# What is a suitable exponential to model a currency or cryptocurrency price increase?

I would like to model a supply and demand cryptocurrency market, not necessarily for Bitcoin, but for any coin.

My difficulty is that I don't know what exponential factor might be realistic to do so.

For example, I was thinking to pick the exponential factor of e to the power of -10 increase per coin, this happens in case you exchange fiat money for crypto. Same exponential factor applicable for decrease, in case that the reverse transaction is performed.

I searched online, and I can't seem to find a value for this factor, or additionally if it is static or dynamic.

For example, with the above data, if the starting value of a coin is \$300 and someone invests \$300,000 to buy 1,000 coins, the value per coin goes to \$300.0457. But if someones invests \$3,000,000 the value goes to \\$345.7, I am wondering if it is realistic given that the total coin supply is 8 Million for example?

Can someone help and reason about the choices?

• Possible duplicate of Theoretical market capitalisation of a crypto currency? Apr 10, 2018 at 0:49
• No! I am trying to model the price change when someone purchases a high amount so that it can perform an attack, and I want it to be realistic, nothing related to the previous. Apr 10, 2018 at 0:57
• Instead of downvoting, try to answer! Apr 10, 2018 at 0:58
• Ah, see, now, the thing is that the answer to your question is on the duplicate. There is not meaningful inherent value to cryptocurrencies. So your question is, as The Saint321 says, meaningless. Apr 10, 2018 at 1:32

There are assumptions in your thinking that probably are not valid. You are observing exponential growth in the short-run and assuming that the valid model is exponential. There is plenty of theoretical reasons to believe that this is not true.

To give you a real counter-example where your observation would have failed you, you should consider the tulip bulb mania. It began rationally enough. A virus infected tulips in Holland and this caused some tulips to become multicolored rather than monochrome. The multicolored tulips were in short supply because people felt they were pretty. The price of a tulip bulb in Holland at the time would have been less than a current dollar.

This led people to buy out the bulbs because supply is perfectly inelastic in the short run. So people put in advance orders for next year's crop. They received receipts. This state of affairs went on for a few years and then people began trading the receipts. A futures market had developed. Prices grew at an exponential rate because speculators entered into the market. After all, nobody had ever lost money in the tulip bulb market.

By the end of the speculation single bulbs were trading at what would be over a hundred thousand dollars per bulb. Then it stopped. You see a tulip bulb has pretty fixed real world utility. It looks nice, but you can grow more. The same thing is happening in cryptocurrencies. While the approximate number of bitcoins, for example, is nearly perfectly inelastic in the short-run, you can always create a new cryptocurrency. There are now hundreds of them. If a central bank comes out with its own cryptocurrency, it will probably collapse all of the private ones as it will be backed by the state. The state will also have an interest in profit maximizing by exhausting the demand for them. If you are wondering about what happened to the tulip bulb market, well go to a greenhouse and buy one.

Prices are growing exponentially for a variety of reasons. You mentioned one of them, which is well understood. Prices grow or shrink, depending on whether you are buying or selling, exponentially in volume. This is due to the fact that the party making a market in them has to charge the carrying cost of the inventory and so the rate of exponential mark-up is related to the half-life of the position, hence the exponential element.

That is true in the stock market, the bond market and the art market. The carrying time of a position determines its price.

In the long run, the value of a cryptocurrency will be equal to the costs avoided. If using a cryptocurrency allows you to avoid a cost created only when using lawful currencies, then that will determine the value of the cryptocurrency. Some, like Etherium, allow you to engage in self-executing contracts. The value of the currency will be based on the savings of using a credit card to do the same thing minus the inconvenience of having to buy and set up the accounts.

Cryptocurrencies are probably worth a very small amount of money. When the speculators leave, it will be done.

For the volume you are looking at a mark-up or mark-down of exp(m(t)*n) where n is volume and m(t) is the carrying cost adjusted for the half-life of the position. If buying from the market maker you would multiply the price by this factor and if you were selling to the market maker you would divide by this amount.

This number is probably unstable at the moment and won't become stable until the market finally falls apart. It won't be in the collapse that you will get a stable m(t), but rather probably a year later. People make a market in tulip bulbs buying them from growers and selling them to retailers. Their mark-up and mark-down do not look at all like the mark-ups or mark-downs during the mania. I like tulips, but probably won't pay a hundred thousand dollars to buy a bulb.

