Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1150.91019
Guasoni, Paolo; Robertson, Scott
Optimal importance sampling with explicit formulas in continuous time. (English)
[J] Finance Stoch. 12, No. 1, 1-19 (2008). ISSN 0949-2984; ISSN 1432-1122

In the Black-Scholes model the problem arises how to select a change of drift which minimizes the variance of Monte Carlo estimators for prices of path-dependent options. The authors follow the approach to a continuous-time setting, where the optimal deterministic drift in the Black-Scholes model is identified as the solution of a one-dimensional variational problem. The main idea is briefly summarized with an heuristic argument, which involves derivatives of non-differential Brownian paths, applies Laplace asymptotic in infinite dimensions, and assumes the validity of a minimax result. In spite of these issues, this characterization of the optimal drift is essentially correct. In continuous time the variational problem reduces to the familiar Euler-Lagrange ordinary differential equation. In the case of Asian options the optimal change of drift admits closed-form solutions.
[Yuliya S. Mishura (Ky{\"\i}v)]

MSC 2000:: *91B28 Finance etc.
60F10 Large deviations
65C05 Monte Carlo methods

Keywords: Monte Carlo method; variance reduction; importance sampling

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.
	Elementary number theory. Primes, congruences, and secrets.

Simple Search

Zentralblatt MATH Berlin [Germany]