Unwinding a Partially Closed SPX Variance Swap

Summary

The document explains how a dealer can handle a client’s request to reduce the notional of an existing SPX variance swap before maturity. It treats variance as additive over time: the position’s value at the unwind date can be viewed as realized cash profit or loss to date plus a remaining variance swap struck at the then-current fair variance level. The remaining swap’s variance amount scales with the fraction of the original term still outstanding.

To reduce the position, the dealer can enter an offsetting swap with the same maturity, then hedge it as they would a newly traded variance swap. The answer gives this decomposition as the key rationale, but does not work through a numerical example or detail the dealer’s replication hedge. It also does not address contract-specific conventions, transaction costs, or how realized variance is calculated, so those details must be checked for the actual trade.

Key ideas

• Variance swap value can be decomposed into realized variance to date and a remaining swap at the current fair strike.
• The remaining variance amount is proportional to the fraction of the original term left.
• Reducing notional can be implemented with an offsetting variance swap of the same maturity.
• The dealer can hedge the offsetting trade using its ordinary variance swap hedging approach.

Tags

# How can we unwind a Index ( SPX ) Variance swap?


# How can we unwind a Index ( SPX ) Variance swap?












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 ?

## Answer by CABLE (score 1, accepted)

https://quant.stackexchange.com/a/55507

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.

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.