Sound options: a perfectly capital-efficient and oracleless design | Czar102 | ETHWarsaw [4]

I'm the founder of Blueprints and the inventor of Touch Market. But today I'm going to be talking about sound options, which is a new primitive I recently designed um that allows us to create arbitrarily shaped option strategies um to have complete control over uh how much we earn, how much our position is worth as a function of the future price. Obviously, this may seem like a very simple task. uh because we can simply deposit funds into some protocol and then have an oracle decide well who gets allocated how much based on uh the payoff function but what we really want to do is make it oracleless entirely. So um but I'll talk about a little later uh first a few words about me.

I uh am a security researcher. Uh I did multiple audits. Uh got several back bounties. Um was top three yet several audit contests and contribute to the space as Sherlock's head of judging. Um right now I'm a founder at blueprints inventive touch market and I I love to explore.

Okay. It's because it was too far from from my mouth, I think. All right. Uh um and I'm an explorer. I love math.

I love thinking about uh why do things work uh how they work, how they can work better than they currently do. Um and this is why I'm interested in sciences informatics as well. And this is uh I think a perfect example of my obsession about working optimally because I saw that the options as they currently are do not work efficiently at all. And even given its very long history has points where uh the options protocols implemented in legal terms could be way more efficient than they currently are. and we're we're going to be talking about that too.

So, um when it comes to the design objectives of our dream, uh Oracle, uh well, uh sound options, uh first of all, we want to be Oracleless. And um I'm saying no cap because uh very often protocols uh say they are Oracleless, but they're not. uh they don't use an external oracle but they do have an internal oracle and um it is very important to distinguish whether a protocol has an internal oracle or not. How do we do that? We can observe the system from the perspective of multiple participants and assume that every participant can have a different p different perception of the price.

For example, they're looking at a different venue. Obviously for assets like ETH or BTC uh this isn't going to make a huge difference usually at least. Um but for assets that are very illquid or have very few venues they trade on this is pretty important. So first of all price is subjective and then the system has to work well from the perspective of every single participant and every single participant can have a different perception of the price and our protocol will work in this scenario. Um it is also important to note when it comes to oraclelessness uh that we cannot have liquidations or any margin systems because uh we can objectively def see whether a liquidation has happened or not and if one participant doesn't think that the price will uh touch the liquidation threshold uh then this will look wrong to them.

So they will see the system as failing. The second property is all to all all positions are tokenizable. We are not interested u in entering positions in a math sense where we have some uh bonds that we deposit and then we can enter some new positions within this whole system. Every single position has to be uh tokenizable. So it cannot convey debt.

This is not a huge limitation. It's rather a refinement of thinking. If we uh we can tokenize always accounts in our current systems, right? So let's think of these positions as even sub accounts uh that are being traded. But what we want to ensure is that we don't lie to each other when it comes to uh being able to convey debt.

And because if one person can have a negative value of some position uh then another one will think they will have a much more positive one which cannot be done. So we want to be very very specific about um what the value is in general. No token can have a negative value. It can have a value of zero. U the value is subjective again.

It can have a value of zero and it can be positive. It cannot be negative. We can simply ignore or transfer the tokens out. Thirdly, they're fully colorized. We're not going to be praying on any price behavior like, oh, I hope the price is going to be stable.

It's not going to jump a thousandx uh in either direction. Uh there's going to be nothing of sorts. Um every single position has to be fully collateralized and we do not accept IOUs. Obviously, this protocol is defined for um uh for arbitrary tokens. So we by choosing the token that is not for example dollars by dollar but dollar I use we can create a system where we actually don't have to collateralize.

So we can have the same um capital efficiency in these terms by using IUS generated by some entity like in TRPI right now. Um and we're not constrained to have this done soundly so without using IUS but we can do that. And then lastly and this is I think the most difficult part because otherwise it wouldn't be nearly at all innovative it can be perfectly capital efficient. And I do not mean capital inefficient capital efficiency in terms of how I think it's popularized when it comes to lending in DeFi. uh because capital efficiency is usually considered to be LTV.

capital efficiency here which we will mean that it does not matter that if if I uh am told that I will receive a certain payout in the future and no matter what the future will be a payout will be at least a certain amount then it means that I'm not actually risking this amount by entering a position which uh means that it's just idle fund sitting there and this is not capital efficient. So we will achieve capital efficiency if there will be a certain scenario uh when it comes to the future price behavior that uh will make our position worthless. And to even talk about what I'm going to be talking about we have to know what payoff functions are. Um and these are simply functions of value. How valuable do I want my position or uh my uh my instrument that I acquired?

