Martingale Measure

A martingale measure is a probability measure under which the discounted price process of an asset is a martingale. In simpler terms, it is a mathematical tool that allows us to price derivatives as if the market were risk-neutral.

Under this measure, the expected future price of an asset is simply its current price adjusted for the risk-free interest rate. This simplifies the pricing of complex derivatives by removing the need to estimate subjective risk premiums.

The existence of a martingale measure is equivalent to the absence of arbitrage opportunities in a market. It is a formal way of justifying the use of risk-neutral pricing formulas.

This concept is essential for any quantitative analyst working with advanced derivatives or complex hedging strategies.