Interpreting Zero Log-Moneyness for a Call Option

Summary

The note defines time-zero log-moneyness for a call with stock price S(0), strike K, and expiry T as the logarithm of the forward stock price divided by the strike. It then asks what it means for a strike to be at the money under this convention, and whether setting the logarithm of the strike equal to log-moneyness is appropriate.

The response identifies zero log-moneyness as the at-the-money condition. Setting the defined quantity to zero implies that the strike equals the spot price grown at the risk-free rate to expiry, S(0) exp(rT). The note is brief: it gives this interpretation but does not discuss dividends, alternative rate conventions, or broader distinctions between spot and forward moneyness.

Key ideas

• Log-moneyness compares the forward stock price with the option strike.
• A call is at zero log-moneyness when its strike equals the forward price under the stated convention.
• The proposed condition equating log strike directly to log-moneyness is not the zero-moneyness criterion.

Tags

# Log-moneyness definition


# Log-moneyness definition












Define the time-0 log-moneyness of a call on stock $S$ with strike $K$ and expiry $T$ to be:

$$\log(S(0)\exp(rT)/K)$$

What does it mean for the strikes K to be at-the-log-moneyness?? I guessed this but i don't think it is right:

$$\log(K) = \log(S(0)\exp(rT)/K)$$

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/36574

I would guess it means K=S(0)*exp(rt), so that log moneyness is zero.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.