Encyclopedia of Financial Models, 3 Volume Set

Basics of Currency Option Pricing Models

SHANI SHAMAH

Senior Consultant, RBC Capital Markets

Abstract: Historically, theorists have devoted a substantial amount of work developing a mathematical model for pricing options and, hence, a number of different models exist as a result. All make certain assumptions about market behavior, which are not totally accurate, but which give the best solution to the price of an option. Professionals use these models to price their own options and to give theoretical fair value; however, actual market rates will always be the overriding determinant. In other words, an option is worth as much as someone is prepared to pay for it. Although the formula for pricing options is complex, they are all based on the same principles.

Historically, option-pricing models have fallen into two categories:

• Ad hoc models, which generally rely only upon empirical observation or curve fitting and, therefore, need not reflect any of the price restrictions imposed by economic equilibrium.
• Equilibrium models, which deduce option prices as the result of maximizing behavior on the part of market participants.

The acknowledged basis of modern option pricing formulas is the often-quoted Black-Scholes formula, devised by Black and Scholes (1973) to produce a “fair value” for options on equities. Of course, currency options differ because there is no dividend and both elements of the exchange carry interest rates that can be fixed until maturity. Therefore, various ...