*Basic

Risk-neutral probabilities are probabilities of potential future outcomes adjusted for risk, which are then used to compute expected asset values.[1] In other words, assets and securities are bought and sold as if the hypothetical fair, single probability for an outcome were a reality, even though it is not, in fact, the actual scenario.[2]

**Intermediate

The benefit of the risk-neutral pricing approach is that once the risk-neutral probabilities are calculated, they can be used to price every asset based on its expected payoff.[3] These theoretical risk-neutral probabilities differ from actual real-world probabilties, which are sometimes referred to as physical probabilities.[4] If real-world probabilities were used, the expected values of each security would need to be adjusted for its individual risk profile.[5] This approach is a structured method of guessing what the fair and proper price for a financial asset should be by tracking price trends for other similar assets and then estimating the average to arrive at your best guess.[6] For this approach, you would try to level out the extreme fluctuations at either end of the spectrum, creating a balance that creates a stable, level price point. You would also be minimizing the possible unusual high market outcomes while increasing the possible lows.[7] Risk-neutral investors are not concerned with the risk of an investment. However, risk-averse investors have a greater fear of losing money. The term risk-neutral can sometimes be misleading because some people may assume that it means that the investors are neutral, unconcerned, or unaware of risk – or that the investment itself has no risk. However, risk-neutral doesn't mean that the investor is unaware of risk; instead, it implies that the investor understands the risks but is not factoring them into their decision at the moment.[8] A risk-neutral investor prefers to focus on the potential gain of the investment instead. When faced with two investment options, an investor who is risk-neutral would solely consider the gains of each investment, while choosing to overlook the potential risk, even though that they are aware of the inherent risk.[9]

***Advanced

Implementing risk-neutral probability in equations when calculating pricing for fixed income financial instruments is useful.[10] This is because you are able to price the security at its trade price when employing the risk-neutral measure.[11] A key assumption in computing risk-neutral probabilities is the absence of arbitrage.[12] The concept of risk-neutral probabilities is widely used in pricing derivatives.[13]

Sources

[1] Editors. Risk-neutral measure. Wikipedia. en.wikipedia.org
[2] Editors. Risk-neutral Probabilities. Pages.stern.nyu.edu
[3] Editors. Understanding Risk-neutral Probability. Web.ma.utexas.edu
[4] Editors. Risk Neutral Probability and Black-Scholes. Math.mit.edu
[5] Editors. Risk Neutral – Meaning, Explained, Example, vs Risk Averse. Wallstreetmojo.com
[6] Chen, J (2022). Risk-neutral Meaures. Investopedia.com
[7] Gisiger, N (2010). Risk-neutral probabilities explained. Papers.ssrn.com
[8] Croughy, M; Galai, D (2019). The relation between the risk-neutral and physical probabilities of default. Worldscientific.com
[9] Editors. Risk-neutrality in Derivative Pricing. Analystprep.com
[10] Editors (2020). Real World vs Risk Neutral: Understanding the Difference. Equitymethods.com
[11] Editors (2022). What is the “risk-neutral measure”? Medium.datadriveninvestor.com
[12] Editors (2020). Risk-neutral Probability Distributions. Qauantoisseur.com
[13] Editors (2023). What is Risk-neutral in Investing and Options Trading? Sofi.com