**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Fundamental theorem of asset pricing

Summary

The fundamental theorems of asset pricing (also: of arbitrage, of finance), in both financial economics and mathematical finance, provide necessary and sufficient conditions for a market to be arbitrage-free, and for a market to be complete. An arbitrage opportunity is a way of making money with no initial investment without any possibility of loss. Though arbitrage opportunities do exist briefly in real life, it has been said that any sensible market model must avoid this type of profit. The first theorem is important in that it ensures a fundamental property of market models. Completeness is a common property of market models (for instance the Black–Scholes model). A complete market is one in which every contingent claim can be replicated. Though this property is common in models, it is not always considered desirable or realistic.
In a discrete (i.e. finite state) market, the following hold:
The First Fundamental Theorem of Asset Pricing: A discrete market on a discrete probability space is arbitrage-free if, and only if, there exists at least one risk neutral probability measure that is equivalent to the original probability measure, P.
The Second Fundamental Theorem of Asset Pricing: An arbitrage-free market (S,B) consisting of a collection of stocks S and a risk-free bond B is complete if and only if there exists a unique risk-neutral measure that is equivalent to P and has numeraire B.
When stock price returns follow a single Brownian motion, there is a unique risk neutral measure. When the stock price process is assumed to follow a more general sigma-martingale or semimartingale, then the concept of arbitrage is too narrow, and a stronger concept such as no free lunch with vanishing risk must be used to describe these opportunities in an infinite dimensional setting.

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (35)

Related people (6)

We study the effects of takeover feasibility on asset prices and returns in a unified framework. We show theoretically that takeover protections increase equity risk, stock returns, and bond yields by removing a valuable put option to sell the firm, notabl ...

Related concepts (9)

Related courses (16)

This paper reviews the mortgage-backed securities (MBS) market, with a particular emphasis on agency residential MBS in the United States. We discuss the institutional environment, security design, MBS risks and asset pricing, and the economic effects of m ...

Related units (2)

In this paper, we present a spatial branch and bound algorithm to tackle the continuous pricing problem, where demand is captured by an advanced discrete choice model (DCM). Advanced DCMs, like mixed logit or latent class models, are capable of modeling de ...

2023Related lectures (63)

Rational pricing

Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments. Arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets. Where this mismatch can be exploited (i.

Asset pricing

In financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either general equilibrium asset pricing or rational asset pricing, the latter corresponding to risk neutral pricing.

Mathematical finance

Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.

FIN-615: Dynamic Asset Pricing

This course provides an advanced introduction to the methods and results of continuous time asset pricing

MATH-470: Martingales in financial mathematics

The aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mat

FIN-609: Asset Pricing (2011 - 2024)

This course provides an overview of the theory of asset pricing and portfolio choice theory following historical developments in the field and putting
emphasis on theoretical models that help our unde

Generalized Method of Moments (GMM)

Introduces the Generalized Method of Moments (GMM) in econometrics, focusing on its application in instrumental variable estimation and asset pricing models.

Financial Market Models: Arbitrage and Completeness

Explores arbitrage-free and complete financial market models, risk-neutral probabilities, structured notes pricing, and option hedging.

Equilibrium State Prices Determination

Explains the determination of equilibrium state prices in asset pricing through consumption market clearing and budget constraints.