Monte Carlo Methods

The term “Monte Carlo” for computational methods involving simulated random numbers was invented by Metropolis and Ulam when they were working at the Las Alamos Laboratory (didn’t some people say that quants were rocket scientists?). Like deterministic pricing schemes, simulation pricing schemes can be used in any Markovian (or, of course, static one-period) setup. In the case of European claims, simulation pricing schemes reduce to the well known Monte Carlo loops. For products with early exercise features, or for more general control problems and the related BSDEs, numerical schemes by simulation are available too, yet these are more sophisticated and will be dealt with separately in Chaps. 10 and 11.