What variance reduction techniques work best for Asian options?

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AcadiFi · Accepted Answer

Arithmetic Asian options have no closed form, but geometric Asians do (Kemna-Vorst). The control variate technique exploits this: estimate arithmetic payoff A_i and geometric payoff G_i for each path, then price P = E[A] = MC estimate of A + beta*(G_true - MC estimate of G), where beta = Cov(A,G)/Var(G) ≈ 1 since A and G are highly correlated (rho > 0.99 typically). For Nordwind's 1-year oil Asian with 12 monthly observations, S = $75, K = $78, sigma = 35%: Plain MC with 10,000 paths gives standard error $0.45. With geometric control variate: standard error drops to $0.02—a 500x variance reduction (22x faster convergence in terms of path count). Other techniques: (1) antithetic variates pair each path Z with -Z, halving variance for symmetric payoffs; (2) importance sampling tilts paths toward in-the-money region for deep OTM options; (3) stratified sampling on the terminal price or average; (4) moment matching adjusts sample moments to match theoretical. ```mermaid flowchart TB M[Monte Carlo
arithmetic] --> C[Control
variate] G[Geometric
closed form] --> C C --> P[Low variance
price] ``` The Kemna-Vorst control variate is the gold standard for Asians because geometric-arithmetic correlation is so high. Nordwind should implement this plus antithetic variates for 1000x+ effective speedup over plain MC.

What variance reduction techniques work best for Asian options?

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