New answers tagged distribution
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Student's t distribution can be regarded as a Normal distribution with variance mixture Y, where Y follows the inverse gamma distribution (1). So to simulate intraday returns consistent with the daily return having a t distribution, you could first sample from the inverse gamma distribution to determine that day's variance and then simulate a Brownian motion ...
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One way to generate excess kurtosis in your sample is the approach below. It doesn't give you a student-t distributed sample but from your comment I understand that might not be a hard requirement.
A simulation with GARCH where the intraday innovations are inputted into to the GARCH model would give you time varying volatility which appears as excess ...
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You're missing that normality and log-normality of returns and prices are simplifying assumptions. Inspecting skew and kurtosis, it's even more obvious that they're assumptions.
Your example that return going to -100, but exceeding +100 defying the normality assumption is a triviality, particularly given we've already established returns aren't perfectly ...
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