Do changes in the frequency of data affect the accuracy of estimation of the trend parameter in a jump diffusion process?
Do changes in the frequency of data affect the accuracy of estimation of the trend parameter in a jump diffusion process?
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Abstract
This paper explores the effect of the frequency of data on the accuracy (measure by variance) of the maximum likelihood estimator (MLE) of the trend parameter μ in a jump-diffusion process à la Press (1967). First, we consider the case without jumps (i.e., the geometric Brownian motion (GBM)) as a benchmark case to show that the frequency of data is irrelevant in this first setting. Then, we consider the case with jumps and highlight that things are different in this second situation. Specifically, the asymptotic variance of the MLE of the trend parameter turns out to be higher compared to the case without jumps. Nevertheless, we also prove that when sampling occurs infinitely often (i.e., high frequency) it is possible to obtain the same accuracy for the MLE of μ as for the GBM, given that for higher frequencies it is easier to “identify” price discontinuities (i.e., jumps) for this model. Mathematical proofs are performed under the assumption that the MLE of μ is estimated given the other parameters, but numerical (Montecarlo) simulations indicate that this is also the case even when all parameters are estimated together.
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