Questions tagged [random-variables]

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Convolution of generalized hyperbolic distribution

I have a question concerning the convolution of generalized hyperbolic distributions. Proposition 6.13 of McNeil, Embrechts, Frey states the following: If $X$ has a $d$-dimensional generalized ...
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Simulate correlated Brownian motions conditioned on future state(s)

Consider a model defined by 2 geometric Brownian motions $$dY_{1}(t) = \sigma_{2} Y_{1}(t)dW_{1}(t)$$ $$dY_{2}(t) = \sigma_{2} Y_{2}(t)dW_{2}(t)$$ with $Y_{1}(0) = y_{1}$, $Y_{2}=y_{2}$ and $dW_{1}(...
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131 views

Process Transforms (Fractional Difference)

Let's say I have a process $X_t$ with unknown variance process $V_t$. Then, I write $\mathrm{EMA}[X_t]$ to be the 5 sec exponential moving average of $X_t$. Consider the transformation $$\sum (X_t-\...
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is it possible to make changes to use the affine property of Normal random variables, rather than the Central Limit Theorem?

I have proven the distribution of a discrete time model, evolving over a uniform mesh with $\delta t = T/L$ is given by $$S(t_{i+1}) = S(t_i) + \mu \delta t S(t_i) + \sigma\sqrt{\delta t}S(t_i)Y_i,$$ ...
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Full Copula View using Meucci's Full Flexible View

I'm currently setting up an "Investment Framework" that should allow the following steps: Investment Committee (IC) has to decide on probabilities for 4 different market states. I have historical ...
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45 views

Equivalent of recovery rate

I'm trying to understand the functioning of "recovery of face-value" approach. Let $V_t$ the fair-value, that is the price that the holder of a defaultable bond must pay for hedging of default of ...
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Can we generate(in high dimension) uniformly distributed variables in a finite volume other than a cube?

I'd like to know if there is in the literature a (computationally cheap) algorithm to generate uniformly distributed variables in high dimension for a volume other than a cube and without using ...