Martingale pricing is a pricing approach based on the notions of martingale

Martingale (probability theory)

In probability theory, a martingale is a model of a fair game where no knowledge of past events can help to predict future winnings. In particular, a martingale is a sequence of random variables for which, at a particular time in the realized sequence, the expectation of the next value in the...

 and risk neutrality

Risk-neutral measure

In mathematical finance, a risk-neutral measure, is a prototypical case of an equivalent martingale measure. It is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market a derivative's price is the discounted...

. The martingale pricing approach is a cornerstone of modern quantitative finance and can be applied to a variety of derivatives

Derivative (finance)

A derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S...

 contracts, e.g. options

Option (finance)

In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

, futures

Futures contract

In finance, a futures contract is a standardized contract between two parties to exchange a specified asset of standardized quantity and quality for a price agreed today with delivery occurring at a specified future date, the delivery date. The contracts are traded on a futures exchange...

, interest rate derivative

Interest rate derivative

An interest rate derivative is a derivative where the underlying asset is the right to pay or receive a notional amount of money at a given interest rate...

s, credit derivatives, etc.

In contrast to the PDE

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

 approach to pricing, martingale pricing formulae are in the form of expectations which can be efficiently solved numerically using a Monte Carlo

Monte Carlo method

Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...

 approach. As such, Martingale pricing is preferred when valuing highly dimensional contracts such as a basket of options. On the other hand, valuing American-style contracts is troublesome and requires discretizing the problem (making it like a Bermudan option) and and only in 2001 F. A. Longstaff

Francis Longstaff

Francis A. Longstaff is the Allstate Professor of Insurance and Finance at the Anderson School of Management, University of California, Los Angeles, and the current Finance Area Chair....

 and E. S. Schwartz

Eduardo Schwartz

Eduardo Saul Schwartz is a professor of finance at the Anderson School of Management, University of California, Los Angeles, where he holds the California Chair in Real Estate & Land Economics...

developed a practical Monte Carlo method for pricing American options.