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Explicit implied vols for multifactor local-stochastic vol models

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  • Matthew Lorig
  • Stefano Pagliarani
  • Andrea Pascucci

Abstract

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under five different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility, $3/2$ stochastic volatility, and SABR local-stochastic volatility.

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File URL: http://arxiv.org/pdf/1306.5447
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Paper provided by arXiv.org in its series Papers with number 1306.5447.

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Date of creation: Jun 2013
Date of revision: Mar 2014
Handle: RePEc:arx:papers:1306.5447

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Web page: http://arxiv.org/

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  1. Martin Forde & Antoine Jacquier, 2009. "Small-Time Asymptotics For Implied Volatility Under The Heston Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 861-876.
  2. Martin Forde & Antoine Jacquier, 2011. "Small-Time Asymptotics for an Uncorrelated Local-Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(6), pages 517-535, April.
  3. Leif Andersen, 2011. "Option pricing with quadratic volatility: a revisit," Finance and Stochastics, Springer, Springer, vol. 15(2), pages 191-219, June.
  4. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "Pricing approximations and error estimates for local L{\'e}vy-type models with default," Papers 1304.1849, arXiv.org, revised May 2014.
  5. Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, University Library of Munich, Germany.
  6. Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Papers 1203.5903, arXiv.org, revised Aug 2012.
  7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
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Cited by:
  1. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "A Taylor series approach to pricing and implied vol for LSV models," Papers 1308.5019, arXiv.org.

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