How valuable do I want it to be depending on the future price of an asset? So um let's define some terms that we're going to be using. The numerator is uh the asset that we consider the measure of value is the asset in which we describe the price. So when I say ETH is at uh $4500, it means that the dollars are the numerator. And this is the first example of a um payoff function that we're looking at.

On the y-axis, we have the value of of my instrument. And on the x-axis, we have the price. So no matter what ETH, in our example, what ETH price is, uh $1 is worth $1. and it's a constant. Now, um the second uh asset we're going to be considering is the speculative.

It's uh the asset which changes value in our thinking. And for example, ETH. And uh as we can see in terms of dollars, as the dollar price of ETH changes, the value rises linearly. The ETH value rises. Is that clear?

Awesome. Now, um what kind of payoffs can we get by simply combining these? Well, it's it's not a fascinating topic really, but I think it's sufficient for many people to get excited because you know people love trading. Uh we can have a constant function like displayed before. We can have a slightly increasing, we can have even more and very increasing depending on the allocation of our funds to numerator versus the speculative.

Uh but this is not interesting and we can see the expressivity isn't high in here. Uh we only have control over uh really two parameters or or even one uh depending on whether we have constraint funds or not. But we want more uh in order to get full control over what kind of kinds of positions are we entering? What is important to me as a position owner? Do I prefer yield?

Do I prefer to iron on upsides or downsides? We would like to customize this function to be perfect for me, perfect for everyone. And depending on the use case, we will use very different payoff functions. In general, uh this idea of defining a payoff function depending dependent on the future price generalizes 80% of finances concepts. It it unifies them.

It's lending. It's um corporate uh debt structure. It is speculation. It is uh liquidity provision. Um mortgages.

The uh well and trunching obviously. So uh the how how to use them is the least of the concern. they they implement practically everything possible without oracles uh without determining uh and without liquidations. That's very important. Okay.

Now, um let's first analyze the simple SP sound options which are the uh basic spells. And for that for the illustration, I'm going to um uh we have to introduce first uh the parameters that we're going to be considering these uh uh these options with respect to. So first of all, we have the asset pair. So we determine the speculative and the numeric asset. uh we also determine the strike price which will be the ratio I'll I'll mention in a second and third expiry it is the time at which the price will be uh is on the x-axis of of the payoffs graphs right so we're interested for example in what the price is going to be at the end of the year and then depending on that I will um determine how valuable do I want my position to We can play a game.

On one hand, I'm going to give you $4500 and on the other there's one ETH. And I'm going to tell you which one do you choose assuming that you can for zero at zero cost swap one into the other. For now, let's say you have a defined price. uh well obviously we're going to choose the the one that's worth more depending on the ETH price. H but the problem arises when we consider the future price because none of us know what the future price is going to be.

Um so the best way is to wait. Uh if I give you the optionality to choose until the end of the year, you probably want to take as much time as you want in order to get as uh to understand as best as possible which asset is going to be worth more and then pick one. Obviously, I'm not going to give you this right for free. I'm probably going to charge you more than $4,500 because that's one of the options that uh you can choose. Um but this uh introduces nonlinearity which is very exciting because we're not now constrained to just a linear function.

Um if I give you a choice you can either choose if if the ETH ETH price is very small below the strike price which is the ratio of the things I'm giving you to choose from. It is 4500 in this case. Um if the price is below it then obviously 4500 is worth more. So you'll choose the cash and the cash has a constant payoff function. Now at $4,500 an interesting thing happened.

Your best strategy changes and this changes to claim the speculative asset Ether and that scales together with the price. So we we have this beautiful payoff and we've gotten rid of linearity um and we can do very interesting things with this. What I will expect from you uh when I give you this choice is I will expect that I will be left with the asset that's worth less the least valuable of the two obviously given the ratio. So, and I'll call this a short option. If uh ETH is worth less, then I'm just going to have the payoff of ETH for low prices, and for high prices, I'm going to be left with dollars.

