A risk-neutral measure that is used to price derivative contingent claims such as average rate options by implementing stochastic discount factors. Equivalent martingale measures are essential for pricing of complex derivative contracts. If markets are complete, an equivalent martingale measure exists, and the existence of such a measure (equivalent martingale measure) ensures that markets are complete. The fundamental theorem of finance is based on the premise that the pricing of a derivative instrument is done appropriately in a market free of arbitrage opportunities, and as such there is a unique equivalent martingale measure (EMM). Hence there are two possible ways to handle derivatives pricing. The first involves the use of the classical models such as Black-Scholes model and Merton model which made attempts to price options through partial differential equation (PDE) solutions. The second uses the equivalent martingale measure.