Calculator Inputs
Example Data Table
| Input | Example Value | Purpose |
|---|---|---|
| Notional Amount | 10,000,000 | Face value used to derive market exposure. |
| Clean Price | 98.75% | Converts notional into mark-to-market value. |
| Modified Duration | 4.85 | Measures first-order price sensitivity to rate changes. |
| Convexity | 32.40 | Improves revaluation under larger yield moves. |
| Annual Yield Volatility | 1.35% | Used in the parametric volatility estimate. |
| Holding Period | 10 Days | Scales risk from daily to horizon terms. |
| Confidence Level | 99% | Selects the tail threshold for VaR. |
| Historical Changes | -12, 8, -5, 14, -9... | Feeds the historical loss distribution. |
Formula Used
Market Value = Notional × Clean Price / 100
DV01 = Market Value × Modified Duration × 0.0001
Daily Yield Volatility = Annual Yield Volatility / √Days per Year
Horizon Yield Volatility = Daily Yield Volatility × √Holding Period
Adverse Yield Move = Z-Score × Horizon Yield Volatility
Delta VaR = Market Value × Modified Duration × Adverse Yield Move
Delta-Convex VaR = Market Value × [Duration × Δy − 0.5 × Convexity × (Δy²)]
P/L ≈ Market Value × [−Duration × Δy + 0.5 × Convexity × (Δy²)]
This model estimates loss from parallel yield shifts. It is useful for approximation, stress review, and portfolio comparison, but it does not replace full revaluation.
How to Use This Calculator
- Enter the bond or portfolio notional and current clean price.
- Add modified duration and convexity from your analytics system.
- Input annual yield volatility and choose a confidence level.
- Set the holding period in trading days.
- Optionally include daily drift and a custom basis point shock.
- Paste historical daily rate changes in basis points for scenario analysis.
- Choose parametric, historical, or both, then press Calculate VaR.
- Review the summary, graph, and scenario table, then export the report as CSV or PDF.
Frequently Asked Questions
1. What does interest rate VaR measure?
It estimates the potential loss of a rate-sensitive position over a chosen horizon at a selected confidence level. It focuses on adverse yield moves and their effect on price.
2. Why does the calculator use duration and convexity?
Duration captures first-order price sensitivity, while convexity improves the estimate when moves become larger. Together, they give a more realistic approximation than duration alone.
3. What is the difference between parametric and historical VaR?
Parametric VaR assumes volatility-based distribution behavior. Historical VaR replays observed rate moves from past data. Using both helps compare model assumptions against realized scenarios.
4. Why is DV01 shown in the results?
DV01 shows the portfolio value change for a one-basis-point move in yields. It is a practical sensitivity measure for hedging, limits, and daily monitoring.
5. Should I enter rate changes in percent or basis points?
Enter historical rate changes in basis points. For example, a move of 0.12% should be entered as 12, while a move of -0.08% should be entered as -8.
6. What does the custom shock result represent?
It estimates profit or loss for a user-defined parallel yield move. This is useful for stress testing, policy review, and comparing losses against VaR outputs.
7. Is historical VaR always better than parametric VaR?
Not always. Historical VaR reflects the sample provided, while parametric VaR depends on volatility assumptions. Each method has strengths and blind spots, so comparing both is often better.
8. Does this calculator replace full valuation models?
No. It is a practical approximation tool for risk monitoring and reporting. Complex instruments, curve trades, options, and non-parallel shifts may require full revaluation models.