 But let's return to the academic session and look at research in the field of payments. The logistics are the same as for the entire conference, i.e. 30 minutes for the presenter, 10 minutes for the discussant and 5 minutes Q&A afterwards. If you have questions, please kindly put them in the chat. Hence, let's move straight to the session. There is an important link between payments and money markets as safe and efficient operation of payment systems has a strong bearing on the smooth implementation of monetary policy and respective money market conditions. This is not only applied for traditional payments, but also innovative endeavors in that field. I'm therefore very happy that we will cover both fields in this session. The first paper analyzes tools to stabilize the exchange rate between stablecoins and fiat currencies. And the second paper analyzes payment behavior in the Federal Reserve's RDGS system in an area of ample reserve. So without any ado, I would like to warmly welcome Ye Li, who will present the paper on money creation in a decentralized finance, a dynamic model of stablecoins and crypto shadow banking. Ye Li is assistant professor of finance at Ohio State University Fisher College of Business. The discussant afterwards will be Jean-Charles Roger, professor of banking at Geneva School of Economics and Management and senior chair at the Swiss Finance Institute. Hans, I would like to immediately hand over to Ye Li for your presentation. Please. All right. So I guess I have 30 minutes. And okay, it's a joint work with Simon Mayer. Simon is now doing his post-all at Booth and he will be joining ASHAC Paris next year. So I'm very grateful for the organizers to include this paper in the program. So far, I have been learning a lot. I myself not only work on microfinance, fintech, but also on the payment system areas. So this paper is really about dynamic model of stablecoin. We want to describe what are the optimal strategies of a stablecoin issuer. And through the lens of the model, we want to talk about optimal regulation. And also we want to utilize this model to think about the incentives behind these stablecoin initiatives led by global networks like Facebook, JPMorgan, et cetera. So it's a very ambitious project. We try to do a lot. Hopefully I can get through a lot of results. And in this space, actually, we don't have a lot of papers to save some time. I didn't include a literature review in this presentation, but in our paper, we did try to cover all related papers. So let me motivate the study a little bit because here we are digressing a little bit away from the traditional system of payment. We all know that there is a blockchain-based financial architecture that is emerging. It includes banking, brokerage, exchanges, basically try to build an alternative financial system that can facilitate the transfer of value in the crypto space. And we know that any financial system needs some SIPA asset. And in the crypto world, basically we need it for two main purposes at this moment. There is a significant amount of portfolio rebalancing activities between stablecoin and the rest of the volatile crypto. And also the owners of crypto often they pledge their crypto assets as collateral to borrow stablecoins for payments. They may use these stablecoins to buy other crypto further leveraging up their exposure, or they may use these stablecoins to buy services and NFT, things that they like. All right. So it's a booming space, but we really don't have a good understanding of the strategies deployed by the stablecoin issuers. What are the key issues? And first for most, can these stablecoins maintain a relatively stable exchange rate with respect to the reference currencies? And the key issue involving stablecoin management is the management of reserves. Therefore, as I present the model, you will see a lot of similarities between our model and the models of corporate liquidity management, but different from corporate liquidity management. Here the stablecoin issuers liabilities, those are the stablecoins, they can debase. It's almost like a country can inflate a way to modify, so on both their currencies. So it's different, it's related to corporate liquidity management problem, but it's different. And also regarding the debasement, the fact that the debt holders, the stablecoin holders, they basically can do some risk sharing with the issuers, you may think of COCO, but it's different because this stablecoin debasement is not predefined. There are not any trigger events. It's quite arbitrary. It happens exposed often to the interest of the stablecoin issuer, so we are going to characterize all that. All right, so just to give you a basic sense, which are the major stablecoins on the market, this is the graph underneath here. And you can see that the run-up of stablecoin issuers quite mirror the run-up of both crypto lending and the growth of decentralized exchanges. Those are the top two panels. As I said before, when you develop a new financial system, I mean, it's not like new conceptually, it's just based on blockchain, based on decentralized ledgers. This new system needs some SIP assets. There are papers, for example, from Gary Gordon and co-authors, arguing that the SIP assets share in a financial system relatively stable. We probably see something similar here as the whole DeFi space grows, the stablecoin volume, the total issuances just go up. So what are the research questions? As I said before, if you read all these articles scattered here and there, you'll see there are a variety of strategies deployed by stablecoin