Pathwise Derivative Estimates

20:41 Mar 6, 2012 

Pathwise Derivative vs Finite Difference For Greeks Computation.
1, Finite Difference approximation:
This is the most widely used & straightforward method, as its name suggests, basically, to estimate dy/dx, we increase x by a very small quantity to x1, re-calculate the option value y1, and then estimate the sensitivity as (y-y1)/(x1-x).
2, Pathwise derivative estimate:
contrary to finite difference approximation, pathwise derivative estimate derivative directly, without simulating multiple times.Simply put, by the chain rule, if we could find another variable z such that , and there are solutions to the two derivatives at the right hand side, the pathwise derivative estimator can be applied, and for most cases, stock price S(T) for European option or S(tau) for American option is an excellent choice of z, tau is the optimal timing for exercise.

12:29 Mar 6, 2012 

"To overcome the shortages of the finite-difference
method, traditionally there have been two categories
of methods for estimating sensitivities: methods that
differentiate paths and methods that differentiate
densities. The former one is known as the pathwise
derivative method or the infinitesimal perturbation
analysis in the literature and the latter is
usually referred to as the likelihood ratio method
(see Computation of Sensitivities in Monte Carlo
Methods)."
Cred că este mai bine să rămână în engleză.

23:00 Feb 29, 2012 

Something like "estimări ale derivatelor pe traiectoriile"

See e.g. http://www.scribd.com/doc/70326656/196/Pathwise-Derivative-E...

Infinitesimal Perturbation Analysis (IPA) is a method for computing a sample path derivative with respect to an input parameter in a discrete event simulation.