Option pricing under normal dynamics with stochastic volatility

TL;DR

This paper develops a model for pricing European call options where the underlying asset follows a normal process with stochastic volatility modeled by the CIR process, using FFT for efficient computation and comparing it with Monte Carlo simulations.

Contribution

It introduces a novel approach combining normal dynamics with CIR-based stochastic volatility and employs FFT for fast option pricing, validated against Monte Carlo methods.

Findings

FFT provides accurate and efficient option prices

Normal implied volatility can be effectively analyzed with the model

Model results align well with Monte Carlo simulations

Abstract

In this paper, we derive the price of a European call option of an asset following a normal process assuming stochastic volatility. The volatility is assumed to follow the Cox Ingersoll Ross (CIR) process. We then use the fast Fourier transform (FFT) to evaluate the option price given we know the characteristic function of the return analytically. We compare the results of fast Fourier transform with the Monte Carlo simulation results of our process. Further, we present a numerical example to understand the normal implied volatility of the model.