Gas storage valuation under multifactor Lévy processes

Abstract

A practical problem for energy companies is instituting a consistent framework across its supply and trading activities to deliver on all-important P&L and at-Risk reporting requirements. With a focus on storage assets and wider natural gas market exposures, we present a gas storage valuation methodology, which uniquely uses a flexible multifactor Lévy process setting that allows for consistent valuation

Practice-relevant model validation: distributional parameter risk analysis in financial model risk management

“…We set up the gas storage valuation problem as per Cummins et al (2018). As we are dealing with a physical storage infrastructure, we need to factor in standard physical constraints and operating characteristics.…”

“…The jump diffusion specification is what allows us to replicate the volatility smile using this model, in a similar manner to the MRVG-1F model. 6 This leads us to the specification of the flexible two-factor Mean Reverting Variance Gamma model (which we label MRVG-2F), as described by Cummins et al (2018), which is a convenient extension of the MRVG-1F model. The inclusion of the second factor allows more flexibility in modelling the covariance structure of the forward curve and therefore should produce storage values more representative of the underlying dynamics.…”

“…where for the MRVG-1F model θ ≡ θ m = {α, σ, ν}, and for the MRJD model θ ≡ θ m = {α, σ, λ, μ}, and n is the sample size. In order to calculate the model option prices, C model i (θ m ), we use the Fourier transform based swaption pricing algorithm developed by Cummins et al (2018).…”

“…From the full parameter set θ ≡ {α, σ, ν, b, c, }, we define the market calibrated parameter set as θ m ≡ {α, σ, ν}, determining the shape of the volatility term structure of the first factor of the model, and we define the historically estimated parameters set as θ h ≡ {b, c, }, determining the shape of the volatility term structure of the second factor of the model. We utilise the market implied moment matching technique of Cummins et al (2018), which involves firstly, inferring the moments of the underlying forward contracts from the prices of quoted options and secondly, calibrating the known model forward price moments to these values. In our exercise here, we focus on matching the first four moments of the forward prices underlying our option quotes.…”

“…Many of the extant gas storage models are inadequately specified to effectively capture the excess kurtosis evident in natural gas market returns, with model performance typically compromised in the pursuit of simpler solutions to the optimisation problem that underlies gas storage valuation. The multifactor MRVG model, in contrast, offers notable benefits in capturing excess kurtosis and time spread volatility, whilst maintaining consistency with the vanilla options market, and offering computationally efficient pricing solutions, such as Fourier transform based methods (Cummins et al 2018). The question that arises is whether this improvement in model specification exacerbates parameter risk exposure.…”