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.
Guasoni P, Robertson S (2008). Optimal importance sampling with explicit formulas in continuous time. FINANCE AND STOCHASTICS, 12(1), 1-19 [10.1007/s00780-007-0053-5].
Optimal importance sampling with explicit formulas in continuous time
Guasoni P
Co-primo
;
2008
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
