American Options in Variance Swap Replication
Summary
The document discusses replicating a variance swap with a strip of delta-hedged out-of-the-money calls and puts when the available single-stock options are American. It asks whether those contracts can be handled like European options if the replication portfolio is held through expiration.
The answer depends on which side of the variance swap is being hedged. A long option portfolio can serve as a super-replicating position for a long variance swap because its holder can choose not to exercise early and retain the options until expiry. This may cost more than using European options. For a short option portfolio, however, the option buyer controls early exercise, which can disrupt the replication. The discussion is conceptual and does not quantify pricing differences or specify adjustments for early exercise.
Key ideas
- A variance swap can be replicated using a portfolio of delta-hedged out-of-the-money options.
- An investor long the options can wait until expiry, making American options usable for a long replication position.
- The American option portfolio may be more expensive than an equivalent European portfolio.
- A short option position is exposed to the counterparty’s right to exercise early.
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Full text
# Replicating a variance swap on single stock # Replicating a variance swap on single stock The general approach to replicating a long varswap is by going long a strip of delta-hedged OTM calls and puts. If we replicate a varswap on a single stock, and listed options available are only American options, does that make any difference? Is it correct to just treat them as European and apply the same replication methodology regardless of options being American or European if we just want to replicate the varswap: if this is the only intention, then I would always hold the American options until maturity to replicate the varswap, hence if I never early exercise then American or European makes no difference? ## Answer by Daneel Olivaw (score 2, accepted) https://quant.stackexchange.com/a/82380 This depends on whether you are replicating a long or short position on the variance swap. If you are replicating a long position (e.g. because you’ve sold a variance swap to a hedge fund) then you need to be long a porfolio of options, hence you have the right to exercise them: holding American options is a valid (super-)replicating strategy as you can merely wait till expiry (though it could be more expensive than using European options). However if you are replicating a short position, for example because you’ve bought the swap from a customer, then you need to short the option portfolio and it is your counterparty to this portfolio which has the right to exercise: in this case the strategy might break down if the counterparty decides to exercise the option(s) before expiry.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.