issuers. They do open market operations. For example, they pull the dollar assets and they use that to trade against the stablecoin the issuer so that the stablecoin price is pegged at $1. Typical thing that you see, for example, in the foreign exchange market intervention. And then they also sometimes charge the stablecoin users some collateral requirements, some margin requirements that serve as the first line of defense. And of course, the second and last line of defense will be the reserves held by the issuer themselves. And then the stablecoin issuers often charge fees on the users and maybe give them some subsidies because there's a network effect. If there are more people use these stablecoins, this will still be in further adoption. So maybe fees can turn into subsidies. Something we also want to capture. There are also repagging activities. Basically, the stablecoin is pegged at $1 per share. And then it is just $2.5 per share after some debasement period. We're also going to try to rationalize this phenomenon. And then there's the issuance of secondary units, which we will interpret as the equity issuance of the stablecoin issuer. I'm going to elaborate more on that later. It was the point of issuance secondary units. So on the theoretical front, what we characterize is really a form of organic instability here. So basically, this fixed exchange rate with the reference currency can last for a long time without any enough instability. But once the debasement starts, there is a slippery slope and the debasement can last for quite a long time. So there's a bimodal distribution of the states of the world here. Some key ingredients that contribute to this behavior is the first and foremost. But on the money demand side, the stablecoin issues, they really value safety. You can motivate the safety preference from the version to information sensitivity because as we all know, if you want to create some asset that can circulate, this asset better deter information acquisition so that transaction counterparties do not have asymmetric information. They do not have this concern over being adversely selected. So we write a continuous time model that will help us to characterize fully the dynamics, especially the back model distribution of states. There are some earlier works in this area. Professor Roche also has a paper, I think it's dated 2013, sorry for the title. So, I mean, if you think about it, it's not just a theoretical exercise. The first voting point here we think is very practical because we rationalize these strategies. We show you how to optimally implement it. It's very helpful for the practitioners. And right now, Sam and I, sometimes we get some requests from the practitioners asking us how to implement these ideas practically. But also here, this key theory of insight is a goal against stability is also very useful because, as you will see, all this can help us predict debasement and the recovery of a stablecoin back to the pack. We are going to talk about more applications in regulation and also why large platforms like Facebook want to issue stablecoin and whether they can successfully maintain the stability of their stablecoin. We're going to focus on over collateralized stablecoin. There is one motivation is the recent proposal in the U.S. Congress that basically tried to auto-law on the collateralized stablecoin. And another reason is that there are some recent events. I'm not going to see specific crypto names. There are several of them. But on the collateralized stablecoins, of course, they're subject to rents and there have been some disasters. Famous people like Mark Cuban lost a lot of money in that. And I think there are tremendous thoughts on undercollateralized stablecoins. So our focus is on overcollateralized ones. And we think we are the first paper that can really provide a uniform theoretical framework to address all the issues on this slide. All right. So you can think about stablecoin issuance as a form of shadow banking. Very simple. I'm going to present a simple model in panel eight here. So basically the holders of the secondary units, also called governance tokens, they act as a junior share, the active share, they will take the loss if the reserve asset declines in value. But also there are fancier, more complicated structure. Basically the stablecoin issuer requires the users to maintain some collateral and maintain a margin requirement that can buffer the first loss. But if the loss is too large, then it is up for the platform to bear the loss. All right. So we are going to, today I don't have time to show you how to extend the basic framework to incorporate this more complicated structure. But it is in the paper. Hopefully I get some time to talk about the results regarding the dynamic optimal margin requirement. All right. But the focus is on panel eight here in terms of the model structure. So a key object is going to be the endogenous token price, a token meaning the stablecoin. So just, you know, it's a shorter word just to save much more time. The price of equilibrium price, PT is going to follow the diffusion process. The shock, the ZT, the standard browning shock, I'm going to introduce on the next slide. But in equilibrium, the drift and diffusion, mu and sigma of the price process is going to be indulgence that they determine. Of course it depends on the open market operations. There will be a unit mass of risk neutral representative users of the stablecoin, if you look at what they want to maximize, DT after DT, right? The last term is very simple. They want to maximize the access return, right? There