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What is the risk-neutral measure?

Risk-neutral measure

The risk-neutral measure is a probability metric widely used in quantitative financial mathematics to price derivatives and other financial instruments. It assumes that the present value of a derivative is equal to its expected future value discounted at the risk-free rate, generally that of three-month U.S. Treasury bills.

Where have you heard about the risk-neutral measure?

As a private investor you may not have heard of the risk-neutral measure. However, if your portfolio contains stock or other options then you may well have heard of the Black-Scholes model used for option pricing. This is a common application of calculating derivative prices using the risk neutral metric.

What you need to know about the risk-neutral measure.

The risk-neutral measure is derived from the broader fundamental theorems of asset pricing, which insist that markets must be arbitrage free. In the absence of arbitrage, the risk-neutral measure is used to calculate the present value of a derivative or other financial instrument by using the risk-free rate to discount the expected future value. If arbitrage is observed then the present and future prices of the asset would vary, and the market would buy or sell the asset until price equilibrium was restored. Hence, in a risk neutral world the future value of an asset is its present value.

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