Combining Forward Variance Swap Strikes into a Fair Strike

Summary

The document asks how to value a variance swap whose cash flow is settled monthly using realized variance calculated from recent daily S&P 500 closes. It contrasts this setup with standard continuous-time variance swap pricing and asks whether QuantLib can be used for valuation.

The response treats the contract as a collection of forward variance swaps and gives a way to aggregate their fair strikes into one strike. The combined strike squared is the discount-factor-weighted average of the individual forward variance strikes squared. This follows from matching the grouped swaps’ discounted payoffs. The explanation is brief and does not provide a derivation, implementation details, or a QuantLib example. It also does not specify how each component strike should be calculated under the contract’s discrete observation and monthly settlement rules, so those conventions still need to be defined for a full valuation.

Key ideas

• A swap with multiple monthly variance cash flows can be viewed as a group of forward variance swaps.
• The combined fair variance strike is formed by weighting each component strike squared by its discount factor.
• The weighting formula equates the combined payoff with the sum of the component payoffs.
• The document does not explain how to calculate component strikes under the contract’s discrete sampling rules.

Tags

# Pricing Variance Swap


# Pricing Variance Swap












I want to calculate the `NPV` of a Variance Swap wherein the cash flow happens every months based on the standard Variance formula of the close prices of S&P500 for prior 30 business days. We may assume the strike as `K`.

Is there any standard formula for pricing this? As far as I know, the standard formula for Variance swaps assume continuous price during the life time of Swap.

I prefer to use `QuantLib Python` library for such valuation.

Any pointer will be highly appreciated.

## Answer by CABLE (score 3, accepted)

https://quant.stackexchange.com/a/55639

Your swap is essentially a few forward variance swaps grouped together and you are asking a single fair strike $K$ so that the payoff will be the same as the sum of the payoff of the forward variance swaps. Therefore $K^2 = \frac{\sum_{i=1}^{n}D_iK_i^2}{\sum_{i=1}^n D_i}$, where $K_i$ are the strikes of the individual forward var swaps and $D_i$ are the corresponding discounting factors.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.