Detecting and modelling the jump risk of CO₂emission allowances and their impact on the valuation of option on futures contracts

Abstract

Modelling CO 2 emission allowance prices is important for pricing CO 2 emission allowance linked assets in the emissions trading scheme (ETS). Some statistical properties of CO 2 emission allowance prices have been discovered in the literature ignoring price jumps. By employing real data from the ETS, this research first detects the jump risk using a jump test and then verifies jump effects in modelling CO 2 emission allowance prices by comparing the in-sample and out-of-sample model performance. We suggest a model which can capture the statistical properties of autocorrelation, volatility clustering and jump effects is more appropriate for modelling CO 2 emission allowance prices. We establish a general framework for pricing CO 2 emission allowance options on futures contracts with these properties and find that the jump risk significantly affects the value of the CO 2 emission allowance option on futures contracts. More importantly, we demonstrate that the dynamic jump ARMA-GARCH model can provide more accurate valuations of the CO 2 emission allowance options on futures than other models in terms of pricing error.

Quantitative models in emission trading system research: A literature review

“…(3) Both statistical and AI models have been introduced to extensively analyse factors in the ETS and goods markets. As for statistical models, timeseries models (e.g., autoregressive moving average model [97] and wavelet analysis [140]) have been used to capture and forecast the dynamic trends in carbon price [162], CER price [140] and their returns [140,162]; and multivariate models (e.g., VAR [51,142,149], GARCHs [143,156] and other regression analyses) have been used to capture the relationship between factors in ETS and goods markets. To address complexity and nonlinearity, increasing number of AI models have been introduced to model the factors in the ETS markets, such as extreme learning machine [44], SVM [44,87], DT [87] and deep learning [98].…”