Financial Risk Manager Part 1

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Explanation:

Explanation

The DV01 (Dollar Value of a 01) measures the price sensitivity of a bond to a 1 basis point change in yield.

Step 1: Calculate the price of the bond without embedded options

Since the call option reduces the bond price, the price of a comparable bond with no embedded options is the sum of the callable bond price and the call option price:

At 3.95%: 97.9430 + 2.1972 = 100.1402
At 4.00%: 97.8910 + 2.1090 = 100.0000
At 4.05%: 97.8566 + 2.0035 = 99.8601

Step 2: Apply the DV01 formula

\text{DV01} = -\frac{\Delta P}{10,000 \cdot \Delta y}

Using the prices at 3.95% and 4.05% (10 bps change):

\text{DV01} = -\frac{99.8601 - 100.1402}{10,000 \cdot (0.0405 - 0.0395)} = -\frac{-0.2801}{10,000 \cdot 0.001} = \frac{0.2801}{10} = 0.02801

Why other options are incorrect:

B (0.01399): Uses only the price difference between 4.00% and 4.05%
A (0.00864): Uses only the callable bond prices without considering the embedded option
C (0.01402): Incorrect calculation using partial information

Explanation:

Explanation

The DV01 (Dollar Value of a 01) measures the price sensitivity of a bond to a 1 basis point change in yield.

Step 1: Calculate the price of the bond without embedded options

Since the call option reduces the bond price, the price of a comparable bond with no embedded options is the sum of the callable bond price and the call option price:

At 3.95%: 97.9430 + 2.1972 = 100.1402
At 4.00%: 97.8910 + 2.1090 = 100.0000
At 4.05%: 97.8566 + 2.0035 = 99.8601

Step 2: Apply the DV01 formula

\text{DV01} = -\frac{\Delta P}{10,000 \cdot \Delta y}

Using the prices at 3.95% and 4.05% (10 bps change):

\text{DV01} = -\frac{99.8601 - 100.1402}{10,000 \cdot (0.0405 - 0.0395)} = -\frac{-0.2801}{10,000 \cdot 0.001} = \frac{0.2801}{10} = 0.02801

Why other options are incorrect:

B (0.01399): Uses only the price difference between 4.00% and 4.05%
A (0.00864): Uses only the callable bond prices without considering the embedded option
C (0.01402): Incorrect calculation using partial information

Comments (1)

Sakshi KheraMay 13, 2026 5:32 AM

The values of call options is not given in q

LeetQuiz .May 14, 2026 5:14 AM

Hello Sakshi, Thank you for pointing that out. We have updated the question to include the call‑option values in the table, so the necessary data is now provided. The DV01 is approximately 0.02801. We add the callable bond price and the call option value to get the option free price and then compute the price change for a 10 bp move. Thank you for your feedback.

A risk manager is analyzing the price sensitivity of an investment-grade callable bond using the firm’s valuation system. The interest rate environment is flat at 4%.

Value in USD per USD 100 face value

Interest Rate Level Callable Bond Call Option
3.95% 97.9430 2.1972
4.00% 97.8910 2.1090
4.05% 97.8566 2.0035

What is the DV01 of a comparable bond—one without embedded options but with the same maturity and coupon rate as the callable bond—closest to?

Interest Rate Level	Callable Bond	Call Option
3.95%	97.9430	2.1972
4.00%	97.8910	2.1090
4.05%	97.8566	2.0035

Exam-Like

Last updated: May 14, 2026 at 05:13

0.00864

37.5%

0.01399

25.0%

0.01402

0.02801

37.5%

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Comments (1)

Sakshi KheraMay 13, 2026 5:32 AM

The values of call options is not given in q

LeetQuiz .May 14, 2026 5:14 AM