Scales balancing assets and fees.

Decoding Asset Pricing: How to Navigate Markets with and without Transaction Costs

Samir D’Costa in Business & Economy December 2025 • 4 min read.

"A clear guide to understanding the fundamental theorem of asset pricing, strict no-arbitrage, and thriving in today's markets."

In the world of finance, understanding how assets are priced is fundamental. The fundamental theorem of asset pricing (FTAP) serves as a cornerstone in this understanding. This theorem links the absence of arbitrage opportunities (situations where you can make a guaranteed profit without risk) to the existence of a consistent way to value assets.

However, the classic FTAP often assumes frictionless markets—a simplification that doesn't hold in the real world. Real-world markets have transaction costs, like brokerage fees or the difference between buying and selling prices (the bid-ask spread). These costs can significantly impact investment strategies and asset pricing.

Recent research has extended the FTAP to include these transaction costs, providing a more realistic framework for investors and financial professionals. This article dives into the core concepts of asset pricing, explores how transaction costs change the game, and offers insights into navigating today's complex markets.

What is the Fundamental Theorem of Asset Pricing (FTAP)?

At its core, the FTAP states that in a market without arbitrage, there exists a risk-neutral probability measure. This essentially means there's a way to 'weight' possible future outcomes such that, on average, assets are priced fairly relative to their risk. Absence of arbitrage is a critical assumption. Arbitrage, where risk-free profits are possible, distorts market efficiency and valuation.

Strict no-arbitrage is stronger than classic definitions. In simple terms, it means you cannot construct a portfolio that starts with zero capital, has no risk of loss, and has a chance of a positive gain. Risk-neutral measure gives a consistent way to price assets by discounting their expected future payoffs. This measure isn't necessarily the 'true' probability of those payoffs occurring, but it’s a mathematical tool to ensure fair pricing. If an asset is not fairly priced according to the risk-neutral measure, arbitrage opportunities would arise until prices adjust.

No Arbitrage: The market doesn't allow risk-free profit
Risk-Neutral Measure: A way to value assets fairly
Fair Pricing: Assets are priced according to their discounted expected payoffs

A strict no-arbitrage condition, as used in the research, reinforces this core idea. It says that not only must actual arbitrage be impossible but also any strategy that appears to create arbitrage must also be invalid.

Navigating the Nuances of Asset Pricing

Understanding the FTAP, especially with transaction costs, offers a more realistic perspective for investors. While perfect, arbitrage-free markets are theoretical, recognizing the impact of real-world costs allows for smarter, more robust investment and risk management strategies. Whether you're a seasoned financial professional or just starting, mastering these concepts provides a powerful edge in today’s dynamic markets.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1111/mafi.12453,

Title: The Fundamental Theorem Of Asset Pricing With And Without Transaction Costs

Subject: q-fin.mf math.pr

Authors: Christoph Kühn

Published: 02-07-2023

Everything You Need To Know

What is the Fundamental Theorem of Asset Pricing (FTAP) and why is it important?

The **Fundamental Theorem of Asset Pricing (FTAP)** is a cornerstone of asset pricing, stating that in the absence of arbitrage opportunities, there exists a **risk-neutral probability measure**. This means there's a way to value assets fairly relative to their risk. This theorem links the absence of arbitrage to the existence of a consistent way to value assets. It's important because it provides a theoretical framework for understanding how assets should be priced in an efficient market. If assets are not priced fairly according to the **risk-neutral measure**, arbitrage opportunities would arise until prices adjust, which could distort market efficiency and valuation.

What is 'no arbitrage' and why is it crucial in asset pricing?

In the context of asset pricing, **no arbitrage** means the market doesn't allow for risk-free profit. This is a critical assumption because arbitrage opportunities, where risk-free profits are possible, distort market efficiency and valuation. **Strict no-arbitrage** takes this further, ensuring that any strategy that appears to create arbitrage is also invalid. The absence of arbitrage is fundamental because it ensures that assets are priced consistently and that markets operate efficiently, reflecting their true economic value based on their expected future payoffs.

How do transaction costs affect the application of the Fundamental Theorem of Asset Pricing (FTAP) in the real world?

In the real world, markets have **transaction costs**, such as brokerage fees or bid-ask spreads. The classic **FTAP** often assumes frictionless markets, a simplification that doesn't hold in reality. These costs significantly impact investment strategies and asset pricing. Recent research has extended the **FTAP** to include these costs, providing a more realistic framework for investors. Understanding how transaction costs influence asset pricing is crucial for developing effective investment strategies and risk management.

Can you explain 'risk-neutral probability measure' and its role in asset pricing?

The **risk-neutral probability measure** is a concept central to the **FTAP**. It's a way to 'weight' possible future outcomes of an asset such that, on average, assets are priced fairly relative to their risk. It's a mathematical tool used to ensure fair pricing by discounting an asset's expected future payoffs. This measure isn't necessarily the 'true' probability of those payoffs occurring. If an asset is not fairly priced according to the **risk-neutral measure**, arbitrage opportunities would arise until prices adjust, ensuring market efficiency.

What are the key takeaways for investors from understanding the Fundamental Theorem of Asset Pricing (FTAP) and related concepts?

Understanding the **FTAP**, particularly with an awareness of transaction costs, provides investors with a more realistic perspective on asset pricing. The key takeaways include: recognizing that perfect, arbitrage-free markets are theoretical, and appreciating the impact of real-world costs. This knowledge allows for smarter, more robust investment and risk management strategies. Mastering the concepts of **no arbitrage**, **risk-neutral measure**, and **fair pricing** provides a powerful edge in today’s dynamic markets, irrespective of experience level.