log moneyness

Log Moneyness

Log moneyness is a dimensionless variable used in option pricing to measure the relative distance between the underlying price and the strike. It is defined as

$$k:=\ln \left(\frac{S}{K}\right)$$

where $S$ is the spot price and $K$ the strike. In forward-based formulations, one often uses

$$k:=\ln \left(\frac{F}{K}\right)$$

with $F$ the forward price, ensuring invariance to discounting and carry.

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Properties

• Sign structure:
  $k=0$ (ATM), $k>0$ (ITM calls), $k<0$ (OTM calls).

• Symmetry:
  Log moneyness linearizes percentage deviations: equal relative moves in $S$ correspond to symmetric shifts in $k$.

• Scaling invariance:
  Invariant under proportional rescaling of $S$ and $K$.

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Role in Option Theory

Log moneyness is the natural strike variable in models where prices follow geometric processes (e.g. the Black–Scholes model). It is standard in the parametrization of implied volatility surfaces, where volatility is expressed as $\sigma =\sigma (k,T)$.

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Disclaimer

This content is AI-generated for informational purposes and may not constitute authoritative academic guidance. Verification from primary sources is recommended before use.
Generated on: April 1, 2026