are both, it's growing on the rate of R and they want higher access return in the back. But the first three terms, I'm going to explain a little bit here. The first term within the first three term, what we call the transaction utility, is really a modern utility specification. It's a textbook treatment. You have the real balance UIT in the utility function and UIT is the dollar value of the stablecoin, not the nominal units, the dollar value. And to capture the network effect, which showed up, for example, in studies of multi-sided network and also monetary economics and social interaction, we have this NT, which is basically the integral of UIT over I's, the aggregate dollar value of the stablecoin holdings. This NT also comes into the specification, so that when we change the parameter alpha, we basically adjust the degree of network effects of this payment system. And this A parameter just represents the quality or productivity of this payment system, how good it is. Later on, we are going to endogenize it in an extension that will speak to why the platform want to build a stablecoin payment system and how they can accumulate transaction data and improve this later, much later. And the second term is just the fees, the old substates in case FT is negative, the stablecoin issues charges the users. And the last term is the safety preference. So if you look at this system here, the innovation of information is really the browning shock. And the loading of the token price on the browning shock is really what we call the information sensitivity. Whether it's a positive loading or negative loading, it's not something that money demands I would like. They want safety and that's how we model it. The absolute value will enter into the utility, sigma p and multiplied by the safety preference parameter eta. They enter there negatively. And that is basically how we model the safe asset demand. All right. So what about the stablecoin issues? We talk about the users, the issues, the management reserve. And here, let me clarify this. NT is really the integral, the aggregate demand equilibrium is equal to the dollar value of the aggregate supply, ST being the supply and PT being the dollar price of the token. We want PT to be pegged at one. That's what we want. But we will show you the basement patterns. So under a constant money velocity, of course, there's a strong assumption some blockchain protocols fit this description. Some do not. But if you adopt this assumption, then the transaction volume and the total dollar holdings of stablecoin NT are proportional. So we impose a maximum throughput NT. There are revenue sources. The reserve will earn a yield and also the platform can earn some trading profits through open market operations. By changing the supply, right, the ST. The ST can be positive, issuing more stablecoins. The ST can be negative, buying back stablecoins and burn them, send them to a retrievable address, basically destroy them. And then there is some shock to the reserve data. The shock is proportional to the outstanding amount of stablecoin. I can think about this as related to cyber attack operational risk in general, but also there can be shocks to the reserve assay itself. Later on, we remember panel A, panel B. So later on, we extend the model, assuming the users also have to post collateral, then the shock will originate from the collateral value that users post. And the risk exposure will be endogenized. Here it's exogenous, it's sigma, right? Later on, when we extend the model, the risk exposure will be dependent on optimal margin requirement. So I think I've already spent 15 minutes here. I'm going to speed up a little bit. I'm going to selectively talk about some results. All right, but let's finish the model setup first. We also have the fee revenues entering into the reserve evolution. And also the reserves can be reduced if the platform or the issuer decides to pay the owners of the governance tokens. Remember, they are literally the equity owners. They are almost like the shareholders of this platform. And if you pay out dividend, of course, you are going to reduce the reserves. And issuer will want to maximize basically the shareholders value, the value of governance token. Of course, this will be the value function here that we later saw. We think our paper also provided the valuation framework for governance token because the value function is really just the present value of all the payouts to the governance token holders. And we allow this dividend process to be any process. We are going to characterize the optimal design. Right now, in the stable coin space, the design of governance token payout is very arbitrary. But here, we are going to talk about what is the optimal design. So we are going to characterize a mark for me in PDEBRA. And this PDEBRA will have the access reserves as the state variable. So access reserve is the reserve minus the dollar value of the stable coin liabilities. And our focus over collateralization basically suggests that once CT, the access reserve falls to the arrow, that's when the issuer does not have more reserves than outstanding stable coin liabilities, that's when liquidation happens. We can allow C to go negative. But as you know, once C goes negative, then all this issue of coordination, failure, and bankruptcy come back into picture, and this just confounds the model mechanism. So our focus on over collateralization is not only motivated by recent regulatory development and recent events, but also we want to keep a relatively clear theoretical framework. All right. So because it's