Monte Carlo & Value-at-Risk

Risk Ch. 7 — Coherent Risk Measures

Initial Price ($)

Expected Return (%)

Volatility (%)

Horizon (years)

Paths

Steps / Year

Seed

Confidence (%)

Portfolio Value ($M)

Mean Terminal—

Median Terminal—

Std Dev—

Min / Max—

P(Loss)—

VaR (95%)—

CVaR (95%)—

Parametric VaR—

Parametric CVaR—

5th Percentile—

25th Percentile—

75th Percentile—

95th Percentile—

dS = μS dt + σS dW (Geometric Brownian Motion)
CVaR_α = E[L | L ≥ VaR_α] (Coherent)

Ch. 7 — VaR Non-Coherence Proposition Ch. 7 — CVaR Coherence Theorem