All great responses here. But, my question is far more basic. It's not the reason why price fluctuates but how, that I seek an answer for? What is going on under the hood that can show me a price change literally every few seconds for an exchange between any two currencies (crypto/ fiat).

The reason I raise this question is because it's far more difficult to dissect the existing financial system (excluding the recent blockchain market). However, it should be easier to answer such questions for a system that has been written from scratch by only one creator (or maybe a group under the same pseudonym).

So, while all you have given reasons enough to justify the change in price, my question still remains unanswered unfortunately.

In simple language what's yielding price P1 at any time T1 and a P2 at T2? There has to be some place somewhere on this planet that impacts those prices and where it is sourced from? How'll you show the cause and effect to a five year old? In this world where all is mathematical (hashing, ECC etc) I expect an answer far more mathematical which is written somewhere that takes certain input parameters and throws an output consistently which is then sourced by different exchanges that people rely on.

Or is it the leading exchange calculating at their end (in their code) based on the trading volume and that's why not open source? Because, my question presumes that all's open source and there should be clear pointers for these prices P1, P2.. to be derived. They are certainly not popping up magically based on the Economics. Someone has to calculate them somewhere (even when applying all the principles that you have stated)?