a Mark Pauling's problem, right? And the only state variable is access reserve. All the indulgence variables will be a function of that, including the token price or the exchange rate. A key question is to what extent it is stable, right? But before I dive into the results, one important insight from this paper is that, well, if reserve is the key state variable here, it's better for the issuers to disclose their reserves. And right now there's a huge debate, especially surrounding Tether, what is the value of their reserves? They claim that they invest a lot of their reserve portfolio into high-quality bonds who issue those bonds. Nobody knows. And right now there are some new stable coin initiative that try to work with a chain link, which is a blockchain overcall system to try to basically bring offline audited information on reserve value onto the blockchains so that people can actually make decisions regarding the stable points based on the audited and the blockchain-based reserve value. So we do some see some development kind of consistent with our model focus on reserve and striving a lot of things here. As I said before, the value function is basically the present value of future payout to governance token holders. And the HGP equation was so big, I don't have time to talk about the boundary conditions, but it's guaranteed by the optimality of choosing the payout boundary. Of course, it's the upper bar, right? That's when the reserves are bonded and that's when you start to pay the governance token holders. Of course, when the reserves are low, you want to survive, right? You are not going to pay out. All right. So the value function takes this particular form. So basically within this governance upper bound defined by the optimal payout, the marginal value of reserve is larger than one. Here, we basically assume there's liquidation once you see history of the arrow, right? You can think about this as an extreme financial distress scenario. It's a dynamic continuous time model. So at any point in time, the marginal value of C taking to consideration all the future passes and a lot of passes leads to the liquidation region. So marginal value of reserve larger than one really suggests a strong incentive to do precautionary saving. And only at the payout boundary, that's when the marginal value of reserve is equal to one, meaning that $1 inside of the HGP balance sheet and $1 paid outside doesn't make any difference. That's when the precautionary saving motive is shut down. All right. So you can category the model. You can fix some parameters to reflect some particular blockchain protocol. And then basically the model will give you a reserve contingent valuation of the governance tokens. So what about the key question of debasement versus pack, right? So we prove that there exists a C delta marketed by this dashed line here. And if the excess reserve is below this value, then that's when you have debasement. And the lower the reserve gas, the more information sensitive, the more volatility the token price has. And also there's a slippery slope of debasement. So basically as C declines, the first derivative will decline even further. Okay. I'm going to show this on the very next slide. But once the excess reserve is above this C delta threshold, that's when you see perfect stability. So the key mechanism is that we have almost a sufficient statistic based on the value function here. You can think about this as the value function based risk version code on code risk conversion parameter. Remember in the objective function, right, the shareholders or the governance token holders, they are risk neutral. But because of the threat of liquidation, financial distress, then you have indulgence risk aversion. And that is declining in the amount of financial slack, meaning the excess reserve. So that's what really driving things here. So I talk about the slippery slope of debasement. Here is the panel B, right? So as the reserve level goes down, you say you can maintain a stable value initially, but then it just collapse. And what is driving that? So now let's think about open market operation and the transaction volume or the total demand in total value of this stable coin. So below the C delta, that is the threshold between stability and instability. Below it, you basically have the transaction volume at the minimum level. You can think about this as the demand for the stable coin that is so unique, only this platform can satisfy. You can set this parameter to a very low level, meaning that there's nothing special about this particular stable point. You can set it to be very high, meaning that this stable point is really different from the rest. And you have to use it basically. Well, and another interesting thing here is that below the C delta, in the instability region, the lower the reserve goes, you can see the more tokens the stable coin issuers they will create, right? So this inevitably will crash the price because as the reserve decline from right to the left, the price already declines. And the demand in panel A declines, but fixed at the lowest level here as a matter of fact, the supply increases. So basically in this case, the stable coin issuer really tried to desperately earn some dollar revenues by issuing more stable coins. But once we pass the critical threshold, then that's when we see the open market operation flip the sign, right? Here, you will issue more stable coins if the reserve accumulates, right? Below the threshold, you issue more when the reserve is being depleted. And of course, once you pass the threshold, the dollar