Black-Scholes ATM Call

Goldman SachsMorgan Stanley

Price a European call with S = K = 100, r = 0, σ = 20%, T = 1 year using Black-Scholes. (Round to the nearest 0.1.)

Approach

With r = 0 and ATM, $d_{1,2} = \pm\tfrac12\sigma\sqrt T$ .

ATM ≈ 0.4·S·σ·√T.