 What I will do is outline the valuation framework that is based on fundamentals as I just said. And more precisely, I will propose a dynamic model that relates the price of token to observable statistics, such as the share of tokens held by active users, or the velocity of circulation of these tokens. So why do you think this is interesting? Right now, the practice in the industry is a bit rudimentary in the sense that crypto investors rely on adult pricing formulas that are based on the quantity theory of money. Now, the quantity theory of money is an antiquated approach that has many defaults, and instead we will propose a micro-funded approach based on the token in advanced constraints. Economists will know what I'm talking about for those that are not familiar with the concept. I will explain it in detail in a couple of slides. Now the advantage of the model is that it will endogenize the velocity of circulation of tokens, and so provide a first step towards micro-funded pricing model for the benchmarking and rating of ICO, which is solely lacking at the moment. On each side, we will clarify the condition under which tokens are valuable and the trade-offs of ICO financing. The two main findings are the following. First, if you rely on tokens, you will foster adoption because tokens that we will see lower the opportunity cost of holding reserves. I will explain that in a few slides. And then this is not really new. Some people have already noticed that, but a more original insight of our approach is that tokens during the adoption phase induce excess price volatility. So what we will get from the model, which I think is quite interesting, is that early on you will have a speculative phase where most token will be held by speculator, not user, and on top of that the price of the token will be very volatile. So volatility and low adoption are two of the most often advanced criticism against token. So observers see that this is a market where you have very low adoption, the price goes up and down, and it's often seen as a symptom of excess speculation. And also we cannot rule out that this is true. Indeed, the market for token is very speculative. What is interesting is that these two features also rise in a fully rational model based on fundamentals. So in some sense, our model explained a little bit, I explained what we see in the token market. So in the interest of time, I will skip the relative literature and directly present the model. So our setup is as follows. We have two markets, a good market where token exchange against the platform's output and a financial market where tokens are bought using fiat money. Although token can be used outside blockchain. Okay, so they have been introduced by blockchain because there is this commitment advantage of blockchain where you can commit to the monetary mass of token. In practice, you could introduce token on a centralized platform and Facebook for instance is thinking about that. So we want to think more of a decentralized environment so the output of the platform will be produced by contributors. Think of them as miners, the contributors to the platform, and the supply from contributor will be increasing in the fiat value of the payment. Okay, the contributors they don't really care about the token they care about the value of this token in fiat. So we have this external currency which we call fiat can be, you can think of it as $1. Now what are the users preferences. So I'm talking about people that want to use the platform so to be precise let's take an example, think about Ethereum. So if it's not really a means of payment it's not a cryptocurrency, although it is used as such right now but normally should be at the core it's a utility token because if you want to access Ethereum's computer. So that's the service you want to access some decentralized computing power, then you have to use the first. Okay, so they're really utility token in that respect because you can only use this computer with the ether with that specific token. So now you're a user. And you want, what is the benefits you get from using this decentralized computer. We assume that the preferences of the following form. So you call it graphic of CDI so C is the amount of services that is consumed from the platform and D I is a dummy variable, which in the index the user so that's for user I, and the dummy text value 011. So when D as value zero, and this occurs with probability one minus lambda, you don't want to use the platform you have no use for the services of the platform. On the contrary, with probability lambda D will be equal to one and then you will return, you will get a utility of UC, okay positive utility you will want to access the platform and the utility you see the small you is just the standard utility increasing concave etc. Now what is the timing. Here comes the token in advance aspect of the model. At the beginning of the period, your short D is revealed so at the beginning of the period you know whether you want to use the platform or not let's say you need you have a smart contract on Ethereum and you realize that you're in a state of the world where you want to execute that smart contract. In the middle of the period, you, the, the financial market open and you exchange tokens, and then at t plus one you start again. Now the key thing is that at the beginning of the period when the shock is revealed, if you don't have tokens, you cannot use the service. So that's what we call the token in advance constraint. The only way you can use the service is that if in the middle of the previous period you bought some token and you carry them over to the next period and you have some reasons. It's a strong assumption. It's a strong assumption, but okay. Economist knows this we are used to use that trick to justify why people hold money. Let me explain what what is the problem of the user now. Some notation. These are the token holdings of the user, small m lambda is the probability at which the user will need the service or is the interest rate. U of C is your utility and P is the price of the token in Seattle money so the exchange rate if you want. The utility flow the PT PT plus one of a user is the following. First, the user has to decide how much tokens he wants to buy, and then he will decide how much to consume. So you want to consume only with the probability lambda right because we probably t one minus lambda you don't need the service. The probability lambda you will decide how much you consume. Okay, so as if you could you consume you get to T of C and what is left of your token because M is your reserve. So C div M minus C divided by PT plus one, you can sell again on the financial market so that's the financial return on what you have not consumed out of your token. So if you have not consumed on C, C cannot be higher than MPT plus one, that's really the token in advance constraint you cannot consume more than the fiat value of your reserves. Now with the complementarity probability one minus lambda, you don't consume and you have the financial value of your token MPT plus one, and then you have to subtract the opportunity cost so the interest