demand for stable coin will increase gradually until the throughput threshold is reached. So I have some results on the fees, but just to summarize in one sentence, the fees much higher in the low C region, and it can turn negative into a subsidy when C is verified, especially near the payout boundary when the issuers, when the stable coin issuer fails, there are already abundant reserves. So if you look at these graphs, right, what we all want to do is to basically tell the practitioners, look at your reserve balance. And here in panel C is the optimal strategy of open market operation. And in panel A, you should have a better understanding of the demand of your stable coins. Of course, you need to calibrate the parameters to a particular protocols. But this is kind of the dynamics we are looking at. And the slippery slope of debasement is quite realistic if you look at the recent debasement events. Just to give you a basic sense, some simulation, of course, this is one task of the system. But you can say that if we give the excess reserve some shocks, some of the shocks will be reflected in the token price. It's also the redemption value because the PT is not only the exchange rate in the secondary market, we also allow the user to redeem dollars from the stable coin issuers. So basically, this gives you the sense of this bimodal distribution, right? The system can buffer a lot of shocks, maintaining a stable exchange rate in panel B here. But if there is a sequence of bad shocks, and then the system cannot collapse. So the bimodal distribution really driven by these feedback effects in the low reserve states, debasement basically implies this information sensitivity of stable coins, this volatility which depressed token demand. And this basically generates lower transaction value and fee revenues that basically allow the stable coin issuer to accumulate reserve very slowly. A slow accumulation of reserves contribute further to the debasement. But in the high reserve state, you have quite the opposite, the virtuous cycle. And then that's why we see the system spend a lot of time in the stability region, but also a lot of time in the stability region, where the governance token holders actually get to pay quite often. But then if you look at the distribution of the exchange rate is at one almost all the time, but then you have a very long left tail based on our simulation. And that is because of the instability region really showed up with a large probability over the long run. All right, so just briefly talk about the issues of governance tokens. What are the things that practitioners need to remember? So first of all, if you have some issues cost, basically when you issue governance tokens, what you do you reach out to the crawl dispersed investors, or maybe you talk to the venture capital investors, you tell them that I have a very good stable point system is a very good payment system in the enabling a lot of things like smart contracting, automatic execution of contracts and stable points around. But right now I have a debasement event. Can I recapitalize? Can I issue some governance tokens to you? In such negotiations, I personally got involved in some of them is very arbitrary. Okay, so clearly there's a cost of issuance. And if you want to avoid that, maybe you just wait until the reserve almost deplete and then you can reach out. This is implication of the model. But once you raise this equity money by issuing governance tokens, there will be a jump predicted by the model in the token price. You don't want to jump in the price because this will basically imply a predictable arbitrage opportunity in the token market. What you can do is that when you raise, when you issue governance tokens, you also issue most stable points simultaneously to mute the jump in the price, do not leave money on the table. But because you do not allow the price to jump, add issuance, add recapitalization, right? So what do you do? You basically repack the token price, add the pre issuance price. So every time you do the issuance of governance tokens, the exchange rate should be repacked downward basically. All right, so what about optimal regulation? Of course, if you set a C lower bar, it's a requirement on the regulator side arguing that the stable coin issuer has to maintain high enough level of access reserves, right? Of course, this will hurt the stable coin issuance in panel B here. It will benefit the users in panel C, and we can have the aggregate inverse U-shaped total welfare, and we can pick the optimal regulation based on this curve. All right, so it's never optimal to assume derelict debasement for the stable coin because risk sharing between the stable coin issuance and the stable coin users can be efficient because even if the users they are averse to volatilities of their stable coins, but if a significant debasement even happens and the stable coin value is expected to recover, they can also earn some expected return by sharing, absorbing this risk from the issuance. So this paper does not suggest regulating stable coin as deposits. All right, so we extend the model to incorporate the optimal margin requirement on the users. So basically user puts collateral first line of defense, and then all the reserve management mechanism we talked about before will be the second line of defense. Intuitively, the margin requirement will decline in the platform's own holding of reserves. So what about the platforms? When they issue stable coins, why major incentives to build a better payment system? And a payment system gathers data, so we extend our model