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2

Something like the following is likely to be acceptable to whoever looks at your VaR methodology. Convert your historical (clean) price to yields of your bond (remember to use the right historical settlement date). I think for this exercise you can get away with ignoring the convexity and also ignoring the accrued, cost of financing, and other P&L due ...


3

Commonly, we employ the Euler scheme for $\Delta\ln(S_t)$, not for $\Delta S_t$. Let us specify the jump part as $$ S_{t+}=S_{t}J\Rightarrow dS_t=S_t(J-1) $$ where $J$ is a strictly positive random variable. (NB: Under Merton we would have $\ln(J)\sim N(\mu_J,\sigma_J^2)$ and $\mathrm{E}(J)=e^{\mu_J+\frac{1}{2}\sigma_J^2}$) And for the solution scheme we ...


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A Lévy process is defined as (Lévy process and Stochastic Calculus, David Applebaum): Suppose that we are given a probability space $(\Omega, \mathcal{F}, P)$. A Lévy process $X = (X (t), t \geq 0)$ taking values in $\mathbb{R}^d$ is essentially a stochastic process having stationary and independent increments; we always assume that $X (0) = 0$ with ...


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The replicate function works best when you fully define your discretization scheme within a function. Then you can simply replicate the function-call x amount of times. Also, try and keep code duplication to a minimum and improve your general syntax. This will help you and your peers that might need to review and/or change your code in the future. ...


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