Questions / Quant trading, Option pricing models
Delta of an at-the-money call
Black–Scholes inputs: S = K = 100, one year, volatility 20%, rates zero. What is the call’s delta? (N(0.1) = 0.5398, N(−0.1) = 0.4602.)
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Answer: 0.5398 delta
- d1 = (ln(S/K) + σ²T/2)/(σ√T) = 0.02/0.2 = 0.1.
- Delta = N(d1) = 0.5398.
Interview shortcut. d1 = σ√T/2 = 0.1, Δ = N(0.1).
Takeaway. An at-the-money call’s delta sits above 0.5 by about σ√T/2 standard deviations.
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