to talk about this incentive. As data accumulates, the platform of course can improve. Through what? For example, targeted personalized advertisement, once you observe payment flow, you can analyze the creditworthiness of the platform users and maybe you can extend some loans. So all this will point to user engagement and revenue enhancement. So there is a virtual cycle between building a stable coin, generating data, data have the platform to grow better. We have all this formalized in the paper, but I'm not going to show any equations here. However, we point out there's attention here because you want to stimulate more transactions, right? You want to stimulate more data acquisition. This suggests that you lower the fees and you can give subsidies. But if you lower the fees, then this is for the accumulation of reserves. These two forces really act against each other. I'm going to skip to this graph. So this copper parameter in the model is really about how fast data accumulates and translates into revenue generating capacity. So if from left to right, we basically have the big data technology improving over time. So what's the prediction here? I want you to focus on panel B and panel D. So as data becomes more valuable, the platform wants to lower fees and to stimulate more user activities. But this actually reduces the reserves and then this basically leads to a higher probability of debasement. All right. And the lower probability of stability basically. So another concern is that if the big data technology becomes more efficient, what about the speed of welfare between users and the stable coin issues? Well, the stable coin issue is an increasing share of the total welfare. The model suggests no, because there are two forces. On the one hand, the higher, the more data accumulated by the platform, the platform basically increases monopoly power. The parameter A here, now being in darkness, is really capturing how unique the stable coin system is, how the users can only do something to gain this transaction utility in this system. But on the other hand, there's network externality. So the platform does have incentive to give users some profits back to stimulate adoption because individual users do not internalize the positive externality of them adopting the stable coin. All right. So these two forces basically give you a relatively stable split of welfare. So we draw the analogy between stable coin and the traditional shell banking and we characterize this organic instability by model system. And in the process, we also want to rationalize all these strategies and want to provide this reserve contingent optimal implementation of these strategies. And the key, of course, is to disclose your reserve so that all the market participants can form rational expectation as in the model about what you do and where the price will go. So should the digital platforms like Facebook issues stable coins, I didn't have time to show this result. But if you increase this ARPA parameter, the network effect, it will bring some stability. We think, well, platforms like Facebook, they have much stronger network effect because they have a lot of user activities that are going on. It's a social platform. But on the other hand, this data acquisition incentive really destabilizes the price because really you want to subsidize the users and this during the reserves. So there's kind of a dilemma here, right? This stable coins built to acquire data becomes unstable due to the incentive of data acquisition. We talk about optimal capital requirement and we do some comparative aesthetics with all these parameters. I really look forward to Professor Roche's discussion. I haven't seen him for quite a while since the pandemic. I want to really thank the organizers for inviting him to discuss the paper. Thank you. Thank you very much. And this is indeed a perfect handover. So let me just give the floor to Jean-Charles Roche for his comments. Thank you very much to the organizers to give me the opportunity to discuss this very interesting paper by Jely and Simon Meyer. It's really a topical issue and I really enjoyed reading the paper. The motivation is clear. I believe that we all know that stable coins are private alternatives to official currencies and they are attracting more and more users. The transaction volumes increase and also the big platforms, the internet giant like Facebook, are trying to leverage their huge user networks to offer such private currencies. So we need a unified framework to analyze the impact of stable coins and social welfare and this may provide useful policy guidance for regulatory interventions. So this paper is particularly welcome and it's also very ambitious. It's using a very sophisticated technology in particular continuous time modeling where you have a crypto shadow bank. I like the title which has many of the hot worlds in it and so it's very attractive because it mixes many important issues. So imagine that you want to start a stable coin. So what would you do? Basically you would invest some of your own wealth, your equity and then you would attract users by offering liquidity services and of course you would invest the deposit into reserves because you want the stability. It's not Bitcoin, it's a stable coin so you want to guarantee some stability to your users. However, you still have shocks on your net revenues and so you want to control basically the exchange rate between the stable coin and say the US dollar. So it's not pretty stable in the sense that the exchange rate may vary a little bit but it's better than a complete uncertainty