The equivalent martingale measure: an introduction to pricing using expectations

Area of Science:

• Quantitative Finance
• Computational Finance
• Financial Engineering

Background:

• The martingale approach offers a robust framework for derivative pricing.
• This method connects financial mathematics with computational techniques.
• No prior financial expertise is assumed for understanding the core concepts.

Purpose of the Study:

• To provide a self-contained introduction to the risk-neutral (martingale) approach for derivative pricing.
• To demonstrate the utility of Monte Carlo methods in this financial context.
• To illustrate the application of the martingale approach to specific derivative pricing problems.

Main Methods:

• Utilizing the risk-neutral or martingale pricing framework.
• Applying Monte Carlo simulation methods for derivative valuation.
• Employing elementary mathematical techniques to derive option prices.

Main Results:

• The martingale approach is shown to be a powerful tool for pricing financial derivatives.
• A clear derivation of the European call option price is presented using elementary methods.
• The applicability to American put options and interest rate derivatives is discussed.

Conclusions:

• The martingale approach, combined with Monte Carlo methods, provides an accessible yet powerful framework for derivative pricing.
• This interdisciplinary approach facilitates the application of engineering and scientific tools to finance.
• The study lays the groundwork for understanding more complex derivative pricing models.