Chapter 7: Common Contracts 325
default swaps are the more commonly traded instruments. The
maturity is typically less than the maturity of the underlying
instrument. A TRS therefore provides a means of packaging
and transferringallof the risks associated with a reference
obligation, including credit risk. TRSs are more flexible than
transactions in the underlyings. For example, varying the terms
of the swap contract allows the creation of synthetic assets
that may not be otherwise available. The swap receiver never
has to make the outlay to buy the security. Even after posting
collateral and paying a high margin, the resulting leverage and
enhanced return on regulatory capital can be large.
Variance swap is a swap in which one leg is the realized vari-
ance in the underlying over the life of the contract and the
other leg is fixed. This variance is typically measured using
regularly spaced data points according to whatever variance
formula is specified in the term sheet. The contract is popular
with both buyers and sellers. For buyers, the contract is a
simple way of gaining exposure to the variance of an asset
without having to go to all the trouble of dynamically delta
hedging vanilla options. And for sellers it is popular because it
is surprisingly easy to statically hedge with vanilla options to
almost eliminate model risk. The way that a variance swap is
hedged using vanillas is the famous ‘one over strike squared
rule.’ The variance swap is hedged with a continuum of vanilla
options with the quantity of options being inversely propor-
tional to the square of their strikes. In practice, there does
not exist a continuum of strikes, and also one does not go all
the way to zero strike (and an infinite quantity of them).
The volatility swap is similar in principle, except that the pay-
off is linear in the volatility, the square root of variance. This
contract is not so easily hedged with vanillas. The difference
in prices between a volatility swap and a variance swap can
be interpreted viaJensen’s Inequalityas a convexity adjust-
ment because of volatility of volatility. The VIX volatility index
is a representation of SP500 30-day implied volatility inspired
by the one-over-strike-squared rule.