A Simple Proof of the Fundamental Theorem of Asset Pricing

TL;DR

This paper offers an accessible, simplified proof of the Fundamental Theorem of Asset Pricing in discrete time, emphasizing a clear distinction between prices and cash flows for practical derivative pricing and risk management.

Contribution

It provides a straightforward proof of the theorem without requiring a real-world measure, simplifying the understanding and application in financial modeling.

Findings

Uniform treatment of all instruments achieved

No need for a real-world measure in models

Facilitates pricing, hedging, and risk management

Abstract

A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all instruments. There is no need for a ``real-world'' measure in order to specify a model for derivative securities, one simply specifies an arbitrage free model, tunes it to market data, and gets down to the business of pricing, hedging, and managing the risk of derivative securities.