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There are many ways answering this, here is one: We assume the asset price at $t=T$, $S_T = S_{T-1} \times (S_T / S_{T-1})$. Assuming continuous compounding, we can write, $S_T = S_{T-1} \times \exp(R_{T-1})$. Working the same way for the previous period, we get $S_{T} = S_{T-2} \times \exp(R_{T-1}+R_T)$. Working all the way back to the initial value of ...


I don't know if there are any additional issues that arise with using goodness off fit with a piece-wise function. When I have fit generalized pareto distributions to series like financial market returns, I have noticed that it is common to differences between the estimated distribution and observed returns at the cutoff points. This is going to be the main ...

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