TVaR

[Quafadas]

Here is a problem, that I want to be able to use Vec, Matrix for.

I'm modelling a financial instrument. I have 10,000 potential outcomes for each instrument.

I can write an extension method, to fairly easily calculate the tVar of each instrument, and a portfolio of instruments.

    def tVar(alpha: Double) : Double = {
        val numYears = thisVector.dimension
        val nte= numYears * (1.0-alpha);
        val fte= Math.floor(nte).toInt;
        val sorted = thisVector.sort
        var i = 0
        var tailSum = 0.0;
        while (i < fte) {
            tailSum += sorted(i);
            i += 1;
        }
        tailSum / fte.toDouble;
    }

TVaR has the advantage of being coherent (I think is the right word), which is a fancy way of saying we can decompose it.

Now, I want to find the contribution of each instrument to the tVar of my portfolio.

Inst 1	inst 2	Inst 3	Portfolio
1	2	1	4
2	4	1	7
3	3	0	6
5	6	0	11

In this simple case, the 50% (<--- normally we want a more extreme percentile, like 99%) tVar of the portoflio is 7 + 11 / 2 = 9.

The contribution of the instruments are
Inst 1 = (2 + 5 ) / 2 = 3.5
Inst 2 = (4 + 6) / 5 = 5
Inst 3 = 1 / 2 = 0.5

Currently, I think calculating that decomponsition isn't possible with Vec / martix?

The obvious solution would be to identify the rows of interest by returning a NArray[Boolean] of the rows of interest, extracting out the sub-matrix / vectors... and from there it's easy.

Woudl you welcome a PR which attempted this?

[dragonfly-ai]

I think you're asking about adding support for a kind of 'decomposition' the details of which resemble slicing?

[Quafadas]

Yes - I don't know how to do this reasonably, without some ability to slice or extract some arbitrary subset of a vector / matrix...

If we can agree a design ... I"m happy to put up a PR...

[Quafadas]

Ideas :

type VecIdx[N] = NArray[Boolean]

Then an extension method which extracts that ... perhaps VecIdx could provide the same runtime constant to things it slices. That might get around the followup dimension check problem?

[Quafadas]

To support the discussion. #14

[dragonfly-ai]

I recently wrote tests for thesubMatrix methods, which may interest you:

https://github.com/dragonfly-ai/slash/blob/main/slash/shared/src/main/scala/slash/matrix/Matrix.scala#L332

Also, the most recent release of SLASH, 0.3, added support for MatrixSpace:
https://github.com/dragonfly-ai/slash/blob/main/slash/shared/src/main/scala/slash/matrix/MatrixSpace.scala

The MatrixSpace class consists of two instances of VectorSpace and can be used to consolidate common runtime dimension types in one fixed path.