The Quantum Price of Bitcoin

By Owain Higham



“All models are wrong, but some are useful.” 

– George E. P. Box



They say Rome wasn’t built in a day, but neither were its maps. Rodolofo Lanciani’s 18m (60ft) wide by 13m (45ft) high marble map took 8 years to create and is so detailed that it’s even possible to see the floor plans of nearly every central bathhouse and temple. Yet even at a scale of approximately 1 to 240, you wouldn’t try to literally go sightseeing across this map—it’s just a representation of the streets and squares of the ancient city. Not to mention that these days it’s not even that useful, being more valuable as a piece of history instead. Ironic, because Lanciani was himself an archeologist of his time. The reality is, if you were roaming the streets today, you would probably use something like Google Maps on your smartphone, armed with its constantly updating reviews of the best coffeehouses and their locations. Why? Because things change and so do our models of them, and money is no exception.


The introduction of cryptocurrencies in 2009 has changed the way we interact with money. Bitcoin’s satoshis (one hundred millionth of a single bitcoin) are essentially the same to the Roman empire’s basic monetary unit ‘Auresus’ as what Google Maps is to Lanciani’s map.


A Quantum Economic Theory of Bitcoin


Valuing our representation of reality with money is even trickier, and almost completely fickle. But being humans, we certainly try, applying numerical values to things all the time. For example, the Mona Lisa is estimated to be worth 50 billion euros. That is the numerical value of our subjective appreciation for that particular piece of artwork. The issue is, prices are just a model of value, and when it comes to money markets, it goes a layer even deeper. A bitcoin futures contract, for instance, is literally money trading money, whether priced bitcoin or US dollars. 


A groundbreaking white paper written in 2020 by University of Oxford mathematician David Orrell compares the valuing mechanism of bitcoin to that of a quantum particle. At first glance, such an idea may seem extravagant to say the least, but it has merit. Due to money’s dualistic nature of precise numbers and abstract value, it shares similar behaviours to electrons with their dual wave nature. When a market participant trades a bitcoin futures contract, their transaction changes the derivative’s available liquidity and shifts the outcome of its price trajectory and future distribution of returns, just as measuring an electron’s position by bouncing photons off it changes its momentum. This is why hedge funds spend billions of dollars trying to calculate the potential market impact of their trading—most of the alpha is in understanding market liquidity and its behaviours.


Approaching The Problem


Bitcoin is already incredibly difficult to price, partly because nobody really knows what it actually is. There is still a lack of consensus as to whether it’s more of a currency or a commodity, never mind an accurate estimate of fair value. Combine that with the fact the asset in question is consistently making new all time highs, and it gets even harder. There is no historical reference point to extrapolate from. These are probably at least some of the reasons why the asset is so volatile.


When it comes to trading, an easy answer to pricing something like bitcoin is to use some form of technical analysis (TA). With the right approach, TA promises a trader the ability to navigate any asset, regardless of their nativity of the fundamentals. The most basic form of TA is support and resistance—lines on a chart where prices previously stalled or reversed. Not a bad start. Such analysis may be able to locate historical areas of supply and demand, but it does little to tell you the statistical probability of those levels having an impact on prices in the future. Making a good decision based on those levels when prices are trading in unmarked territory as the asset makes new highs is even harder, because such levels don’t even exist. Any support and resistance that is visible on the chart will be short-term by definition, and those zones should be given even lower importance weighting. 


To really have confidence in price levels, they need to be based on the thickness of the order book. There’s no need for guesswork when your support and resistance levels are based on the quantity of bids and offers, since you can trust in the fact that they are based on the very numeral building blocks of the financial asset you are observing. 


The mechanics of market microstructure are such that barring the market participants withdrawing their liquidity, the only thing that can change the current price is one or multiple other participants trading all of the available liquidity on the bid or ask and totally consuming it. With Bookmap, you intuitively see these support and resistance levels thanks to the color-coded heatmap, each shade showing how deep the liquidity really is.


Now we have a good basis for identifying areas of supply and demand, but how do we go about successfully trading around these levels? Before we can do that, we have to narrow down the price of what we are looking at.


Consolidating Order Flow


Cryptocurrencies trade on exchanges across the world on a 24/7 basis, and there are countless different products. The futures market has derivatives based on the value of bitcoin, Bitmex’s perpetual futures contract being a good example of this. The contract, which prices bitcoin against the USD, is settled in BTC. It also has its own funding rate, which fluctuates every 8 hours based on the supply and demand of borrowing BTC to long or short the product. All these factors have a large impact on your underlying P/L, since even trying to do something as simple as hedging your BTC exposure at a ratio of 1 means you have to take into account margin exposure, potentially having to reload your account if the exchange rate moves far enough, as well as deciding whether to trade the perpetual or a monthly contract, rolling it over at expiry.


There is also the spot market, where BTC is traded directly for other currencies: some versus fiat, others for crypto tokens. For example, the BTC/USDT pair on Binance is the rate of BTC vs Tether, a stablecoin token that is supposed to be pegged to the value of the USD. But when the other currency the cryptocurrency is paired against is only backed by $0.74 in cash and cash equivalents, the ongoing case could potentially have an asymmetrical impact on the price you see and trade (something about which we have previously written).


A good idea when it comes to trading in this universe would be to narrow things down to a handful of the largest and most important spot pairs and derivative products, and visualize their combined order flow in its entirety. With the release of Bookmap’s new addon Multibook, it is now possible for traders to take multiple different instruments (even from different exchanges) and combine all their liquidity and volume into a single chart. The heatmap will show you the whole picture of cross-exchange liquidity, and the volume delta is truly cumulative. 


Multibook currently comes with defaults for BTC-USD and ETH-USD respectively, and there is nothing stopping you combining spot and futures, since the addon allows you to create your own synthetic instruments. You could watch the pairs with the deepest liquidity but only send orders to the exchange with the lowest fees. Or perhaps if you are worried about slippage, you could trade only on the largest exchanges, even if the order flow trading signal you are basing your entry on is in fact coming from a different pair on a separate exchange identified with Multibook.


Pricing cryptocurrencies is as much of a science as it is an art. When the price of a new monetary technology like bitcoin is so intangible, the next best thing you can do as a trader is make sure the quality of the data you are basing your decisions on is of high quality. The focus should be on liquidity, and Multibook’s can help you intuitively visualize order flow while tuning out the noise; the heatmap perhaps being the closest thing we have to an eternal map (read: model) of value and its constantly changing price.


Everyone is highly encouraged to join Bookmap’s Discord community. Also feel free to open up a discussion on the forum, where you can make suggestions for future tools and where other traders and developers may be able to help with your particular approach.


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