Option pricing models

The at-the-money approximation

Prices or inverts an at-the-money option in your head, to better than a per cent.

CATM≈0.4 S0 σTC_{\text{ATM}} \approx 0.4\,S_0\,\sigma\sqrt{T}

Where

0.40.4
From Φ(x)≈0.5+0.4x\Phi(x) \approx 0.5 + 0.4x near zero.

Assumptions

  • At the money and low rates. It degrades away from the strike and on long-dated options.

Sanity check. At S=100S = 100, σ=20%\sigma = 20\%, T=1T = 1 it gives 8 against an exact 7.97.

Where this is taught