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FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models

In a Vasicek model with k = 0.5, a 4-year zero-coupon bond has ln A(4) = −0.0150. The current short rate is 4%. Using P = A·exp(−B·r0) with B = (1 − e^(−kT))/k, what is the bond price per 1 of face value?

The price is about 0.9193. First compute B = (1 − e^(−2))/0.5 = 1.7293. The log price is ln A − B·r0 = −0.0150 − 0.0692 = −0.0842. Exponentiating gives 0.9193, equivalent to a continuously compounded yield of about 2.10%.

  1. A0.9193Correct
  2. B0.9332
  3. C0.8395
  4. D0.9473

Explanation

B = (1 − e^(−2))/0.5 = 1.7293. The exponent is −0.0150 − 1.7293 × 0.04 = −0.0150 − 0.06917 = −0.08417. P = e^(−0.08417) = 0.9193. Omitting A gives 0.9332. Using B = T gives 0.8395. Entering ln A with the wrong sign gives 0.9473.

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