Risk Neutral Option Pricing With Neither Dynamic Hedging nor Complete Markets

TL;DR

This paper demonstrates that European option prices can be derived without relying on dynamic hedging or complete markets, using simple assumptions like Put-Call Parity, and allows for pricing with distributions of infinite variance.

Contribution

It provides a novel proof that option valuation can be based on mean derived from forward prices under general distributions, bypassing traditional Black-Scholes assumptions.

Findings

Option prices can be derived without dynamic hedging.

Pricing is valid under distributions with infinite variance.

Heuristics used by traders are more robust than previously thought.

Abstract

Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets and other strong assumptions. We confirm that the heuristics used by traders for centuries are both more robust, more consistent, and more rigorous than held in the economics literature. We also show that options can be priced using infinite variance (finite mean) distributions.