What quantity is subtracted to estimate the forward variance here?
Reveal the worked answer
Total variance sigma squared times maturity.
Then divide by the remaining interval before taking a square root.
Advanced Options · ADV-22 · Core
Volatility term structure
How much event risk belongs to each maturity?
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: Read a contract and its premium, Rights, obligations and expiration, Defined payoff risk is not margin, Read the whole multi-leg ticket
Term structure describes IV across maturities under a comparable strike or moneyness convention. Calendars and diagonals buy and sell different portions of that structure. A high front IV can reflect a near event rather than an inexpensive short-volatility opportunity.
Calendar means different expiries at the same strike; changing strikes as well creates a diagonal.
Understand the mechanism
Volatility itself is not additive through time. Under a simple integrated-variance comparison, sigma squared times T is the relevant total quantity. A high short-dated annualized IV can still represent less total variance than a lower longer-dated IV.
Forward variance calculations require matched conventions and do not guarantee the future realized volatility.
Walk through the process
Identify where events fall and compare total variance. Stress front and back expiries independently. A long calendar can be damaged if back-month IV falls or spot leaves the area where its structure is useful.
Do not use a same-expiry terminal payoff engine to value a still-live far leg.
Model and implementation boundary
These are complete fictional reading examples, not live opportunities. Terminal identities assume the stated common settlement. Multi-expiry values require a surviving-leg model. Costs, assignment and financing can alter realized outcomes; a mathematical bound alone does not guarantee the same operational loss path.
A worked example
Fictional seven-day IV is 60% and thirty-day IV 35%. Total variance is 0.006904110 and 0.010068493. The implied forward variance rate over the remaining 23 days is (0.010068493−0.006904110)/(23/365)=0.050217391.
Its square root is about 22.409% annualized. This is a model-consistent comparison, not a promise about the next 23 days. The graph shows total variance rather than averaging the two quoted IVs.
Open the calculation without leaving this lesson
Volatility term structure—worked comparison
Vertical: Total variance (annual decimal volatility squared × years)
Horizontal: Calendar days remaining
1. Fictional example
Read the graph as a data table
| Calendar days remaining | Fictional example |
|---|---|
| 7 | 0.00690411 |
| 30 | 0.0100685 |
What would invalidate the reading?
A trader averages IV60 and35 directly or describes a calendar as having a fixed maximum payoff at the first expiry. Both confuse distinct time concepts.
Check your understanding
Try the question before revealing its answer. These are reading checks, not trading certification or a site completion record.
What is the critical failure to avoid?
Reveal the worked answer
A trader averages IV60 and35 directly or describes a calendar as having a fixed maximum payoff at the first expiry. Both confuse distinct time concepts.
Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome.
Return to the question: How much event risk belongs to each maturity? State the observed facts, the assumptions and the failure condition separately.
Sources, assumptions and downloadable script
External references support definitions and conventions. Worked scenarios and prose are original. No current quotes or dealer inventory are claimed.
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