The efficient and accurate valuation of financial derivatives, for example options, is one of the main tasks of computational finance. Thereby, the fair value of a derivative is determined by the payoff structure of the financial product at hand and a suitable stochastic model for the financial market. The resulting problem is then either an expectation (usually a multivariate integral) or a partial (integro-) differential equation. In most cases there exist not closed-form solutions for these problems and numerical methods have to be used for their computation.
Current challenges are more and more complex financial products, such as compound or multi-asset options, as well as sophisticated market models, such as jump-diffusion models.