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7

Not so fast! I think it is of the utmost importance to first examine whether the data points are real outliers, i.e. noise that is contaminating the data, or perhaps the most important pieces of the time series! For example when you look at US stock market data of the last 50 years and remove only the ten biggest moves because they are outliers you get a ...


3

The Papageorgiou paper is presumably referring specifically to quasi-random sequences used in path generation. Researchers had noticed that, in high dimensions, QR sequences tend to have good space coverage for the first couple of dimensions: but terrible coverage for the latter dimensions: (Plots here are points 101-200 from a 32-dimensional QR ...


2

The is many techniques for Outliers Detection. I separate them into Global and Local techniques. -One of the Global techniques I usually use is the Winsorization which consiste on replacing the extremes values on the density distribution by the value corresponding to a certain quantile. For example, you replace all the values bellow the 5% quantile by this ...


2

$u$ is the value of the option, and is in fact a scalar (which, of course, is a function its several underlyings). You're studying a single option on a basket, not a basket of options. As for the two different formulas: you can pick the correct one just by looking at the units of its terms. The rate $r$ is the inverse of a time; each volatility $\sigma_j$ ...


2

It could be much more simple: if you use the method of moments (MM) then you estimate the mean and the variance and for example the kurtosis of your sample. Then you fit the parameters to these statistics. Alternatively you use maximum-likelihood (MLE). For MM: from wikipedia you get the mean and the variance. In your notation you can fit $b = \bar{r}$ so ...


2

You can find a brief but useful explanation of Brownian bridge techniques in Andersen and Piterbarg (page 125), which includes references for further reading. It's probably the best place to start. They discuss valuing barrier options specifically, and discuss the performance issues mentioned here. Later (pg 647), they use Brownian bridges in constructing ...


1

1) Brownian Bridge is used in Quasi Monte Carlo pricing of asian options to reexpress paths in a basis where few selected components/subspaces bring the most contribution, so as to align these to the best distributed dimensions/subspaces of a low discrepancy sequence. This allows for better coverage and thus faster convergence and paths amount reduction. ...


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The word cubature is just a replacement for quadrature in the infinite dimensional setting, such as the Wiener space as in the answer from @TheBridge. The term is used in the context of integrating functionals of stochastic processes $$ E[F(X)] $$ where X is random variable valued in a functional space such as a the solution of a SDE or simply the Brownian ...



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