Economics Insights @ CBS

In many services (e.g., the wireless service industry), consumers choose a service plan according to their expected consumption. In such situations, consumers experience two forms of uncertainty. First, they may be uncertain about the quality of their service provider and can learn about it after repeated use of the service. Second, they may be uncertain about their own usage of minutes and learn about it after observing their actual consumption.

We derive and analyze Monte Carlo estimators of price sensitivities ("Greeks") for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is to investigate connections between Malliavin estimators and the more traditional and elementary pathwise method and likelihood ratio method.