odd handling of tensors by blsprice

Hi

I am trying to investigate the shape of the scalar field of the Black Scholes option pricing formula.

In matalb to vary all 5 of the parameters rather than inputing a vector for each parameter, you have to do it by inputting a tesseract.

In the folowing code each tesseract is 12*12*12*12*12

Tess       = ones(12,12,12,12,12);

StockPTess = Tess.*[1:12];
StockPTess = permute(StockPTess,[2,1,3,4,5]);

StrikePTess= Tess.*[1:12];

RateTess   = Tess.*[0.05:0.05:0.6];
RateTess   = permute(RateTess,[1,3,2,4,5]);

TimeTess   = Tess.*[1:12];
TimeTess   = permute(TimeTess,[1,3,4,2,5]);

VolTess    = Tess.*[0.2:0.2:2.4];
VolTess    = permute(VolTess,[1,3,4,5,2]);

Price  = blsprice(StockPTess,StrikePTess,RateTess,TimeTess,VolTess);````

Instead of outputing a 12*12*12*12*12 matrix, this exports a 12*20736 matrix, from the help page i can see no indication of which entries in the matrix correspond to which element of the tesseract that I expected to get out.

Answer 1

[Harry]

After testing this function I found that with the above set up:

columns 1-12 vary with strike price and the strike prices repeat from 13-24 etc

columns 1-12 all correspond to the same intrest rate as do 13-24 - this

pattern repeats until 144; and the cycle begins again at 145

columns 1-144 all correspond to the same duration of option; and so on

columns 1-1728 all correspond to the same volatility

this means that we can reshape the matrix to get the tesseract:

PriceTess =reshape(Price,[12,12,12,12,12]);