TSLA Widget · Mon, Oct 5
Andy Pants · live · Yahoo
Market: …
Black–Scholes (call)
C = S N(d1) − K e−rT N(d2)
d1 = [ln(S/K) + (r + σ²/2) T] / (σ √T)
d2 = d1 − σ √T
- S
- spot
- K
- strike
- T
- years to expiry
- r
- risk-free rate
- σ
- volatility
- N(·)
- normal CDF
- C
- call price
Normal CDF N(x)
N(x) = 1/√(2π) · ∫−∞x e^(−t²/2) dt
N(x) = ½[1 + erf(x/√2)]
- N(x)
- probability a standard normal ≤ x
- N(d₂)
- ≈ risk-neutral prob. call ends ITM
- N(d₁)
- call delta
- N(0)
- = 0.5 · N(1) ≈ 0.841 · N(−1) ≈ 0.159
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