Mimicking: Martingales with Matching Marginals

A stochastic process can be viewed as a collection of random variables and is often used to represent the evolution over time of some random value, or system. Its marginal distributions are its one-dimensional distributions, for example, those at fixed times. Processes are not uniquely defined by their marginal distributions, even with additional properties, such as being a martingale. We will explore such phenomenon.

Motivated by questions in finance, we are interested in constructing new processes from existing ones while preserving the marginal distributions and the martingale property. We call this mimicking. This would enable us to develop alternative models for asset prices, with the hope of improving upon the existing ones, while retaining the (European) option prices. We will also look at a few methods of mimicking for certain types of processes.

Requirements and pre-requisites:

Some knowledge of probability and random processes would be an advantage. Prior exposure to R would be beneficial.

Relevance:

This course will be relevant to anyone with an interest in stochastic processes.