this question is actually related to set the stop loss and stop return. Say after a liquidity shock, I want to place two stops, one being stop loss and another being stop return. If I use, say 10 seconds return for the next one minute to collect historical data, I am pretty sure the return is not iid, most likely serial correlated.

If return is iid, I believe I can simulate 6 step price using monte carlo simulation to find return expectation for different stop loss and stop return pair.

But in this case, it is not iid, what is the approach to find the return expectatoin based on historical data, when the expectation is like barrier option that is path dependent?

  • $\begingroup$ You need to fit a time series model that incorporates your estimated autocorrelation profile. Then the monte carlo will simulate the path using iid variables for the innovations at each timestamp $\endgroup$ – Ezy Nov 20 '18 at 11:13
  • $\begingroup$ @Ezy that sounds reasonable, is there any paper or link i can refer? $\endgroup$ – tesla1060 Nov 20 '18 at 11:24
  • $\begingroup$ The standard read on this is g.co/kgs/dYQeWn $\endgroup$ – Ezy Nov 20 '18 at 11:26
  • $\begingroup$ @Ezy thanks, will read up to build better fundamental understandings. $\endgroup$ – tesla1060 Nov 21 '18 at 1:48
  • $\begingroup$ You might want to give a look at the Filtered Historical Simulation technique, that is, remove autocorrelation and heteroskedasticity, shuffle innovations, then simulate autocorrelated and heteroskedastic returns. $\endgroup$ – Lisa Ann Apr 18 '19 at 7:32

perhaps you can fit the historical return data into best-fit statistical profile; such as beta, lognormal, or even specifying the 4-moments for the distribution directly.

You can then generate a monte-carlo run where the sample draws from a 4-moment distribution (by 4-moment, I refer to specifying the mean, variance, skew, and kurtosis directly).

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