Variance Swap Pricing Calculator

Inputs

Choose a method, fill values, then submit.

All rates are annual, decimals allowed.

Pricing method

Use strip method when you have option mids.

Variance notional

Currency per variance unit (annualized).

Variance strike K_strike

Example: 0.04 equals 20% vol squared.

Maturity T (years)

Use 0.5 for six months.

Risk-free rate r

Enter decimal, like 0.05 for 5%.

Implied volatility σ (percent)

Annualized ATM vol estimate for the term.

Option strip rows

Use puts below forward and calls above forward. Provide mid prices (undiscounted premium currency units).

Strike K	Type	Mid price	Remove

Tip: more strikes improves the integral accuracy.

Reset

Example data table

These are illustrative values to test the tool quickly.

Notional	T (years)	r	K_strike	σ (percent)	Computed fair variance
10,000	1.00	0.05	0.0400	22.00	0.0484
25,000	0.50	0.03	0.0225	18.00	0.0324

For strip method, click “Seed example” inside the strip section.

Formula used

1) Present value from fair variance

A variance swap pays the difference between realized variance and strike variance. At inception, its value uses the fair variance estimate:

PV = e^-rT · N_var · (K_fair − K_strike)

N_var is variance notional (currency per variance unit).
K_strike is the agreed variance strike (annualized).
K_fair is the fair variance implied by the market.

2) Implied variance shortcut

K_fair ≈ σ²

This uses a term implied volatility estimate, typically near-the-money and maturity-matched.

3) Model-free option strip approximation

A common model-free approximation uses a weighted integral over out-of-the-money options:

K_fair ≈ (2e^rT/T) · [∫₀^F P(K)/K² dK + ∫_F^∞ C(K)/K² dK]

This tool approximates the integrals with trapezoids over your discrete strike grid. Add wide, dense strikes to reduce truncation error.

How to use this calculator

Select a method: implied variance or option strip integration.
Enter notional, strike variance, maturity, and rate.
For implied method, provide annualized implied volatility percent.
For strip method, enter forward price and option rows.
Use puts below forward and calls above forward.
Press Submit to view results below the header.
Download CSV or PDF to document the calculation.

FAQs

1) What is a variance swap?

A variance swap is a contract that exchanges future realized variance for a fixed variance strike. It is often used to trade volatility directly without directional exposure to the underlying price.

2) Why is the strike in variance units?

Variance swaps settle on variance, not volatility. Variance is volatility squared, so a 20% volatility strike corresponds to 0.20² = 0.04 in variance units.

3) What does a positive PV mean?

Positive PV means the fair variance estimate exceeds the strike variance. That situation benefits the variance receiver (long variance), assuming the same notional and discounting conventions.

4) When should I use implied variance?

Use implied variance when you only have a maturity-matched implied volatility estimate. It is fast and reasonable near the money, but it ignores smile and tail effects.

5) When should I use the strip method?

Use the strip method when you have multiple option mid prices across strikes. It uses more information from the volatility smile and usually improves the fair variance estimate.

6) Why do I need puts and calls around the forward?

The model-free approximation integrates out-of-the-money puts below the forward and out-of-the-money calls above it. This split matches the payoff replication structure for a log contract.

7) How accurate is the discrete integration?

Accuracy depends on strike coverage and spacing. Sparse strikes or narrow ranges cause truncation error. Add more strikes and extend farther into tails to stabilize the integral.

8) What assumptions does this calculator make?

It assumes inputs are consistent with a single maturity and that option prices are mid quotes. It ignores bid-ask, discrete sampling adjustments, and corridor conventions unless you approximate them via the input grid.