like in the case of the Bitcoin. So the interesting thing here, one interesting dimension of this paper is that it introduces explicitly network effect in the sense that users utility increases with the number of stable coins in circulation. And so it's a beautiful academic exercise where you mix those cash management models in continuous time with network models or platform models to cited markets and Simon and Yelin optimize the character as the optimum policy of a monopoly platform. Let's say where you character of several dimensions, you have the price, you have the issues policies, you have the volatility policy etc etc. And they find that the policies are not optimal and so therefore there's a room for policy interventions and they consider different types of regulation in particular capital requirements, volatility, constraint etc. And on top of that they are giving us interesting bonuses that is they also look at an alternative business model where the users are supposed to post collateral and they also touch upon the difficult issue of big data, the role of platforms in issuing these monies in order to collect data about the users and to use this data to sell it. So it's a very interesting extension. So in my opinion this is a very rich and ambitious paper on a topical issue basically should stable coins be regulated and how it's very elegant modeling. It introduces network effects into a continuous time model of banking. We have very sophisticated solution techniques and interesting results. So basically the main results are as follows that is you have an optimal strategy of the platform which has several dimensions first of all over collateralization. You don't want the platform or the stable coin to default. So you always keep positive reserves. However the stable exchange rate is only guaranteed when excess reserves exceed a certain target and so there are two targets. In fact they have the stable exchange rate target and also a second target in which above which the platform can pay dividends because it's a private business so you want to pay dividends to your shareholders. And conversely when you have low excess reserves then the platform uses basement by analogy with monetary policy. It's essentially issuing more token in order to provide some absorbing capacity for the shocks. So the main results are really I would say I focus on two of them but there are others. First of all the unintended consequences of regulation in the sense that mandating a fixed exchange rate may hurt welfare which is not obvious. It's a surprising in some way because in the idea that it limits risk sharing between platform and users the sum degree of risk sharing is optimal so you don't want to have a fixed exchange rate. And the second thing is that capital requirements are unable to completely eliminate the basement strategy. My opinion is that it's a very interesting set of results. However I would say that in my point of view the paper is still primary because several assumptions and modeling strategies need more justification. And let me give you a few examples of that. First of all I believe that the model is not fully specified. It's too much in reduced form. So the user's flow utility for example should be derived from fundamental. Users are myopic here and I believe this is part of the dimension of monies which is the store value. So you want to end the speculation aspect also. So I'm a bit buzzed by this myopic behavior. I would like to have a more broader horizon, a longer horizon for the users. So the store value is not entirely modeled but the payment function is not a model. Is there in the sense that the transaction, you talk a lot of transaction but they don't appear explicitly in your model. For example you have fees and the fees are proportional to holdings, not of transaction. You don't specify when you use your stable coin for buying or selling goods. Sorry. Similarly there is a cap on the aggregate number of tokens and you call that a cap on volume. The number of tokens is the same as the volume. There is a speed velocity, a speed of circulation of the money. So I would like to have a more micro foundation for that. And also for the main equation which is this exchange rate determination where Pt is result from a kind of a diffusion equation. It was not clear to me how this was obtained and in particular I don't see how the platform can control the volatility. The other thing is that I believe the network effect has two stylized. It's very interesting to introduce platforms but then you have indirect externalities and at least you would have to have two kinds of users, the consumers and the merchants. And the fact that for example the value for merchants is higher when there are more consumers who use it. The values for consumers is higher when you have more merchants. So this indirect externalities, they are not captured. And more generally I believe it's a bit strange to study the management of exchange rates because basically it resembles the management of exchange rates by central banks. In a model where you only have one means of payment that is you don't model the competition between other means of payments. Suppose there is a CBDC, suppose there is a traditional physical cash, how does this affect? Yeah, it's really a partial equilibrium center. Oh, sorry. And so that was it. In conclusion, I would say that this is very promising, very impressive also. Congratulations on what you did. But I'm still a bit frustrated because I would like to see more micro foundations. Thank you very much. Thank you very much, Jean-Charles, for