Risk-Neutral Probabilities

Risk-neutral probabilities are probabilities of potential future outcomes adjusted for risk, which are then used to compute expected asset values. 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 that is not in fact the actual scenario.

Risk-neutral probabilities are used to try and determine objective fair prices for an asset or financial instrument. You are assessing the probability with risk taken out of the equation, so it doesn’t play a factor in the anticipated outcome.

By contrast, if you tried to estimate the anticipated value of that particular stock based on how likely it is to go up or down, considering unique factors or market conditions that influence that specific asset, you would be including risk into the equation and thus would be looking at real or physical probability.

The benefit of this risk-neutral pricing approach is that the once the risk-neutral probabilities are calculated, they can be used to price every asset based on its expected payoff. These theoretical risk-neutral probabilities differ from actual real-world probabilities, which are sometimes also referred to as physical probabilities. If real-world probabilities were used, expected values of each security would need to be adjusted for its individual risk profile.

You might think of this approach as a somewhat formalized and structured method of guessing what the fair and proper price for a security or other financial asset should be by tracking price trends for other similar assets and then estimating the average to arrive at your best guess. 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 essentially be minimizing the possible unusual high market outcomes while increasing the possible lows.

Implementing risk-neutral probability in equations when calculating pricing for fixed-income financial instruments is useful. This is because you are able to price a security at its trade price when employing the risk-neutral measure.

A key assumption in computing risk-neutral probabilities is the absence of arbitrage. The concept of risk-neutral probabilities is widely used in pricing derivatives.

The term “risk-neutral” can sometimes be misleading because some people may assume it means that the investors are neutral, unconcerned or unaware of risk, or that the investment itself has no risk or has a risk that can somehow be eliminated.