One final note, money is a dominated asset. It is always the least valuable asset in the system. To understand why, open up your wallet and take out a dollar bill. Is it earning you any interest? Is it causing a car to be produced? Can you eat it? Would you prefer to use it for toilet paper or Charmin?

US money holds its value only because the government requires people to pay their taxes with it. Private money existed before the Civil War and the government ran the competition out. Since you have to pay taxes with it, it would be helpful if it was useful for other purposes. Since everyone has to pay taxes, everyone needs it, although only just enough of it. Most people do not carry all their money wealth with them. They put it in banks. Banks are the sink for all these dominated assets because they sell them through loans to people who need them the most and buy them through deposits to those who have an excess amount.

Since cryptocurrencies cannot be used to pay taxes and there are no deposit or loan relationships present, it is difficult to imagine how much value they could maintain in the long run. Only a handful of private currencies exist in the United States, such as BerkShares. They will hold as much value as possible when people can go to a bank and borrow them to pay for a car. If that doesn't happen, then they will be even more dominated than cash.

• Thank you for your amazing answer and for having no complex to explain thoroughly and in a kind manner. I am a computing engineer who wants to model this as a Proof of Concept, to prove my point I just want a realistic price increase per coin. Can you explain the formula above so I can use it for example? Apr 10, 2018 at 16:38
• I will increase the price by e^-10 but at some point the available supply will be low. Do you have suggestions on how the available supply increase this value dynamically? As for the exponentials, I will use them because they adapt to the properties I want to attach. Apr 10, 2018 at 16:41
• I really cannot help much more because I do not know enough about what you are doing. However, since I have performed validation work on currency trading software before, be aware that it isn't likely that you are trying something successful that hasn't been tried before. Based on the types of questions that you are asking, it sounds like you are missing a lot of math that you would need to produce a successful app. There is only a very restricted set of neural networks that could work and you cannot use a non-Bayesian method either. Apr 11, 2018 at 0:24
• The formula above, for the bid-ask spread, is one possible solution present in the economics literature on liquidity costs. It links time, interest and volume. You may want to rethink this as the failure rate on this type of project by a novice would be very substantial. I gave you one option to consider, but not the universe of options to consider. Depending on your specific goal some parts of the literature would work, but others would not. Apr 11, 2018 at 0:31
• If you are going to continue down this path and you are using a neural network type system, I would urge you to read up on the literature on the validation of non-deterministic systems. If you are going to use a Bayesian method, then you will need to understand the generative process and you don't. Good luck, but this isn't a starter project in currencies. It would be like deciding to build a car from scratch, but it has to be a formula one qualified vehicle. Apr 11, 2018 at 0:34

If I understand correctly you are asking for a model of the price of bitcoin based on the number of transactions.

This is impossible for a number of reasons. 1) Theres not necessarily a relationship between those two variables

2) Even if there is a relationship between the two variables then there may be other variables which have an equal or stronger effect (very likely) making the variable a bad predictor.

3) If there is a relationship, and that relationship is not causal then knowing the relationship would cause it to cease to exist as people begin to trade on arbitrage with that model which would cause it to stop being effective.

4) If I could model the price of bitcoin I certainly wouldn't be telling you, instead I'd be living it up on some private island.

The question makes no sense and is by far too complicated of a question. This is the type of topic that requires a research paper and will not necessarily provide results.

This is why you are getting downvoted. Because there is no logical answer to what you are asking.

• I did not ask for predictions, and just for you information Bitcoin is a very general example, you take DOLLAR if this makes you happy. What I am asking for is what is a reasonable exponential factor as you can see from the example. Apr 10, 2018 at 12:36
• I gave you the total coin supply, the current price, the investment, and I am just asking if it is reasonable. I do not have a background in economics. Apr 10, 2018 at 12:37
• @TheSaint312 "This is impossible for a number of reasons. 1) Theres not necessarily a relationship between those two variables" No, I am talking about the exchange of fiat money to crypto. Apr 10, 2018 at 12:40
• Also, I am writing a python simulator, so don't get offensive with my question and comments, calm down and understand what I am looking for, SOME REALISTIC APPROACH. Apr 10, 2018 at 12:41
• Listen I"m sure whatever you're doing makes sense to you but at least in the way you've described it it sounds like you're asking some general model for the price of bitcoin which is not a reasonable question for SE or really anyone without a large research team. It's cool that you're writing a Python simulator but I have no idea what that has to do with anything. Apr 10, 2018 at 23:08