An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model

TL;DR

This paper introduces a new, efficient formula for spread option pricing in a copula-based market model that simplifies computation to a single integral, applicable to various affine models.

Contribution

It presents a novel spread option pricing formula that is computationally efficient and versatile for different affine univariate stock price processes.

Findings

The method requires only a one-dimensional integral for pricing.

It performs well compared to Monte Carlo simulations across multiple models.

The approach is applicable to models like Variance Gamma, Heston, and GARCH.

Abstract

In this study, we propose a new formula for spread option pricing with the dependence of two assets described by a copula function. The advantage of the proposed method is that it requires only the numerical evaluation of a one-dimensional integral. Any univariate stock price process, admitting an affine characteristic function, can be used in our formula to get an efficient numerical procedure for computing spread option prices. In the numerical analysis we present a comparison with Monte Carlo simulation methods to assess the performance of our approach, assuming that the univariate stock price follows three widely applied models: Variance Gamma, Heston's Stochastic Volatility and Affine Heston Nandi GARCH(1,1) model.