Probability Measure Change

A probability measure change is a mathematical technique that shifts the focus of a probability distribution to make complex calculations more tractable. This is frequently used in derivative pricing to move from the physical probability measure ⎊ which describes how the asset price actually moves ⎊ to a risk-neutral measure, where the expected return of the asset is the risk-free rate.

By performing this change, the valuation of the derivative becomes the discounted expected value of its future payoff. This concept is fundamental to the risk-neutral pricing theory that underpins the entire derivative market.

Understanding this shift is essential for quantitative analysts who need to build models that are consistent with market-observed prices. It allows for the elegant pricing of complex instruments by simplifying the underlying stochastic processes and ensuring that the valuation is arbitrage-free.