Abstract
We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (Rev Financ Stud 6(2):327–343, 1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (J Comput Financ 10(2):129–155, 2006) for the Heston model such that the first uniform variable does not influence the stochastic volatility path and then conditionally modifying its marginals to fulfill the barrier condition(s). We show that this method is unbiased and never does worse than the unconditional algorithm. In addition, the conditioning is combined with a root finding method to also force positive payouts. The effectiveness of this method is shown by extensive numerical results.
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References
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Acknowledgements
This research is part of a project funded by the Research Fund KU Leuven. Dirk Nuyens is a fellow of the Research Foundation Flanders (FWO). This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office.
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Achtsis, N., Cools, R., Nuyens, D. (2013). Conditional Sampling for Barrier Option Pricing Under the Heston Model. In: Dick, J., Kuo, F., Peters, G., Sloan, I. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2012. Springer Proceedings in Mathematics & Statistics, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41095-6_9
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DOI: https://doi.org/10.1007/978-3-642-41095-6_9
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