Hi all, I have implemented a GARCH-EVT with t-copula model for running my montecarlo simulation, and I was wondering if there is a model or at least some leads to also simulate daily high and low at the same time ? Many thanks
yes, you can implement the brownian bridge to get simulated intra-day levels... now, the real question is - what exactly are you trying to do?
Excessive! And requires estimating parameters at a higher frequency than his garch estimate. Easier to just fit a t distro on high and low conditional on log return and log retuirn ^ 2. Use an ML fit and then just draw from those fitted distros. Should be adequate. What he is trying to do, clearly, is simulate market prices, duplicating the stylized facts of the market distro intact, but having no mutual information with his predictors.
Emilio, thanks for that but I am not sure I get you right. Do you suggest that I regress high and low with multifactor daily log returns and log variance using a MLE approach, then calibrate a t-distribution on the error terms, and draw my results from that? Sle, Brownian bridge could be a solution, but very demanding in terms of computations for thousands of simulations. Besides, I am not really comfortable using a Wiener process and unconditional variance (especially for higher frequency data). I could obviously use another GARCH-EVT model to create the bridge, but as Emilio points out, I would need to estimate my GARCH parameters at a higher frequency, but: "a GARCH model that is estimated on high-frequency data does not predict lower-frequency volatility well" (Alexander, 2001). Reference: Alexande, C. (2001) "Market Models: A Guide To Financial Analysis" UK: Wiley
Emilio, thanks for that but I am not sure I get you right. Do you suggest that I regress high and low with multifactor daily log returns and log variance using a MLE approach, then calibrate a t-distribution on the error terms, and draw my results from that? Sle, Brownian bridge could be a solution, but very demanding in terms of computational needs for thousands of simulations. Besides, I am not really comfortable using a Wiener process and unconditional variance (especially for higher frequency data). I could obviously use another GARCH-EVT model to create the bridge, but as Emilio points out, I would need to estimate my GARCH parameters at a higher frequency, but: "a GARCH model that is estimated on high-frequency data does not predict lower-frequency volatility well" (Alexander, 2001). Reference: Alexande, C. (2001) "Market Models: A Guide To Financial Analysis" UK: Wiley