Functional quantization of rough volatility and applications to volatility derivatives

O. Bonesini, G. Callegaro and A. Jacquier

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We develop a product functional quantization of rough volatility. Since the optimal quantizers can be computed offline, this new technique, built on the insightful works by [Luschgy, H. and Pagès, G., Functional quantization of Gaussian processes. J. Funct. Anal., 2002, 196(2), 486–531; Luschgy, H. and Pagès, G., High-resolution product quantization for Gaussian processes under sup-norm distortion. Bernoulli, 2007, 13(3), 653–671; Pagès, G., Quadratic optimal functional quantization of stochastic processes and numerical applications. In Monte Carlo and Quasi-Monte Carlo Methods 2006, pp. 101–142, 2007 (Springer: Berlin Heidelberg)], becomes a strong competitor in the new arena of numerical tools for rough volatility. We concentrate our numerical analysis on the pricing of options on the VIX and realized variance in the rough Bergomi model [Bayer, C., Friz, P.K. and Gatheral, J., Pricing under rough volatility. Quant. Finance, 2016, 16(6), 887–904] and compare our results to other benchmarks recently suggested.

Keywords: functional quantization; Riemann–Liouville process; rough volatility; series expansion; Vix options; Volterra process (search for similar items in EconPapers)
JEL-codes: F3 G3 J1 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2023-12-03
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Published in Quantitative Finance, 3, December, 2023, 23(12), pp. 1769-1792. ISSN: 1469-7688

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