Gas storage valuation under Lévy processes using the fast Fourier transform

Mark Cummins, Greg Kiely and Bernard Murphy

Abstract

In this paper, we present the modeling benefits of using Lévy processes and the fast Fourier transform (FFT) in the valuation of gas storage assets and, from a practi- tioner’s perspective, in creating market-consistent valuations and hedging portfolios. This valuation methodology derives the storage asset value via stochastic backward dynamic programming, drawing on established FFT methods. We present a modifi- cation to this algorithm that removes the need for a dampening parameter and leads to an increase in valuation convergence. The use of the FFT algorithm allows us to employ a wide range of potential spot price models. We present the characteristic function of one such model: the mean-reverting variance-gamma (MRVG) process. We provide a rationale for using this model in fitting the implied volatility smile by comparing the process moments with the more common mean-reverting diffusion model. We next present the dynamics of the implied spot price under a general single- factor Lévy-driven forward-curve model; using these results, we go on to present the forward-curve-consistent conditional-characteristic function of the implied spot price model. We derive a transform-based swaption formula in order to calibrate our models to market-traded options, and we 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 perform an informative scenario-based analysis on the relationship between the implied volatility surface and the asset value. Convergence results for the valuation algorithm are presented, along with a discussion on the potential for further increasing the computational efficiency of the algorithm. Finally, to provide increased confidence around the fit of the MRVG model proposed, we conduct a formal model-specification analysis of this model against a benchmark mean-reverting jump-diffusion model.