Obviously, uh you may have a different perception of price, but that's okay. I can be happier than this. I can get the more valuable one to me at least. Uh but in general in a general scenario, it's not a problem if I get more. Uh uh I'm definitely not going to be unhappy.

Um but uh this is what I expect and this is the worst case scenario. And uh we can see that this makes sense. Now um it's scaled a little bit, but this is the short option, the blue one. The red one is uh the choice option. And as we can see, they sum up to this purple one, which is the sum of $4,500 and one E, right?

So, uh, we haven't lost any value. That's great. Uh, we can also observe that, um, payoffs are always additive. Whenever we have a a payoff, if we deposit um a certain amount of cash and speculative asset and we distribute them into two tokens, one being able to claim one, the other being left with what's what's there. uh the sum of the payoffs are equal to each other.

Uh so these two sum up the reserves. This is an important observation. Now we don't really have to hold all the assets till till maturity. Instead uh you can just claim one of the assets and do whatever you want with that when I give you the choice. um and potentially uh switch to the other one just before expiry for example when you actually want to make the decision and this is where we start differentiating so if we take out initially um the numerator then we lower the function by the value of the numerator right and this is called a call I'm pretty sure many of you know these uh these functions uh on the other hand if we take out the speculative we subtract a linear function And this is what we left with.

And up to this point, uh, Trotfi has kept up. Now, we're going to, uh, introduce things that haven't been invented yet. First of all, if I expect uh, the short option to be the min minimum of these two assets, then um, I let you claim one of the assets and then potentially switch. Why would I allow you to switch only once? There's no point.

I ex I already expect to have the least valuable one, least valuable uh instrument of of those two deposits. So I can actually give you the right to swap back always. If you take one and swap, you can swap back and forth until expiry. And at expiry I'm going to claim what's left which is going to be the least valuable one according to my expectations. Um for those who uh who are more interested in options this is called time value and time value of American options are is lost uh when never exercising them.

This is why it's usually best to exercise them at expiry. Uh but in here we don't have to lose this time value. We can maintain it. So whenever we um exercise a call which is the right to buy an asset, what we really do is we deposit some numerator what we pay for and then we change this back into this uh this choice payoff and then we take out the speculative which is what we're supposedly buying and getting a put. And now we we don't destroy any payoffs and all the value maintained.

Um, so this is all the options we have. We have a sound call, sound put, and a sound short. Uh, also note that the sound short, I'm calling it short, but this is not a short um exposure to an asset. Whenever the price is rising, I cannot lose. I never lose.

I can either earn or stay constant. Uh, this is called short because of Trotfi. Trotfy's naming. Uh, uh, we're going to see here here. So in TROFI uh and please don't don't remember this uh or don't don't look at it too hard uh because we instead of the value we have the P&L and it can be negative and uh what what they do they don't think in terms of collateralizing so they don't have the ex the necessity for these functions to be always non- negative right we cannot lie to ourselves that was uh that was the goal in here uh so whenever we would think uh values negative.

That's not the case. Someone would just leave the token. Um uh but TRFI can do that. In TRFI uh you can have something of negative value because you're assumed that you'll never uh you'll never go bankrupt. And this is very interesting in this case where this is a actually mathematical function which is constant and decreases and it goes there and there and probably enters the earth and goes on the other way.

uh goes on the other way. Um and it's infinite loss. Do you know any frames that can cover an infinite loss? Great example. One one example.

Awesome. Uh yeah, but normally uh and that happened I I think during the bailout. This is exactly what happened. Um but it's unsound to think this way. And what do we do about it?

Well, we can come up with a very creative solution to this. What if we hedged it? We bought a a speculative asset which has an increases towards infinity and we hedge it this way. Then we can cover infinite depth, right? Well, uh then it means that this whole position, you know, the collateral is added to the position and what becomes of it?

It becomes a short put option. And this is why we only have three options only single short and two relevant here. They're also decreased as you can see uh by their price because they think of of them in terms of the P&L. Uh so the price is included here as well. Okay.

