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First-Order Pricing of Futures Derivatives with Multiscale Stochastic Volatility

Article arXiv papers · Author: Jean-Pierre Fouque et al.
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Summary

This paper presents a method for computing a first-order approximation to the prices of derivatives on futures under multiscale stochastic volatility. It offers an alternative to a singular perturbation approach and is designed to work without additional assumptions about payoff regularity. The method also supports a straightforward procedure for calibrating the model to implied volatilities. Its core argument may extend to interest-rate and compound derivatives, provided a first-order approximation of the underlying derivative is available.

The authors describe the model as particularly suitable for commodities because it combines mean reversion in the spot price with volatility operating at multiple scales. They report validating it through calibration to options on crude-oil futures, with a good fit to implied volatility. The document provides no calibration details or comparative error measures, so it does not allow an independent assessment of the fit or how the approach performs across other products and conditions.

Key ideas

  • The method computes a first-order approximation for derivative prices on futures under multiscale stochastic volatility.
  • It is presented as an alternative to singular perturbation techniques.
  • The approach does not require extra assumptions about payoff regularity and supports implied-volatility calibration.
  • The model combines mean-reverting spot prices with multiscale stochastic volatility, a setup proposed for commodities.
  • Calibration to crude-oil futures options is reported to fit implied volatility well, without further fit statistics in the document.

Tags

FuturesCommoditiesOptionsVolatilityDerivatives pricing
Full text
# Multiscale Stochastic Volatility Model for Derivatives on Futures


# Multiscale Stochastic Volatility Model for Derivatives on Futures









In this paper we present a new method to compute the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility of Fouque \textit{et al.} (2011, CUP). It provides an alternative method to the singular perturbation technique presented in Hikspoors and 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 model 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 it to options on crude-oil futures, and it displays a very good fit of the implied volatility.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.