Recently I created a simulation of a GBM. The time between the prices were sampled from an exponential distribution. The log rate of return was sampled from $\sigma \sqrt { { t }_{ i }-{ t }_{ i-1 } } { Z }_{ i }+(\mu -\frac { { \sigma }^{ 2 } }{ 2 } )({ t }_{ i }-{ t }_{ i-1 })$ where ${ Z }_{ i }\sim N(0,1)$.

When I estimated the drift of prices from the simulation without using the time between the prices, I was able to get back the drift I programmed into the simulation.

So I concluded that the time between prices doesn't affect the estimation of parameters of a GBM.

Is this conclusion correct?


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.