Multiscale stochastic volatility model for derivatives on futures

Jean Pierre Fouque, Yuri F. Saporito, Jorge P. Zubelli

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we present a new method for computing the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility studied in Fouque et al. (2011). It provides an alternative method to the singular perturbation technique presented in Hikspoors & Jaimungal (2008). The main features of our method are twofold: firstly, it does not rely on any additional hypothesis on the regularity of the payoff function, and secondly, it allows an effective and straightforward calibration procedure of the group market parameters to implied volatilities. These features were not achieved in previous works. Moreover, the central argument of our method could be applied to interest rate derivatives and compound derivatives. The only pre-requisite of our approach is the first-order approximation of the underlying derivative. Furthermore, the model proposed here is well-suited for commodities since it incorporates mean reversion of the spot price and multiscale stochastic volatility. Indeed, the model was validated by calibrating the group market parameters to options on crude-oil futures, and it displays a very good fit of the implied volatility.

Original languageBritish English
Article number1450043
JournalInternational Journal of Theoretical and Applied Finance
Issue number7
StatePublished - 16 Nov 2014


  • commodities
  • futures price
  • options on futures
  • perturbation method
  • Stochastic volatility


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