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8

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 ...


8

This is in fact a tricky matter. As you say one way is to calculate delta by an analytic formula, i.e. calculate the first derivative of the option pricing formula you are using with respect to the underlying's spot price. The second way is to do it numerically, i.e. change the spot price by a small value $dS$, calculate the value of the option and then ...


4

Working on trigonometric polynomial decomposition, the first step is to take a big look at Fourier transformation. It is very powerfull, well documented and probably well implemented on your favorite language. It will give you the decomposition of your time series. You can remove highest frequencies, which correspond to noise, to have a good estimation.


3

Building upon +Imorin answer, you should have a look specifically at discrete cosine transforms. It's a standard approach when trying to express finite sequences as a sum of cosines. I would start from there, especially as it's implemented in every common language (R, Matlab, Python for starters). Only then evaluate if you need more.


2

It may be the case with certain exotics that greeks are derived analytically through approximations. In that case at certain boundaries you may get different results from such approximation over the numerical approach. Why do you not approach the numerical case similarly than most banks and hedge funds when they "shock" their options books: Simply shift your ...


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

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 ...


1

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 ...


1

I guess that, in your model, the stock does not pay dividends. The price of an European Call option written for a stock that does not pay dividends is always higher than its intrinsic value. Therefore, in that case, Prices of European and American Call options are equal. Note that this is not true for Put options, since Put values are short interest ...


1

$u$ 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 $\sigma_j$ ...


1

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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