lost on your token. So in the previous period, instead of buying reserve, you could have play place, place your money on the financial market and earn the interest rate are in other, in other terms, one plus MPT is the carry cost of your results. Okay. Now, remember that. So, one thing you notice is that if you use the token you know exactly how much you need. So that's an assumption we could have met. You have this stochastic so maybe in some case you need a lot of them some you need a little bit of them. There's no randomness in that respect. This simplifies the analysis quite a bit because then what you can show is that the user will only buy the amount of token which it will always sorry it will always consume all the token he has taken in results. So the size of justification on this assumption so in a way it's a strong assumption, but we believe that it capture a few realistic feature of the token market. First, the technology decentralized application and smart contracts often require an immediate reaction immediate access to the con to the smart contract. So for instance of a financial smart contract, then the state of the world happen. If you have not provided your smart contract with tokens, then you won't be able to do the transaction and you will lose the benefit of your smart contract. So usually you have to respond immediately. Okay. Another feature that is supporting or token advance constraint is that maybe you can buy the token on the fly but it turns out that if you do so, you have significant transaction fees. So the exchange rate from Binance where we tried to buy maker token against us dollar with a credit card so that's on the fly nearly nearly automatic. So the exchange rate was 555. Okay, now you can see in the right box that if you spend the exchange rate you only get 0.98 makers, meaning that they charge you an interest rate of 1.5% if you want to buy on the fly. So the interest rate is transaction fees. You prefer to hold reserve in advance by low transaction fee and then use them when you need them. So in the model we take this assumption to the extreme we say you cannot do it on the fly it's too costly and more in between approach will introduce a transaction fee and really endogenize your results. So that being said, let's look at the problem of the agent. So as I said, there is no uncertainty about how much consumption you will need if you need to consume. So what you do is you minimize your token holding so you just buy the quantity of tokens which is equal to the amount of consumption you will need in case you are hit by a positive utility shock. So we can forget about C or set C equal to MP and then the problem is simpler you just maximize your reserve under first you have the utility lambda U then one minus lambda is when you don't use the token and then you have the opportunity cost one plus R. What you see one thing is that M is indexed with respect to T and the price is T plus one because if you remember the timing you choose your reserve in the middle of the previous period. So your reserve are what you bought at T plus one your reserve at T plus one are what you bought at T so empty. Now, if you just take a first order condition you get the law of motion for price. And it's very simple. It is given by two components you have a capital gain so the token might appreciate or depreciate PT plus one minus PT, and then you have a convenience here, which is the utility you get from the token when you consume it. So what is the utility is the marginal utility you prime minus one which is the price everything is multiplied by PT, because the price I mean the, you get as much services as the value in fiat of your tokens. Okay, so this convenience here will be positive so the marginal utility will be higher than one you will have a positive rent when you use the service. And this will incentivize user to all token. So this is the basic structure from upon which we will build. First you can look at the steady state price very easy. So let big M denote the overall mass of tokens so this is the amount of tokens that is supplied by the platform. So typically you make a nice you and you say, I create one billion token, and we will assume that this mass never change over time so there is no monetary creation no token burning. It's a simplification will be very interesting to look at that in future research. And I think this afternoon we have a paper who does just that. So the masses constant this is a strong assumption but by the way it. It is satisfied by several tokens so for instance maker as a constant mass more or less. So in that user index by eye and market clearing holds when the number of token held by user and I is equal to M because user are symmetric right now. And then you get the steady state price. And this expression PR is a steady state price is that money is neutral. So that's the first thing. It's not very surprising. If you create more tokens at the SEO stage, let's say two times more token you just divide the price by two, and you change nothing so it's really a real economy and the monetary mass has no real effects. So now, let me go to the real model. So the fundamental model the one we really want to build. And it's about credit gradual adoption. So what we will see is that you will have a feedback loop between the price of the token and user adoption but for that we need to have some dynamics. So now the utility of consumption also depend on a shifter Z, which capture technological progress. So you can think right now they're trying to move to Ethereum 2.0 that's typically a technological shock suddenly if your own is supposed to become much faster easier to use less delay lower cost so over time your platform gets better and better. Now the shifter we are economists we don't model technology we take it as given, I will assume that technology for the geometric Brownian motion it moves over time randomly. So we can show that the law of motion of price in continuous time. So P dot, which is the expectation of DP, and not divided by pts sorry it's a typo to have corrected it. So it's a bit of abuse of notation but it's coming from, I guess it's self explanatory so P dot is the evolution of our time, you can see that the value function or so the flow utility of users in continuous time as the same form of discrete time so lambda times the utility you get minus the token you lose when you access the service, the capital gain P dot and the opportunity cost minus R. And you can show that the optimal holding of token M star is equal to one divided by P times U prime minus one. Now one interesting thing in this expression is exactly the same as the steady state except for one term P dot divided by P. I don't know how can I note my slide okay. So you see the term P dot divided by P on the right in the last expression. And this is telling you that if the price of the token increase you are you have the incentive to hold more token. It's not surprising now you have this token that give you a service but on top of it maybe it's gaining value over time because more people are adopting the service. So then you have more incentive to hold the token. And so