Forward Variance

The previous reasoning can also be used to calculate the expected variance over a forward starting window.

Suppose we know:

- the strike for a short-maturity VS expiring at time t

- the strike for a longer maturity VS expiring at time T

We want to find the expected realised variance, F, between t and T.

Since variance is additive, the fair strike of the forward-starting variance swap is easily calculated:

• Long T/(T-t) variance notional of spot variance maturity T

• Short t/(T-t) variance notional of spot variance maturity t, but with payment delayed until maturity T.

Note:

- More variance is need on the longer leg (tends to be less liquid) than the shorter leg.

- The total notional of the two legs will be greater than the notional of the forward.

This can have a practical impact of increasing the bid/offer of forward starting variance swaps.

Forward starting variance increasingly quoted as single level --> bid/offer converging to similar levels as seen for spot variance.

Forward variance swaps are useful for:

- taking a direct view on the future value of implied variance.

- taking a direct view on the future shape of the variance term structure curve.

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