Exotic options pricing under special Lévy process models: a biased control variate method approach

Abstract Option pricing plays an important role in financial engineering. No explicit formulas can be derived for many exotic options when the underlying asset prices follow more realistic models. The Monte Carlo simulation method is the only feasible approach to obtain numerical values of these options usually. To overcome the slow convergence - the main drawback for the Monte Carlo method, variance reduction and quasi-Monte Carlo methods are proposed. This paper proposes the application of biased control variate method to speed up the evaluation of exotic options prices by simulations under a special type of Levy processes. We construct very efficient biased control variates for both fixed and floating strike lookback options, as well as barrier options.