Estimating the sensitivity of a simulation with respect to changes in the parameter values is an important part of establishing the validity of the conclusions. If a simulation estimates an expected value at certain value of the parameters with 0.32 ± 0.05 but the derivative with respect to one parameter, say the volatility parameter σ, is 5, this indicates that a change of the volatility of on...

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We develop methods for estimating price sensitivities by simulation for Lévy-driven models. The methods combine pathwise derivatives and likelihood ratio method estimators with alternative approaches to approximating and simulating Lévy processes. We develop estimators based on exact sampling of increments, time-change representations of Lévy processes, saddlepoint approximations to the score f...

The aim of this paper is extensively investigate the performance of the estimators for the Greeks of multidimensional complex path-dependent options obtained by the aid of Malliavin Calculus. The study analyses both the computation effort and the variance reduction in the Quasi-Monte Carlo simulation framework. For this purpose, we adopt the approach employed by Montero and Kohatsu-Higa to the ...

In fact, this assumption is incorrect and, whilst the Ancient Greek astronomers made huge contributions to astronomy, their knowledge was built upon the solid foundations laid by other great cultures. The Mesopotamian [1] and Zoroastrian astronomers and astrologers, in the Fertile Crescent and the empty deserts of Persia, made many sophisticated observations and devised complex theories to desc...