Filter by Categories
Accounting
Banking

Derivatives




Exponential Brownian Motion


A process that reflects the time-evolution of an asset price. It is a stochastic process commonly used in finance to describe the evolution of traded assets over time. In the realm of derivatives, it is used for European style options and stock prices. In a mathematical form, it is expressed by the stochastic differential equation (SDE):

SDE-GBM

Where: α denotes the drift and γ denotes the volatility of the exponential Brownian motion process x(t).

This process is a continuous-time stochastic process in which the logarithm of the randomly varying value (e.g., a price) follows a Brownian motion (BM). Specifically, it is a non-negative variation of Brownian motion. When a Brownian Motion is exponential, the returns from the an asset trading in an active market (a stock) are compounding and stock prices cannot be negative- i.e., cannot drop below zero due to the nature of the issuers (limited liability corporations). Similar to its original version, the Brownian motion, it is a Markov process: “the future given the present state is independent of the past”

It is known for as geometric Brownian motion (GBM).



ABC
Derivatives have increasingly become very important tools in finance over the last three decades. Many different types of derivatives are now traded actively on ...
Watch on Youtube
Remember to read our privacy policy before submission of your comments or any suggestions. Please keep comments relevant, respectful, and as much concise as possible. By commenting you are required to follow our community guidelines.

Comments


    Leave Your Comment

    Your email address will not be published.*