Option pricing in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. Simulation

TL;DR

This paper develops a discrete-time simulation method using Euler--Maruyama approximation to estimate European call option prices in a stochastic volatility model driven by an Ornstein--Uhlenbeck process, analyzing convergence and accuracy.

Contribution

It introduces a simulation approach for option pricing with Ornstein--Uhlenbeck driven stochastic volatility and evaluates its convergence properties.

Findings

Convergence rate of option price estimates is established.

Discretization errors are quantified and analyzed.

Simulation accuracy improves with finer discretization.

Abstract

We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation scheme is implemented. We determine the estimates for the option price for predetermined sets of parameters. The rate of convergence of the price and an average volatility when discretization intervals tighten are determined. Discretization precision is analyzed for the case where the exact value of the price can be derived.