P dot divided by P reduces the carry cost it reduces the opportunity cost of holding reserve. And so it incentivize adoption. Of course if P dot is negative it's exactly the opposite if you expect the token to depreciate, then you will have less of them. Okay. Now, we will have also heterogeneous users so they have different technological proficiency so some users are very good with computers. Maybe some of them at the conference the computer scientists so they have adopted a blockchain a long time ago, and then the economist are very bad so they have a low, low chi. This is a fixed cost and you adopt the service only when your flow utility V is superior to the fixed cost by one divided by chi because the fixed cost is inversely proportional to your proficiency. And so you can show that the user base is there's one minus G time one divided by V so that the number of user at each point in time that uses the service it depends on the level of technology Z and on the evolution of price grow faster, you have more users because they see it as a financial instrument. So now let me get to the main slide and the main insight of the paper. The oppression appreciation rate of token cannot exceed the interest rate. Because if it were to exceed the interest rate, you will have no cost of holding them and so infinite demand. So, token cannot appreciate at a rate faster than this of course it's a risk adjusted right now we are doing everything under a risk neutral measure. So you can show that optimal token holdings and massive user are bonded from above so you have M star is bonded from above by an upper bar and is bonded from above by an upper bar. What does this mean, it means that for every level of productivity, there is a price level P upper bar, such that user demand cannot clear the market when the price is higher than P upper bar. So let's maybe it's easier to understand with a graph. What you can show is that there is, if you plot the price against the productivity, you can show there is an investor regime and a user regime. In the user regime, the token price grows at a rate which is lower than R. In the investor regime, the token price grow at the rest are it cannot grow faster because otherwise you will have infinite demand for it. Okay. So investor regime is a speculative regime where the market is not cleared by user. The point is that very few people are using the token and that the demand is most of the token are held by speculators. I call them investor because I don't want to be polemical but you can think of them as speculators they only all the token for financial gains and never think about using it. In the user regime, it's the opposite. All the token are held by users. Okay. So to repeat, now you have the law of motion of token will depend on whether the marginal order is a user or an investor is a marginal order is a user. You have the same law of motion than before. And you have this term here you prime P and divided by N which is minus one which is the convenience here. Now, people are holding token because they want to use them. And this convenience here, lower the pressure pressure right which is necessary for them to invest in the token. On the other end is the investor regime. People, the marginal holder, never thinks about using the services is just there to speculate so the price has to appreciate at the interest rate. Okay, which is higher than the one in the so the appreciation rate is higher than in the user regime. So now, very quickly, I can replace P dot by using it goes later. So that's the UP prime plus the sigma square divided by two p second for those who are familiar, and I get a differential equation with two regimes. And I can so I skip the detail I really don't have time you can find the two boundary conditions so the price at zero has to be zero because it's an absorbing state and then you have a condition at infinity. So if you have a differential equation, a second order already complicated one non linear and piecewise but still second order already and you have two boundary conditions so you can solve for it. So what we will do. So now I think, how long do I have like 10 minutes. No, no, like three minutes. Okay. Okay, so we calibrated the model on maker. So what you have here is a share of users so the share of people that held the token, but wants to use the services and the price so we are able to calibrate the model the point here as you see is that on average only 10% of token held by user 90% of token held by speculator. So it's difficult to explain but our model can fit that. And what we show is the you see, we have this price that goes from the speculator regime enter the investor regime. The adoption right goes up the velocity is positively correlated with the price. So this is all microfunded. And what you see is that the return. So we are still in the investor regime by the way but when we will get to the user regime if we do eventually the return will drop to the interest rate because they know you have a convenience yield, and the volatility will decrease and that's the main new insight of the model. Why is the volatility decreasing so why do you have high volatility in the speculator regime. It's not a coincidence. So what you show is the price function, you can solve for it in the investor regime is a convex function of the Z time beta with beta spirit one why do you have convexity. If you remember your sense in equality. And it's the same thing with it was later, if you take a convex transformation of a variable, the expected value of the convex transformation is higher than that of the underlying variable. And this is exactly what happened you take the fundamental Z you take a price function with convex and this creates higher return and you need this higher return to incentivize investor to acquire the token. So my point is that volatility is not due to speculation necessarily it's a way to raise the return of the token above its fundamental level. If you take a speculator, find it profitable to all the token. Now the result is that of course, bad news will have a very bad effect and good news we have a very good effects a lot of fluctuation. Okay. And, okay, so let me set two things. First, there is a paper by Kong and I think it will an extension will be present later on Kong and quarter will be present presented later on in that conference which is very related to our model. But we use token in advance they use token is a utility function. Okay, so they don't have a speculator regime that's the main difference. And let me conclude. Sorry for rushing a little bit. So let me conclude so we have a valuation framework that is based on fundamentals. We have a matrix used by investors such as the velocity of circulation of tokens which is commonly used by people in the crypto community but we don't really have a model that explains why it should be important, micro funded model. And then the main new insight I think is that we rationalize the extreme volatility of token during the adoption phase, because this excess volatility is precisely what allows token to have return that is high enough to attract speculators. That's it. Thanks a lot.