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FX Derivatives Trader School by Giles Jewitt

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Chapter 11ATM Curve Construction

ATM curves can be constructed in two steps. First, a core ATM curve is established. Then additional parameters are introduced so the correct ATM implied volatility is generated for all possible expiry dates. Note that within this chapter, some calculations are approximate.

Variance

The key measure for building ATM curves is

equation

where c11-math-0002 is the ATM implied volatility to time c11-math-0003 (measured in years). For example, the variance of a 3mth ATM option with 12.0% implied volatility is c11-math-0004.

Variance can be thought of as a measure of cumulative spot movement. It has two powerful properties:

  1. Variance over any time period must be nonnegative.
  2. Variance is additive (i.e., variance over two days = variance on first day + variance on second day).

Variance can be used to calculate the forward ATM implied volatility (usually called forward implied volatility or just “forward vol” by traders) between two dates in the future. Given ATM implied volatility c11-math-0005 to time , ATM implied volatility ...

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