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Review of Derivatives Research

Erschienen in:

11.01.2019

Empirical performance of reduced-form models for emission permit prices

verfasst von: Steffen Hitzemann, Marliese Uhrig-Homburg

Erschienen in: Review of Derivatives Research | Ausgabe 3/2019

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Abstract

The value of emission permits in environmental markets derives from the particular design features of the underlying cap-and-trade system. In this paper, we evaluate a model framework for the price dynamics of emission permits which accounts for these features in a reduced-form way. Based on permit futures and option data from the European Union Emissions Trading System, the world’s largest environmental market, we show that model variants which represent the design of the system most accurately provide the best fit to historical futures prices and achieve the best option pricing performance. Our results suggest that the specific design of cap-and-trade systems directly translates to the dynamic properties of emission permit prices, and that models tailored to environmental markets are the best choice for related pricing and risk management decisions.

Vorheriger Artikel Implied risk aversion: an alternative rating system for retail structured products

Nächster Artikel Valuation of an option using non-parametric methods

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The G7 member states have agreed on this goal at the 41st G7 summit in June 2015. Subsequently, 195 countries worldwide have signed the Paris climate agreement, of which only the United States has announced the intention to withdraw.

By now, a double-digit number of cap-and-trade policies are in force all over the world, including systems in the European Union, in several states of Canada and the US, in South Korea, and in several provinces and cities in China.

Theory predicts that within a compliance period, the standard cost-of-carry relationship holds because permit spot and futures contracts can be traded without any frictions, see Hitzemann and Uhrig-Homburg (2018). Uhrig-Homburg and Wagner (2009) and Rittler (2012) show that this is also true empirically.

For \(R_t=0\), simply drop the last term \(e^{-r(T_m-{\overline{t}})^+}e^{\lambda _{m+1,t}}\) in (9) and all subsequent equations.

Unlike Grüll and Taschini (2009) and others, we exclude more sophisticated standard models, e.g., normal-inverse Gaussian (NIG) processes, from our analysis, since our focus is on the performance of reduced-form models within a pure Itô framework. We leave it open for future research to consider a reduced-form model framework for emission permit prices based on general Lévy processes.

The choice of this parametrization, which we label by CSCH due to its affinity to the hyperbolic cosecant, is mainly motivated by its simplicity and its favorable empirical behavior.

The ECX is the world’s largest carbon futures exchange and is operated by Intercontinental Exchange (ICE), http://www.theice.com.

In Phase I from 2005 to 2007, it was forbidden to bank emission permits into the next compliance period, which led to a collapse of permit prices once the market realized that the economy was long of permits. In the ongoing Phase III from 2013 to 2020, the EU ETS undergoes a structural reform that addresses the large surplus of emission permits in the system.

The only non-generic point is the initialization procedure. Since the transition equation is non-stationary in all of its components, we initialize the unscented Kalman filter by using diffuse priors (see Harvey 1989, pp. 121–122). In particular, we employ the approach of Rosenberg (1973) to treat the initial state as fixed and unknown, and infer it by maximum likelihood estimation (see Durbin and Koopman 2001, pp. 117–188).

For the model parametrization \(z^{CH}_k\), the parameters \(\alpha _1,\ldots ,\alpha _m\) are set to 1 and not included into the numerical optimization.

We abbreviate by writing (CS)CH when a statement holds for both the CH and the CSCH parametrization.

Similar two-stage procedures are frequently applied for other model classes, see for example Broadie et al. (2007).

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Titel: Empirical performance of reduced-form models for emission permit prices
verfasst von: Steffen Hitzemann
Marliese Uhrig-Homburg
Publikationsdatum: 11.01.2019
Verlag: Springer US
Erschienen in: Review of Derivatives Research / Ausgabe 3/2019
Print ISSN: 1380-6645
Elektronische ISSN: 1573-7144
DOI: https://doi.org/10.1007/s11147-018-09152-7