What is the price of a three-years to maturity risky bond that pays 3% annual coupon if the callable at face value (assuming a face value of $100)? What is the dollar value of the embedded call option? Note: An identical bond is currently trading with an OAS of 200 bps, and your analysis of inte suggest that the proportional standard deviation of interest rates is 20%.
What is the price of a three-years to maturity risky bond that pays 3% annual coupon if the callable at face value (assuming a face value of $100)? What is the dollar value of the embedded call option? Note: An identical bond is currently trading with an OAS of 200 bps, and your analysis of inte suggest that the proportional standard deviation of interest rates is 20%.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:## Price of a Risky Callable Bond
### Yield Curve Explanation
The graph displayed above represents the yield curve for US Treasury Strips, specifically the BVAL curve. The x-axis illustrates the tenor, which is the time to maturity, measured in years, while the y-axis represents the yield, expressed in percentage points.
- The curve generally slopes upwards, indicating that longer tenors are associated with higher yields. This reflects the common market expectation that investments with longer maturity dates demand higher returns, compensating investors for increased risk over time.
#### Detailed Data Points:
- **3H to 30Y Tenors**: Specific data points are marked on the curve for selected tenors ranging from 3 hours (3H) to 30 years (30Y). Notable values are provided both on the curve graph and in tabular form below.
- **Yield Values**:
- **3H (hours):** 0.428%
- **6H:** 0.478%
- **1Y (year):** 0.582%
- **2Y:** 0.802%
- **3Y:** 1.006%
- **4Y:** 1.187%
- **5Y:** 1.363%
- **7Y:** 1.670%
- **8Y:** 1.793%
- **9Y:** 1.893%
- **10Y:** 1.981%
- **20Y:** 2.329%
- **25Y:** 2.517%
- **30Y:** 2.379%
### Table of Spot Rates
Below the graph, a table lists spot rates for specific tenors ranging from 1 year to 10 years. These spot rates are:
| Tenor (yr) | Spot Rate |
|------------|-----------|
| 1 | 0.58% |
| 2 | 0.80% |
| 3 | 1.01% |
| 4 | 1.19% |
| 5 | 1.36% |
| 6 | 1.67% |
| 7 | 1.67% |
| 8 | 1.79% |
| 9 | 1.89% |
| 10 |

Transcribed Image Text:**Question:**
What is the price of a three-year-to-maturity risky bond that pays a 3% annual coupon if the bond is callable at face value (assuming a face value of $100)?
What is the dollar value of the embedded call option?
**Note:** An identical bond is currently trading with an OAS (Option Adjusted Spread) of 200 basis points, and your analysis of interest rates suggests that the proportional standard deviation of interest rates is 20%.
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