FRM一級金融市場產(chǎn)品例題解析

題目一：

A pass-through mortgage-based security (MBS) assumes a 200% PSA prepayment speed. The pool has an original weighted average maturity (WAM) of 360 months but now has an age of 60 months (five years).

What is the model's assumption, at this month 60, for the single month mortality (SMM) rate?

A. 0.92%

B. 1.00%

C. 1.06%

D. 1.14%

答案：C

解析：100% PSA levels off at 6% CPR for months 31 to maturity. 200% PSA implies 12% CPR after 30 months. Therefore, SMM = 1 - (1-CPR)^(1/12) = 1 - (1-12%)^(1/12) = 1.06% ,在 31 個月至到期之間，100％ PSA 水平為 6％CPR。200％PSA 意味著 30 個月后CPR 為 12％。 因此， SMM = 1-（1-CPR）^（1/12）= 1-（1-12％）^（1/12）= 1.06％

關聯(lián)考點：PSA與SMM之間的轉(zhuǎn)換計算

易錯點分析：根據(jù)規(guī)定，100PSA代表標準的提前還款率，正常情況下，每個月增加0.2%，只到第30個月增加到6%（0.2%*30）就不再增加，如果是200PSA說明其提前還款率是標準提前還款率的2倍，也就是增加到第30個月后是6%*2=12%，此后便不在增加，這個是要作為常識記住的。

題目二：

Consider day count convention and, specifically, the following example:

A semiannual bond with $100 face value has a 4% coupon. Today is August 3. Assume coupon dates of March 1 and September 1. Which of the following statements is true?

A. Corporate bonds accrue more interest in July than T-bonds.

B. Corporate bonds accrue more interest from March 1 to September 1 than September 1 to March 1 .

C. Corporate bonds accrue more interest than T-bonds for this period (March 1 to August 3).

D. The T-bond accrued interest is $1.76 for this period (March 1 to August 3).

答案：C

解析：July accrued T-bond interest is 31/184 = 0.1685;

July accrued corporate bond interest is 30/180 = 0.1667.

T-bonds accrue 155/184 = 0. 8424 x $2 = $1.6848;

C-bonds accrue 152/180 = 0.8444 x $2 = $1.6889.

關聯(lián)考點：T-bond（actual/actual)和公司債(30/360）的計息慣例

易錯點分析：對T-bond（actual/actual)和公司債(30/360）的計息慣例不夠熟悉，記憶出現(xiàn)偏差。