Option Pricing with Fourier Series

Abstract

We propose a simple and fairly general approach for valuing European options in closed-form. This approach leads to a single formula for the price of a European option. This formula is easy to implement, fast to execute, and only involves working with real numbers, in contrast to the Fourier transform based option pricing formulas. It also applies many option pricing models existing in the literature. Furthermore, the formula and the derived expressions of option Greeks are payoff as well as model independent, in the sense that their structure remains unchanged for any payoff and any pricing model, unlike existing pricing formulas.