σ
μ
implied vol · K
K
max(S−K,0)
u
d
β
ρᵢⱼ
fat tails
PnL · drawdown
yield · T
dSₜ = μSₜ dt + σSₜ dWₜ
C = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)
σₚ² = wᵀΣw
d₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T
∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0
Sharpe = (Rₚ − R_f) ⁄ σₚ
VaR₉₉ = μ − 2.33σ
ρ = Cov(X,Y) ⁄ σₓσᵧ
E[Rₚ] = Σ wᵢ·E[Rᵢ]
φ(x) = e^(−x²/2) ⁄ √2π
E[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)
dXₜ = θ(μ − Xₜ)dt + σ dWₜ
σ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁
C − P = S − K·e⁻ʳᵀ
Δ = ∂V/∂S Γ = ∂²V/∂S²
p = (e^(rΔt) − d) ⁄ (u − d)
rₜ = ln(Pₜ ⁄ Pₜ₋₁)
E[Xₜ₊₁ | ℱₜ] = Xₜ
f* = (bp − q) ⁄ b
z = (x − μ) ⁄ σ
P(N=k) = λᵏe^(−λ) ⁄ k!
Θ = −∂V/∂T
ν = S·φ(d₁)·√T
min wᵀΣw s.t. wᵀμ = μ*
∫
Σ
∂
∞
λ
uant
Craft
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