Option Pricing without Price Dynamics: A Probabilistic Approach

TL;DR

This paper introduces a probabilistic method to determine the tightest bounds on option prices using no-arbitrage principles and call option prices, without relying on specific asset price models.

Contribution

It develops a novel approach that reduces option pricing bounds to linear optimization problems, independent of underlying asset dynamics.

Findings

Effective algorithms for computing option price bounds

Numerical results demonstrating algorithm performance

Bounds applicable to multi-asset options

Abstract

Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct maturities and the no-arbitrage condition, but without any assumption on the price dynamics of underlying assets. We show that the problem reduces to solving linear optimization problems that we explicitly characterize. We report numerical results that illustrate the effectiveness of the algorithms we develop.