Forward-Start Variance Swaps and Future Variance Expectations

Summary

The document clarifies an example about a forward-start variance swap and whether a statement about implied volatility contains a typo. It explains that the relevant forward-start swap strike represents today’s expectation of the variance-swap strike for a future period. In the example, that period is the one-year interval beginning one year from now, so the profit or loss depends on whether the realized swap strike at that future time is above or below the stated threshold.

The response distinguishes this future swap-strike comparison from a direct comparison with today’s implied volatility. It notes that the source discussion mixes variance-swap strikes with implied volatility and skew, which can obscure the reasoning. Relating the strike to forward-start implied volatilities requires an appropriate formula and sufficient prior explanation. The excerpt gives no calculation, market data, or trading evidence, so it serves as a conceptual interpretation of the example rather than a pricing or implementation guide.

Key ideas

• A forward-start variance-swap strike reflects today’s expectation of a variance-swap strike for a future period.
• The example concerns the one-year variance-swap strike observed one year from now.
• The future profit or loss depends on whether that future strike is above or below the stated threshold.
• Implied volatility and skew should not be conflated with the future variance-swap strike.
• Connecting the strike to forward-start implied volatilities requires an appropriate formula and context.

Tags

# Calendar spreads through variance swaps


# Calendar spreads through variance swaps












Please refer to this image from the famous paper JUST WHAT YOU NEED TO KNOW ABOUT VARIANCE SWAPS by Bossu et al. 2005 (page 6).

The underlined part, is there a typo? "if the 2-year IV is above 20.5....." would be the correct thing, right!?

## Answer by Frido (score 1)

https://quant.stackexchange.com/a/77144

No, there is no typo, just sloppy language.

I don't know which book this is from, but the example concerns a forward start variance swap. The forward start variance swap strike is today's expectation of future variance swap strike.

In this example, it's the expectation of the 1 year varswap strike in 1 year's time.

So if in one year's time the one year varswap strike is above/below 20.5 there will be a P/L.

Unfortunately the author starts talking about implied vols and skew and all that. So unless this example was preceded by a discussion of the Chriss-Morokoff formula which expresses the (forward start) varswap strike in terms of (forward start) implied vols , in my opinion the author could have done better.

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.