Binomial tree method for option pricing: Discrete cosine transform approach

Abstract

This paper discusses a new pricing method of European options through the binomial tree model using a discrete cosine transform. The discrete cosine transform has been used as a fundamental tool for image compression, including the creation of JPEG files. A discrete cosine transform was also recently used to derive the price of financial options. This method also enables us to derive the option prices using a binomial tree model. Using this approach, we derive the option prices on the classical Black and Scholes, exponential jump–diffusion, and exponential CGMY models. Because we compute the characteristic function numerically, we can derive option prices in various models without knowing the specific form of the characteristic functions. This study can unfold new research areas such as option pricing on various models, including the non-parametric jump and Lévy diffusion models.