Hybrid Monte Carlo methods in computational finance

Monte Carlo methods are highly appreciated and intensively employed in computational finance in the context of financial derivatives valuation or risk management. The method offers valuable advantages like flexibility, easy interpretation and straightforward implementation. Furthermore, the dimensionality of the financial problem can be increased without reducing the efficiency significantly. The latter feature of Monte Carlo methods is important since it represents a clear advantage over other competing numerical methods. Furthermore, in the case of option valuation problems in multiple dimensions (typically more than five), theMonte Carlo method and its variants become the only possible choices. Basically, theMonte Carlo method is based on the simulation of possible scenarios of an underlying process and by then aggregating their values for a final solution. Pricing derivatives on equity and interest rates, risk assessment or portfolio valuation are some of the representative examples in finance, where Monte Carlo methods perform very satisfactorily. The main drawback attributed to these methods is the rather poor balance between computational cost and accuracy, according to the theoretical rate of Monte Carlo convergence. Based on the central limit theorem, theMonte Carlo method requires hundred times more scenarios to reduce the error by one order...

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