How is the price determined for a decentralized currency like bitcoin?

So far, I have got mixed responses from elsewhere including theoretical explanations of supply/ demand, trading bots and on similar lines. But, no answer in simple enough language and with authority that explains the price (thus the volatility) of the cryptocurrencies.

Is this somewhere in the code that takes some input parameters to deterministically reach a price, maybe based on the hashing power, difficulty level etc? Or is it more complex? Can someone please explain the inner workings? My curiosity is only to understand the correlation between cryptocurrencies and the Economics in the absence of a centralized governing/ intervening body.

Furthermore, how do different exchanges reach on the consensus for a price? Is it their own algos determining the price on the fly or is it more like a moderator picking on price with a predetermined fluctuation? Or is it more like how remitters reach to a daily price which is close enough to each other (to allure genuine customers, but not as much for an arbitrage)?