From the Samuelson Volatility Effect to a Samuelson Correlation Effect: An Analysis of Crude Oil Calendar Spread Options
Journal of Banking & Finance, Volume 95, October 2018, Pages 185-202
39 Pages Posted: 27 Sep 2014 Last revised: 23 Feb 2019
Date Written: November 4, 2016
Our first aim in this paper is to introduce a futures-based model able of capturing the main features displayed by Crude Oil futures and options contracts, such as the Samuelson volatility effect and the volatility smile. We calculate the joint characteristic function of two futures contracts in the model in analytic form and use it to price calendar spread options. In an empirical application we show that the model, in contrast to simpler nested models, can be successfully calibrated to market prices of vanilla and calendar spread options. Our second aim is to use this model to analyze the dependence structure of Crude Oil futures contracts. To this end, we propose analytical expressions giving the copula and copula density directly in terms of the joint characteristic function. These tools allow us to perform an in-depth analysis for pairs of futures, and we observe a phenomenon we call the Samuelson correlation effect.
Keywords: Multi-factor stochastic volatility, Futures curve modelling, Option pricing, Calendar spread options, Crude oil, Fourier inversion methods
JEL Classification: C02, G13
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