What does the fundamental theorem of asset pricing ensure?

The fundamental theorem of asset pricing provides a crucial link between the absence of arbitrage opportunities in a market and the pricing of financial assets. Specifically, it states that in a no-arbitrage market, there exists a risk-neutral measure under which the discounted price processes of assets are martingales.

This implies that when you apply this risk-neutral measure, if you discount the future cash flows of the assets at the risk-free rate, the expected value of these discounted cash flows will equal the current price of the assets. In simpler terms, the theorem characterizes the pricing of financial instruments in a way that guarantees that there are no arbitrage opportunities—this means that it is impossible to create a risk-free profit through trading.

The importance of this theorem is foundational in the field of financial economics as it guides derivative pricing and the formulation of asset valuation models. It provides a framework through which one can evaluate assets while assuming rational behavior from investors, thus shaping the underlying principles behind quantitative finance.

Other options do not accurately capture the essence of the fundamental theorem of asset pricing. While interest rates and the pricing of assets under market conditions are related concepts, they do not reflect the core idea of the no-arbitrage condition or the martingale property of asset