I would like to run a Monte-Carlo simulation for annual cashflows up to 20 years. Cashflows are basically given by multiplying a fixed production amount and end of year price per production amount. In Regards to the price I have got a daily log return time series and I presume that my price process has the dynamics of a Geometric Brownian Motion (constant drift, constant diffusion). The process is calibrated to the historical time series with 255 data points. As the production amount is fixed, I am not going to simulate anything.
Now I am struggeling with the time increment for the Geometric Brownian Motion simulation discretized by a standard Euler Scheme.
- Let's choose
dt_1=1/255, as we calibrated the process to daily price returns. But the point is, that I would like to simulate 20 future annual data points. The result are e.g. 1000 Samples per year until 2038. Each path has the expected form of a GBM. Sample variance per year is low. Nevertheless there is a misfit between the time increment and the time grid of the simulation horizon.
- Let's choose
dt_1=1/20, which corresponds to the time grid of the simulation horizon. Resulting samples seem plausible again, but the sample variance is higher. Again there is a misfit between calibration time increment and the simulation time grid.
Could you clarify which simulation time increment for the Geometric Brownian Motion is right and why.
Thanks in advance,