Thank you for the feedback I've received so far. I'm no professional when it comes to creating models, although I have taken an introductory course in the subject as I found it interesting.

Quote from: bitcoinbitcoin113 on March 20, 2013, 04:30:09 AM

In my opinion it makes more sense to model different scenarios rather than try to include the chance of failure into the value calculation. I get that its an attempt to incorporate that risk into the calculations, but really seems non-intuitive to me. If I understand correctly, the chart you show doesn't represent any outcome you are expecting in reality, the downslope to the right is actually supposed to be due to a chance of 1 btc=0 usd.

Yes, the chart is a bit non-intuitive in that it doesn't represent any actual outcome, but rather the expected output. Perhaps an analogy would help. If someone is selling lottery tickets for 1 BTC each, and the lottery prize is 1 million BTC, then a rational actor would base his decision on whether to buy a lottery ticket based on the expected value of a lottery ticket. If there were 500'000 tickets sold, then the probability p of a ticket being the winning ticket is p=1/500'000. So the expected value is now V = p * 1 million BTC or 2 BTC. So in this case, it is rational to buy lottery tickets since they have an expected value greater than their cost.

The chart is my attempt at doing something similar with bitcoins. The question I'm attempting to answer is essentially this: If I have 1 BTC in my hand right now, how much can I expect it to be worth at some future date. There are two pieces of the model. One models future growth with an exponentially decaying growth rate. The second models some inherent risks of the new technology.

Quote from: Canaanite on March 20, 2013, 09:37:14 AM

You cannot try and put Bitcoin expected growth into a formula yet, Too many unkown parameters and not enough historical information
If you want to estimate future prices in case of success you should compare it to other similar coins of companies

I think you are suggesting modeling bitcoin prices based on stock prices? There is already a model that does this and it's called a biased random walk. You start out at some initial value v0 and then move up or down with probability p0 or p1 respectively. If p0 != p1 then it's biased. This type of model is often used with stock prices and in fact doing a linear regression on stock prices in order to calculate the best fitting line through the stock prices is one example of this. However, from what little I know about computational investing, most stock models would fail to capture the dynamics we have seen in action in the bitcoin market. This was my motivation for coming up with the different model with growth based on a decaying exponential. To be sure it is a gross simplification, and can and should be refined further. I believe there is value in starting simple and evolving complexity.

Quote from: nwbitcoin on March 20, 2013, 09:51:09 AM

This is an exercise in futility! Wink

You can't predict the value of anything unless you have at least some information on what is going to cause that growth.

In the field of modeling, many models are based on knowledge of physical laws which regulate a system. In such cases, one can develop some confidence about the basis for ones models. However, there are other cases where there is little or no knowledge of the physical laws which regulate a system. And in such cases, mathematical models can still be created based on observing the data and coming up with reasonable equations to model the data. There is no doubt that many of these types of models turn out to be failures, but many of them also turn out to be quite accurate and useful. For example, Schelling's Segregation Model or the Standing Ovation Model are simple models that make gross assumptions about individual behaviors that turn out to be quite accurate when applied on an aggregate basis. A more complex yet highly illustrative model that lacks a physical basis for reality and yet is well regarded is the Solow Growth Model.

Quote from: segfault on March 20, 2013, 12:39:28 PM

I'd hope we could project a very rough growth curve given the set inflation rate and available information (difficulty, network peers, transaction volume etc). We don't have an active forward market so getting a real liquid future value is out, but we should at least be able to project with some reasonable confidence levels against the major currencies.

Since we don't have (and probably never will have) an understanding of the many forces driving the price of Bitcoin, I don't see any choice but to make some gross assumptions based on intuition and then see how well models based on these assumptions fit the existing data. One really good example of this can be seen here: http://en.wikipedia.org/wiki/Neoclassical_growth_model Of course they do have the advantage of being able to tune their model based on how well it fits measured economic growth in the real world. We lack historical data in the same domain as Bitcoin against which we could tune our models.

Quote from: qwk on March 20, 2013, 01:03:54 PM

The growth rate can not be expected to simply decline. I expect a slow and steady, almost linear growth rate at the very beginning. After passing a certain tipping point, i'd expect a huge growth to adapt to the "masses" which would eventually fade into a steadily declining growth as you predict it.
So: linear -> exponential -> degressive? Something like that...

Actually, I don't disagree with this. I left off the linear growth rate because I believe we are now in the exponential part of the growth. For the purposes of predicting the future expected value, fitting the past data in the linear growth phase is not necessary as far as I can see.

Quote from: Jason on March 20, 2013, 04:06:19 AM

The risk factors are definitely not constant with time.
The discovery of fatal flaws in the protocol becomes more and more unlikely over time.
The same goes for the ability of national or even multinational efforts to outlaw it.

Your points are well taken, and again I have no significant disagreement. However, I still believe that as a first order approximation, modeling the risk factors as being constant is not too bad. Consider:

In my opinion, the risk of multinational efforts to outlaw bitcoin have not peaked yet. It will have to grow considerably more before it is seen as a clear and present danger to TPTB.
New threats to bitcoin will constantly arise as new technology is invented which could pose a threat (quantum cryptography has already been discussed and while it wouldn't necessarily kill bitcoin, it would require some major changes to be made to the protocol)

Factor these into the equation, and add the caveat that the risk factors are only approximately constant with time. This suggests that this portion of the model may be reasonable for the next few years (with appropriate parameterization), but will become increasingly unreliable beyond that as we are unable to foresee what threats may or may not exist in the future. However, if you have a different model in mind, please share it as I would certainly be interested in it.