Gas Storage Valuation Under Lévy Processes Using the Fast Fourier Transform
49 Pages Posted: 8 Feb 2015 Last revised: 5 Oct 2015
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Gas Storage Valuation Under Lévy Processes Using the Fast Fourier Transform
Gas Storage Valuation Under Lévy Processes Using the Fast Fourier Transform
Date Written: October 4, 2015
Abstract
In this paper we study the modeling and computational benefits of using Lévy processes and the Fast Fourier Transform (FFT) in the valuation of gas storage assets and, from a practitioners perspective, in creating market consistent valuations and hedging portfolios. The valuation methodology derives the asset value via stochastic backwards dynamic programming, where we use an alternative formulation of the methodology proposed by Jaimungal and Surkov [2011]. The use of the FFT algorithm opens up a wide range of potential spot price models. We compare one such model, the Mean Reverting Variance Gamma process, to a simple Mean Reverting Diffusion and demonstrate it's superiority in replicating the shape of the market implied volatility surface. We derive a transform based swaption formula in order to calibrate our models to market traded options, and use these calibrated models to then value a stylized storage asset and calculate the hedging positions needed to monetize this value. We demonstrate how one can incorporate one's view on the shape of the implied volatility surface in the valuation of the asset by investigating the effect of changes in the volatility surface on the asset value. Convergence results for the valuation algorithm under both models are presented, along with a discussion around the potential for increasing further the computational efficiency of the algorithm.
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