this review. Let me see. I think there are no questions on the chat. So if you want to respond maybe to the comments of Jean-Charles and if I may, I would also maybe add one question, which would be interesting. You seem to argue that capital requirements are not a good tool because they cannot eliminate the debasement. So however, they may be successful in raising welfare. So what other policy tools would you consider then superior than as compared to capital requirements? So if you could maybe also cover that, that would be very great. And so the final word is then for you. Thank you so much. And I want to thank Professor Rocher for this great discussion. I totally agree that on the user activity side, we do not have a very good micro foundation. It's a very reduced form and we try to refer to this money utility literature and this and that try to justify, but it would help to model the transaction more explicitly. And I think at some point in my presentation, I said the link between transaction volume and stable coin portings is there if you are willing to assume constant money velocity. But the issue is that if there is debasement and information sensitivity of the stable coin varies over time, then the money velocity is probably not constant. So we do recognize that because if people worry about adverse election, why person A, person B, stable coin and person B need to verify, well, whether this stable coin issue has enough reserve solvent and then it takes some time, it affects money velocity. So this I totally agree. When it comes to the exchange rate determination, I think we need to clarify better in the paper. Right now, we do allow as general as possible the users, they can treat this stable coin amongst themselves. They can redeem it from the redeem dollars from the stable coin issuers. But I guess it's not a very clearly written. So when it comes to how the stable coin issuer can control volatility, so there is kind of a degree of commitment within DT here that we do assume. So basically, at any point in time, the stable coin issuer will publish its strategy saying that if my reserve will move in this direction by this much, by this percentage, I'm going to issue this amount of stable coins or repurchase this amount of stable coin. So within DT, there's a little bit of commitment here. And we think this can be implemented through smart contracting, but to the extent that this model restricts open market operation to any extent, this is the restriction. So basically, we have to publish open market operation strategy contingent on your post shock reserve level at any point in time, post shock meaning after DT. So we really need to make this clear. Right now, it's not in the paper. And the rest of the points are very well taken. We are also thinking about a follow up paper on computation, whether it's with the Fiat money or with another stable coin issuer. So now I want to get to Helmut's question regarding the regulation. So here we actually favor capital requirement as a welfare enhancing regulation, relative to regulating stable coin as deposits because for deposits, we know there's not going to be debasement because there's deposit insurance for small value deposits at least. So this is the mechanism to eliminate debasement. But through the lens of the model, fully eliminating debasement is not that necessary actually. You can allow some risk sharing between the platform and the users. So the basic logic is this, the platform at times can be even more risk averse than the stable coin issuers because if they are in distress state, very close to running out of reserves, they can be even more effectively risk averse than the user themselves. In this case, the user can basically sell some insurance to the stable coin issuers, i.e. absorbing some of these excess issuers of stable coin and give some dollars to the stable coin issuers for them to self-recapitalize. So through the lens of the model, debasement is not something that we want to achieve. We do want to achieve better welfare and that can be achieved through capital requirement. So regarding other forms of regulation, we haven't thought about it very much, but one dimension that we think we can go is to think about this reserve management featuring indulgence choice of risk taking. Right now, the reserve earns a fixed yield, R, and then the risk exposure is fixed at Sigma. Well, in the external model, the risk exposure can be adjusted through margins, but it's not linked to the yield. What if the stable coin issuers have some incentive of reaching for yield at the expense of taking out more risks? And this incentive is not modeled in the paper, but it's clearly there when you talk to the practitioners. And if we have this and then probably the analogy of liquidity requirement can be introduced into this space too, basically you cannot allow excess risk taking in the reserve portfolio beyond the capital requirement. Could you kindly conclude? Because I guess we are running out of time. I'm done. Thank you. Okay, excellent. Because I just realized we have also two hands raised. So I would certainly offer them the floor to speak. So Tiziana Rosalind and Daryl Duffy, if you could maybe be brief, because we are a little bit behind schedule and then Yelik could also be possibly very brief in a response. Thank you. Then let me thank you to the presenter and the discussant for this excellent paper and the review. It's clear that digital assets stable coins remain high on the agenda for the future. So this paper was not only very good, it was also very timely in the current debates.