Abstract
In this paper, we propose an importance-sampling based method to obtain unbiased estimators to evaluate expectations involving random variables whose probability density functions are unknown while their Fourier transforms have explicit forms. We give a general principle about how to choose appropriate importance sampling density under various Lévy processes. Compared with the existing methods, our method avoids time-consuming numerical Fourier inversion and can be applied effectively to high dimensional option pricing under different models.
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Acknowledgments
The research by Denis Belomestny was made in IITP RAS and supported by Russian Scientific Foundation grant (project N 14-50-00150). The second and third authors are grateful for the financial support of a GRF grant from HK SAR government (Grant ID: CUHK411113).
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Belomestny, D., Chen, N., Wang, Y. (2016). Unbiased Simulation of Distributions with Explicitly Known Integral Transforms. In: Cools, R., Nuyens, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-319-33507-0_9
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DOI: https://doi.org/10.1007/978-3-319-33507-0_9
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