Risk-neutral probabilities are a concept in finance that provide a way to determine the expected return of an asset or financial holding. These probabilities are adjusted for risk, meaning that the associated expected return reflects the associated riskiness of the asset.

Risk-neutral probabilities attempt to isolate the effect of uncertainty on the value of an asset or financial holding. By adjusting for risk, these probabilities can give a more accurate representation of the expected asset value.

Calculating risk-neutral probabilities requires making an assumption that there is no arbitrage. Arbitrage is the process of taking advantage of price discrepancies in order to make a riskless profit. If an arbitrage opportunity exists, then the risk-neutral probabilities will be inaccurate because the expected return won't accurately reflect the associated risk level.

The concept of risk-neutral probabilities is often used in pricing derivatives. Derivatives are financial instruments whose value is based on an underlying asset. Risk-neutral probabilities are used to price these instruments because they allow for taking into account the possibility of different outcomes and associated risks.

In conclusion, risk-neutral probabilities are used to calculate the expected asset value of financial instruments. Risk-neutral probabilities are adjusted for risk, meaning that the associated expected return reflects the associated riskiness of the asset. In order to accurately calculate risk-neutral probabilities, the assumption that there is no arbitrage must be made. And finally, the concept of risk-neutral probabilities is often used in pricing derivatives.