A Model for the Valuation of Carbon Price Risk

Dannenberg, Henry; Ehrenfeld, Wilfried

doi:10.1007/978-3-642-20592-7_9

“…to the approaches developed by Dannenberg andEhrenfeld (2011), Lin andLin (2007) price is finally shown to be dependent upon the current level of convenience yield, the price of a zero-coupon bond with maturity at time T , the speed of mean-reversion of the convenience yield, the long-run mean yield, the convenience yield market price of risk, and the variance of the change in the marginal convenience yield. According to the authors, such a two-factor model that assumes a jump diffusion process for the underlying and a stochastic, mean-reverting convenience yield provides a satisfactory formula for the pricing of inter-Phase carbon futures.…”

Section: Futures Pricementioning

confidence: 90%

On the Stochastic Properties of Carbon Futures Prices

Chevallier

¹

,

Sévi

²

2012

View full text Add to dashboard Cite

Pricing carbon is a central concern in environmental economics, due to the importance of emissions trading schemes worldwide to regulate pollution. This paper documents the presence of small and large jumps in the stochastic process of the CO2 futures price. The large jumps have a discrete origin, i.e. they can arise from various demand factors or institutional decisions on the tradable permits market. Contrary to the previously established literature, we show that the stochastic process of the carbon futures prices does not contain a continuous component (Brownian motion). The results are derived by using high-frequency data in the activity signature function framework Tauchen (2010, 2011)). The implication is that the carbon futures price should be rather modelled as an appropriately sampled, centered Lévy or Poisson process. The pure-jump behavior of the carbon price could be explained by the lower volume of trades on this allowance market (compared to other highly liquid financial markets).

show abstract

“…The first theoretical pricing of emissions allowances spot prices with jumps is given by Dannenberg and Ehrenfeld (2011) under a discretized form of the standard Vasicek process. After a stochastic shock occurring between t and t + 1, the spot market price is 'pulled back' towards the mean level by the mean reversion formula.…”

Section: Spot Pricementioning

confidence: 99%

“…This modeling of the jump size is chosen to achieve an approximately unbiased price modelling. Overall, Dannenberg and Ehrenfeld (2011) suggest to adopt a Mean-Reversion Jump Diffusion (MRJD) process for allowance spot prices.…”

Section: Spot Pricementioning

confidence: 99%

“…to the approaches developed by Dannenberg andEhrenfeld (2011), Lin andLin (2007) . Assuming a non-zero mean-reverting convenience yield, the inter-Phase carbon futures price is finally shown to be dependent upon the current level of convenience yield, the price of a zero-coupon bond with maturity at time T , the speed of mean-reversion of the convenience yield, the long-run mean yield, the convenience yield market price of risk, and the variance of the change in the marginal convenience yield.…”

Section: Futures Pricementioning

confidence: 99%

“…Concerning the latter category, the mathematical papers by previous literature (especially Dannenberg and Ehrenfeld (2011), Ç etin and Verschuere (2009), Borovkov et al (2011) have derived smart modeling strategies to model the importance of jumps in the price process of CO 2 (see the Review section 2).…”

Section: Sensitivity Analysismentioning

confidence: 99%

See 2 more Smart Citations

On the Stochastic Properties of Carbon Futures Prices

Chevallier

¹

,

Sévi

²

2013

Environ Resource Econ

View full text Add to dashboard Cite

Pricing carbon is a central concern in environmental economics, due to the importance of emissions trading schemes worldwide to regulate pollution. This paper documents the presence of small and large jumps in the stochastic process of the CO2 futures price. The large jumps have a discrete origin, i.e. they can arise from various demand factors or institutional decisions on the tradable permits market. Contrary to the previously established literature, we show that the stochastic process of the carbon futures prices does not contain a continuous component (Brownian motion). The results are derived by using high-frequency data in the activity signature function framework Tauchen (2010, 2011)). The implication is that the carbon futures price should be rather modelled as an appropriately sampled, centered Lévy or Poisson process. The pure-jump behavior of the carbon price could be explained by the lower volume of trades on this allowance market (compared to other highly liquid financial markets).

show abstract