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You got some things wrong: You don't have to devide sd by $\sqrt{n}$, the division is already part of the definition of $sd$. The $t$ distribution has a parameter $\nu$, the degrees of freedom. The variance of a standard $t$ distributed random variable $T$ is $$ VAR(T) = \nu/(\nu-2). $$ Thus you have to define $\sigma = sd * \sqrt{(\nu-2)/\nu}$ and a ...


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It is entirely similar to the Normal Distribution case. In that case you use for example mu minus 1.65 times the daily standard deviation, because 1.65 is the fivepercentile point of the normal distribution (i.e. in Excel NORMSINV(0.05) = -1.65... ). Here it is the same, but instead of -1.65 you use the appropriate five-percentile point for the student t ...


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The best solution is to matrix-price these bonds first. For each bond, either find a comparable bond or use your own judgment to determine the appropriate spread to a benchmark curve (e.g., OAS to LIBOR), then use the daily LIBOR curve and the corresponding OAS to obtain the daily prices.


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Note that \begin{align*} \mathbb{E}\big(L \mid L\geq q_\alpha(L)\big) &= \frac{\mathbb{E}\big(\pmb{1}_{\{L\geq q_\alpha(L)\}} L\big)}{\mathbb{P}\big(L\geq q_\alpha(L) \big)}. \end{align*} The formula follows immediately.



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