Forward Volatility Inputs
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Example Data Table
| Scenario | Near Maturity | Far Maturity | Near Volatility | Far Volatility | Estimated Forward Volatility |
|---|---|---|---|---|---|
| Base Equity Curve | 30 days | 90 days | 18.00% | 22.00% | 23.75% |
| Moderate Upward Slope | 60 days | 180 days | 20.00% | 24.50% | 26.46% |
| Stable Term Structure | 45 days | 120 days | 19.50% | 19.80% | 19.98% |
Formula Used
The calculator estimates the volatility implied only for the forward period between two maturities. It works from total variance, not by subtracting volatilities directly.
w(T) = σ(T)2 × T
σforward = √[(σ22T2 − σ12T1) / (T2 − T1)]
Where:
- σ1 = implied volatility at the near maturity
- σ2 = implied volatility at the far maturity
- T1 and T2 = time to maturity in years
- w(T) = total variance to maturity
If you select total variance mode, the calculator first treats the entered values as w(T1) and w(T2), then computes forward variance directly.
How to Use This Calculator
- Select whether you want to work from implied volatility inputs or total variance inputs.
- Enter the near and far maturities, then choose days, months, or years.
- Provide either the two implied volatilities or the two total variances.
- Choose percent or decimal input style, output style, annualization basis, and precision.
- Press the calculate button to show results above the form and below the header.
- Use the CSV or PDF buttons to export the calculated result table.
Why Forward Volatility Matters
Forward volatility isolates the market’s expected uncertainty for a later interval, instead of blending all uncertainty from today to final expiry. That makes it useful for calendar spreads, variance analysis, scenario testing, and interpreting the shape of an implied volatility term structure.
Frequently Asked Questions
1. What does forward volatility measure?
It measures the implied volatility for the period between two maturities, not from today to a single expiry. It isolates the future segment’s expected uncertainty.
2. Why can’t I subtract the two volatilities directly?
Volatility scales with the square root of time, so direct subtraction is incorrect. You must convert each maturity into total variance first.
3. Why does the calculator show a negative forward variance error?
That happens when the longer maturity carries less total variance than the shorter one. It usually signals inconsistent inputs, stale quotes, or mismatched conventions.
4. When should I use 252, 360, or 365 as the basis?
Use the same day count convention as your pricing source. Equity desks often prefer 252, while broader calendar conventions commonly use 360 or 365.
5. Can I enter decimal volatilities instead of percentages?
Yes. Choose decimal format first, then enter values such as 0.20 for 20%. The calculator will preserve your selected output style.
6. What is total variance mode useful for?
It is helpful when your model or data source already provides cumulative variance by maturity. In that case, the calculator skips the volatility-to-variance conversion step.
7. Does this calculator work for options and volatility surfaces?
Yes. It is commonly used in option term-structure analysis, forward-start pricing, calendar spread evaluation, and checking consistency across expiries.
8. Is a higher forward volatility always bearish?
No. Higher forward volatility signals larger expected future uncertainty, but it does not specify direction. It may reflect event risk, earnings, macro releases, or hedging demand.