

Excess spread at the end of year 2 = L – B

where,

L = interest from surviving loans = (0.035 + 0.022)*(100 – 8) * 1,000,000

= EUR 5,244,000

B = bond coupon interest due to both junior and senior bonds

= USD 6,300,000 (given)

Therefore, excess spread = 5,244,000 – 6,300,000 = EUR -1,056,000 (negative).

Second:

Recovery principal amount in year 2 = R2 = 0.45 * 8 * 1,000,000 = EUR 3,600,000, which would flow into the overcollateralization account (OC).

Therefore, since the OC had a net EUR 0 at the beginning of year 2, then the interest shortfall (calculated in the first step above, as negative) should be paid from the OC account, leaving the OC with a net amount = 3,600,000 – 1,056,000 = EUR 2,544,000. (See discussions on page 166-167, [CR-8]).

A is incorrect. = EUR 600,000 is the result obtained by ignoring the number of defaults in year 2 and using an incorrect formula: B – L = 6,300,000 – (0.035 + 0.022)*100*1,000,000 = EUR 600,000

B is incorrect. EUR 1,056,000 is the excess spread as derived in C above.

D is incorrect. EUR 3,600,000 is the recovered principal in year 2 as derived above