Section 1.4
Price simulator
Section objective
Master the impact of a move in maturity, in the risk-free rate or in funding on the price of the zero-coupon bond.
The time has come to handle the three factors yourself: move the maturity, the risk-free rate and the funding, and watch what happens to the price of the zero-coupon bond.
nominal 100 · results in percent of nominal
Scenarios
Zero-coupon price
84.79
that is 84.79 per 100 of nominal
Total rate r
3.30%
2.60% + 70 bp of funding · continuous compounding
Sensitivity · DV01
0.0424
loss for +1 bp of rate
Price path to maturity
Sensitivities · effect of a shock on this configuration
| Scenario | Price | Δ price |
|---|---|---|
| Current configuration | 84.79 | – |
| Maturity +1 year | 82.04 | −2.75 |
| Rate +100 bp | 80.65 | −4.14 |
| Rate −100 bp | 89.14 | +4.35 |
| Funding +50 bp | 82.70 | −2.09 |
Head calculation
Estimated discount: r × T = 3.30% × 5.0 = 16.5% → price ≈ 83.5.
Exact formula: 84.79. Gap: −1.29%. The approximation is usable out loud.
The "Head calculation" line below the table constantly compares the r × T approximation with the exact formula. Vary the maturity: you will see the precise point at which the spoken estimate stops being honest.
Conventions used
The simulator uses a single rate for the chosen maturity (no curve), under continuous compounding, the convention of option models and the basis used throughout the module: P = N × e−rT. Actual days and the day-count basis (30/360, act/365) are ignored: their effect is of the order of one hundredth of a percent and adds nothing to understanding. The DV01 is computed as a linear approximation from the duration, equal to the maturity under continuous compounding.
Question 1 / 5
In the simulator, start from the reference case (5 years, risk-free rate 2.60%, funding 70 bp, price 84.79%) and take the maturity to 10 years without changing anything else. What price do you get?
Question 2 / 5
Still from the reference case, two moves: (a) raise the risk-free rate by 100 bp, (b) raise the funding by 100 bp. What does the simulator show?
Question 3 / 5
Bring the risk-free rate back to 0% and the funding to 40 bp, over 5 years. What do you read, and what does it reproduce?
Question 4 / 5
Push the risk-free rate to −0.40% with zero funding. The simulator shows 102.02% and a warning. How should it be read?
Question 5 / 5
The simulator shows a DV01 of 0.0424% on the reference case, and 0.0719% after moving to 10 years. Why is it not exactly doubled?