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...

We define a new concept termed the activity signature function, which is constructed from discrete observations of a process evolving continuously in time. Under quite general regularity conditions, we derive the asymptotic properties of the function as the sampling frequency increases and show...

We derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an Itô semimartingale over a shrinking time interval. The spot characteristics of the Itô semimartingale are allowed to have dynamics of general form. In particular, their paths can be...