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Efficient valuation method for the SABR model

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  • Hyukjae Park

Abstract

In this article, we show how the scaling symmetry of the SABR model can be utilized to efficiently price European options. For special kinds of payoffs, the complexity of the problem is reduced by one dimension. For more generic payoffs, instead of solving the 1+2 dimensional SABR PDE, it is sufficient to solve $N_V$ uncoupled 1+1 dimensional PDE's, where $N_V$ is the number of points used to discretize one dimension. Furthermore, the symmetry argument enables us to obtain prices of multiple options, whose payoffs are related to each other by convolutions, by valuing one of them. The results of the method are compared with the Monte Carlo simulation.

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  • Hyukjae Park, 2013. "Efficient valuation method for the SABR model," Papers 1308.0665, arXiv.org, revised Nov 2013.
    • Handle: RePEc:arx:papers:1308.0665
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    1. Jan Obloj, 2007. "Fine-tune your smile: Correction to Hagan et al," Papers 0708.0998, arXiv.org, revised Mar 2008.
    2. Dufresne, Daniel, 1989. "Weak convergence of random growth processes with applications to insurance," Insurance: Mathematics and Economics, Elsevier, vol. 8(3), pages 187-201, November.
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