Martingale pricing

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Martingale pricing is a pricing approach based on the notions of martingale and risk neutrality. The martingale pricing approach is a cornerstone of modern quantitative finance and can be applied successfully to a variety of derivatives contracts, e.g. options, futures, interest rate derivatives, credit derivatives, etc.

In contrast to the PDE approach to pricing, martingale pricing formulae are in the form of expectations which can be efficiently solved numerically using a Monte Carlo 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 a significant research effort is ongoing with the objective of finding efficient Monte Carlo techniques to value this kind of contracts.