Chapter 12Volatility Smile Market Instruments and Exposures
In the interbank broker market, at each market tenor, three market instruments define the volatility smile:
At-the-money (ATM) contracts define the implied volatility for a specific strike close to (or exactly at, depending on the market conventions for a given currency pair) the forward for the given tenor.
Butterfly (Fly) contracts define the implied volatility differential between the wings of the volatility smile and the ATM—a measure of the height of the wings of the volatility smile.
Risk reversal (RR) contracts define the implied volatility differential between strikes above and below the ATM—a measure of how skewed or tilted the volatility smile is.
Butterfly and risk reversal contracts are most often quoted at 25 delta (25d) and 10 delta (10d) strikes. An example run of market instruments at market tenors is shown in Exhibit 12.1.
Exhibit 12.2 shows the relative positioning of different deltas within a stylized volatility smile. Recall that it is the market convention to trade the out-of-the-money side.
The following approximations link the ATM, 25d butterfly, and 25d risk reversal ...
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