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New answers tagged monte-carlo

1

Let's say your return realization for path $i$ is $r_i = \beta\cdot f_i$, where $f_i=(f_{1i}, f_{2i}, f_{3i})$ - factors realizations, and $\beta$ - factor coefficients. So, your VaR is $VaR=percentile(r_i,\alpha)$, where $\alpha$ - confidence. The simplest Monte Carlo stopping criterion is to keep adding paths $i$ and computing VaR on the growing sample ...

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Do $N$ MC simulations of $M$ samples, calculating your estimate of VaR for each one $\{\widehat{VaR}_i\}_{i=1}^N$ and you now have an IID sample! Take the sample (or unbiased) standard deviation for your estimate of VaR (this is probably what you mean by error) $SD(\widehat{VaR})=\sqrt{\frac{1}{N-1} \sum_{i=1}^N (\widehat{VaR}_i - \overline{VaR})^2}$ and of ...

0

This is perhaps not a concrete solution to your problem but the space in the comments is limited :) In your setupt you are not actually pricing an option on a basket but on a dynamically allocated portfolio. Thus conventional pricing and hedging approaches won't apply. Also you are underestimating porfolio optimization algarithms. To find an optimal ...

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A very simple approach could be the following: draw a random number for each day for each stock. If you refer to "average/mean" by return and to "standard deviation/variance" by volatility, you could use these for the distribution parameters of the random numbers per stock. If you dislike that values can go below zero, apply Euler's exponential function on ...

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I would define the weights $w_1,\ldots,w_n$ as whatever number you want and the basket given by $$B_t = \sum_{i=1}^n \frac{w_i}{W}S_t^{(i)}\ , \qquad W = \sum_{i=1}^nw_i$$ so the weights always sum to one. This doesn't make much sense, however, because you are changing the product, not a market variable. This meaning that when the weights change, the ...

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The approach of reflecting is expensive, since the $d$-simplex has $d$ maximal faces, all of which have to be checked for intersection at each step. Additionally, if the random walk moves into a corner, the number of moves which have to be discarded can become very high. Depending on the configuration of the constraints this could well be your best solution. ...

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In fact you can calibrate $\theta(t)$ piecewise constant and $\alpha$ and $\sigma$ to bond prices only. You don't need the swaption prices in mM. If you let $\sigma(t)$ depend on $t$ (this is called the generalized Hull-White model) then you need information about the options market. For the model as you write it you don't necessarily need MC to calculate ...

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