In the Black–Scholes model, consider the problem of selecting a change of drift which minimizes the variance of Monte Carlo estimators for prices of path-dependent options.
Employing large deviations techniques, the asymptotically optimal change of drift is identified as the solution to a one-dimensional variational problem, which may be reduced to the associated Euler–Lagrange differential equation.
Closed-form solutions for geometric and arithmetic average Asian options are provided.
Monte Carlo methods Variance reduction Importance sampling Large deviations
Mathematics Subject Classification (2000)
91B28 60F10 65C05
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