A novel Monte Carlo approach to hybrid local volatility models

Anthonie W. van der Stoep*, Lech A. Grzelak, Cornelis W. Oosterlee

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
31 Downloads (Pure)


We present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994, 7, 18–20], [Int. J. Theor. Appl. Finance, 1998, 1, 61–110] models. In particular, we consider the stochastic local volatility model—see e.g. Lipton et al. [Quant. Finance, 2014, 14, 1899–1922], Piterbarg [Risk, 2007, April, 84–89], Tataru and Fisher [Quantitative Development Group, Bloomberg Version 1, 2010], Lipton [Risk, 2002, 15, 61–66]—and the local volatility model incorporating stochastic interest rates—see e.g. Atlan [ArXiV preprint math/0604316, 2006], Piterbarg [Risk, 2006, 19, 66–71], Deelstra and Rayée [Appl. Math. Finance, 2012, 1–23], Ren et al. [Risk, 2007, 20, 138–143]. For both model classes a particular (conditional) expectation needs to be evaluated which cannot be extracted from the market and is expensive to compute. We establish accurate and ‘cheap to evaluate’ approximations for the expectations by means of the stochastic collocation method [SIAM J. Numer. Anal., 2007, 45, 1005–1034], [SIAM J. Sci. Comput., 2005, 27, 1118–1139], [Math. Models Methods Appl. Sci., 2012, 22, 1–33], [SIAM J. Numer. Anal., 2008, 46, 2309–2345], [J. Biomech. Eng., 2011, 133, 031001], which was recently applied in the financial context [Available at SSRN 2529691, 2014], [J. Comput. Finance, 2016, 20, 1–19], combined with standard regression techniques. Monte Carlo pricing experiments confirm that our method is highly accurate and fast.

Original languageEnglish
Pages (from-to)1347-1366
Number of pages20
JournalQuantitative Finance
Issue number9
Publication statusPublished - 10 Mar 2017

Bibliographical note

Accepted Author Manuscript


  • Heston
  • Hull–White
  • Hybrid
  • Local volatility
  • Monte Carlo
  • Regression
  • SABR
  • Stochastic collocation
  • Stochastic interest rates
  • Stochastic local volatility
  • Stochastic volatility


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