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jason · 2020年02月16日

问一道题：NO.PZ2016082406000024

  1. FRM II
  2. Credit Risk Measurement And Management

问题如下：

A two-year zero-coupon bond issued by ABC Co. is currently rated A. The market expects that one year from now the probability that the rating of ABC remains at A, is downgraded to BBB, or is upgraded to AA are, respectively, 80%, 15%, and 5%. Suppose that the risk-free rate is flat at 1% and that credit spreads for AA-, A-, and BBB-rated debt are flat at 80, 150, and 280 basis points, respectively. All rates are compounded annually. What is the best approximation of the expected value of the zero-coupon bond one year from now?

选项：

A.

97.41

B.

97.37

C.

94.89

D.

92.44

解释：

ANSWER: A

After one year, the bond becomes a one-year zero-coupon bond. The respective values are, for AA, A, and BBB, PAA=1001+0.0180=98.23P_{AA}=\frac{100}{1+0.0180}=98.23, 97.56, and 96.34. Note that prices are lower for lower ratings. The expected value is given by P=∑πiPi=5%×98.23+80%×97.56+15%×96.34=97.41P=\sum\pi_iP_i=5\%\times98.23+80\%\times97.56+15\%\times96.34=97.41.

compounded annually,不是连续复利形式吗,为什么是用单利算出来的

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orange品职答疑助手 · 2020年02月16日

同学你好，compounded annually是每年复利的意思，连续复利是continuously compounded

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