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Client A comes to dealer to trade variance notional $1m at T=0. The trade is executed with dealer short volatility with strike of 20.

term Payoff of dealer = notional*( Stike^2 - realized vol^2 )

now at t=T1 the client , comes back with the order to reduce the notional of variance swap by half.

How can the dealer hedge the remaining portfolio ?

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Since variance is additive, your var swap at $t=t_1$ is the same as the realized cash pnl plus a new var swap traded on $t=t_1$ with strike being $K_1$ rather than $K_0$, with a variance amount being $\frac{T - t_1}{T}$ times the original variance amount, where $K_1$ is the fair strike on $t=t_1$ and $K_0$ is your old strike traded on $t=0$.

If you would like to unwind (part of) the var swap, what you are doing is just trading a new var swap with the same maturity as the old var swap. Therefore the dealer just hedge as how they normally hedge when trading var swaps.

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  • $\begingroup$ Yes, it is included in the cash pnl needed to be settled when unwinding. $\endgroup$
    – CABLE
    Commented Jul 8, 2020 at 2:41
  • $\begingroup$ Thanks for this. if I try to solve this by equation I can cancel by exposure to realised volatility and I am left with . Following term. $Notional*( K_{t,T}^2 - K_{0,T}^2)$. 1) Will the dealer charge this cost to exit the swap ? 2) People often quote this as vega cost /charge. what exactly is that ? How exactly the dealer estimate this vega cost to be charged to the client ? $\endgroup$
    – user3426614
    Commented Jul 8, 2020 at 16:30
  • $\begingroup$ 1. This is included in the cash to be settled when unwinding. Probably I should not use the term realized cash pnl, what I mean by this is actually the sum of the realized vol pnl + implied vol pnl. 2. I have not heard of this term. When unwinding, you usually quote different dealers rather than just the one with whom you trade the original swap to find the best $K_1$. The key point is that this so called "unwind" is essentially just short/long a new var swap to offset your original long/short var position. Therefore there is no "cost", you just trade as normal. $\endgroup$
    – CABLE
    Commented Jul 8, 2020 at 17:24

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