# Tag Info

7

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

C is not used for any particular reason in numerical optimizations other than for legacy reasons. However, there are areas where C is preferred over C++ though even C is not the preferred language of choice. To mind comes programming FPGAs. Though VHDL and Verilog are by far the standards. But "behavioral synthesis" allows to utilize C or C relatives such as ...

4

who told you that ? I am used to create new trade systems in C++ to make the customers requirements feasible. CERN used C++ to prove higgs boson particle. I see people using C to program embedded like microwaves or fridges :D but it is just my opnion, I would like to hear others.

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 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

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 ...

1

I don't know how widely used C is over C++ when it comes to doing numerical optimization; however, if there is a preference towards C it likely comes from the fact that C++ name mangling is not standard making C++ libraries very hard to integrate into other languages and environments. With C you get a well known calling convention making it straightforward ...

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