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,


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.