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Mathematical finance is an old science but has become a major topic for numerical analysts since Merton [97], Black—Scholes [16] modeled financial derivatives. An excellent book for the mathematical foundation of option pricing is Lamberton and Lapeyre's [85]. Since the Black—Scholes model relies on stochastic differential equations, option pricing rapidly became an attractive topic for specialists in the theory of probability, and stochastic methods were developed first for practical applications, along with analytical closed formulas. But soon, with the rapidly growing complexity of the financial products, other numerical solutions became attractive. Applying the Monte-Carlo method to option pricing is very natural and not difficult, at least for European options, but speeding up the method by variance reduction may become tricky. Similarly, tree methods are very intuitive and fast but also rapidly become difficult as the …