I think the problem with the reflecting barrier is located at equation (A.4). Link to paper
(A.4) dZt = (r-q)Yt dt + v Yt dWt + Yt dLt
where Yt is the price of the asset without the barrier, (r-q) are carry terms (q is dividend, r is interest rate), v is vol, dWt is diffusion term, and the process Lt is a ‘reflection function’. dZ is then the change in the asset price with barrier.
Thomas writes “The RGBM process as specified in equation (A.4) is a semimartingale
, because it can be decomposed into a local martingale (the Wiener term) and two finite variation processes, the drift and the reflection.”
But simulation shows that the process is negatively autocorrelated. Can a semimartingale be autocorrelated? Surely not.