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Explicit implied volatilities for multifactor local-stochastic volatility models

Listed author(s):
  • Matthew Lorig
  • Stefano Pagliarani
  • Andrea Pascucci

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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Paper provided by in its series Papers with number 1306.5447.

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Date of creation: Jun 2013
Date of revision: Nov 2014
Handle: RePEc:arx:papers:1306.5447
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  1. Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Papers 1203.5903,, revised Aug 2012.
  2. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "Pricing approximations and error estimates for local L\'evy-type models with default," Papers 1304.1849,, revised Nov 2014.
  3. Leif Andersen, 2011. "Option pricing with quadratic volatility: a revisit," Finance and Stochastics, Springer, vol. 15(2), pages 191-219, June.
  4. Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, University Library of Munich, Germany.
  5. Jan Baldeaux & Alexander Badran, 2014. "Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(4), pages 299-312, September.
  6. Martin Forde & Antoine Jacquier, 2011. "Small-Time Asymptotics for an Uncorrelated Local-Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(6), pages 517-535, April.
  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, vol. 6(2), pages 327-343.
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