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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 ...


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 ...


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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