And so uh when it comes to comparing these two as I said uh there's a single short payoff because we cannot cover infinite debt. We do not assume anything about the price. It can go up a million%. We can undo the exercise and when exercising a call, we get a put. When exercising call, we get a a a put, we get a call.

Uh we never lose any time value. And then it is counterparty independent. So uh we think of them as separate positions and because of that we're not uh dependent uh on someone's solvency and uh the counterparty doesn't have isn't within uh the option parameters which is very important because now all options can be funible. Now what we've been waiting for how do you introduce multile strategies? Uh for now we've been thinking of options at only one strike price but we can obviously have several different strike price.

We can have any strike prices that we want and we can add them as we said um options are additive uh payoff functions are additive and this is an example infy they call it a uh uh a bull spread and it's a pretty uh useful a useful position in in many cases. For example, we want to speculate if the price is here, I can have insane huge leverage without liquidations um just by defining it. That's amazing. And it's unlimited. I can have this as vertical as I want.

But um when we try to replicate these uh using baskets, uh we approach a problem. It's not capital efficient. Um it as we can see um towards infinity this function is constant. So we cannot use any calls because uh calls are towards infinity. They have a slope of one and we cannot counter this with any other payoff.

So we can only use uh shorts and puts. Now uh put increases the uh slope by one. So here we have slope zero. Uh here we have positive slope. Uh so we'll use puts in here and then shorts in here because they decrease the slope.

When we do that, this is the put I was talking about the uh this is the call I was uh the short I was talking about. When we sum these up, we get this uh the the purple line. And it has the shape that we wanted, but there's something wrong with it. It's very high. um it's uh it it it doesn't have a zero for example.

So at all prices it's going to have a value of at least K1. This is the height of K1. And this is pretty inefficient. Uh when we have these two options we uh start to be capital inefficient. Now we want to fix it.

So we want to generalize it to any functions and even uh even functions that do not have uh are not only linear uh peacewise linear or paceway are fine. uh but uh we can generalize this to any functions or some rough some constraints uh when it comes to the ability to colorize uh for example sign if I think the price is in uh at the end of 2025 is going to be close to a whole thousand or we can have continuous leverage it has been tried before in squeeze but there was funding instead we can have continuous leverage up to a certain point and then just linear Um and uh we can just prepay for this and have a guarantee liquidation as a guarantee that it's going to work. Uh we can also uh define LP liquidity and for example uh the square root function is the payoff of uh of LPS in UN V2 and it it XY= K follows from this curve and all LP behavior follows from this curve which is uh given uh the parameters. Uh so how to replicate this smoothness? uh well we just have to spread out uh the the options strikes across a range so we kind of have option density instead of options sitting at a certain point.

So uh let me propose a set of very very simple rules that is going to solve our problem of capital efficiency. First of all, uh we can always deposit. We can deposit both numerator and the speculative. This is pretty simple. And then uh we get the payoff function.

We represent all um all positions with a payoff function. We get a payoff function either constant or um or linear. Secondly, we can um uh merge and split them. And by that I mean if I have any certain position I can turn it into multiple positions um whose sum is the initial position and the other way around that is uh that's exactly what we did initially. We split uh the sum of of numerator and speculative into two options a choice and a a short one.

uh but we have a limitation uh we can do that as long as the functions are non- negative otherwise uh we cannot and yeah you may think well now we probably needed a rule that you know pins these prices uh pins the values of the positions to what we actually define them to be um but these are actually sufficient already these are sufficient to describe calls and puts and all the mechanics about them. So, uh when we have uh let's say I want to create a call option, I deposit some speculative using the first rule, then I split it. I split it into a short option and a call option using the second rule because these sum up to the initial one. Uh now, in order to exercise it, all I need to do if I have a call is I deposit the numerator. So I take it higher and create a choice payoff and take out uh and take out the speculative because well I can do that because now the payoff function contains a speculative and I'm left with a put.

So I can already exercise calls and puts uh simply based on these two rules. Now the only rule we we're missing is the for short options. So we have a third rule and it says um for all uh everything every um every position on our protocol at expiry turns worthless except for except for short options or in general concave payoffs when you consider baskets of them. Um except for these options which are we can just claim the remaining reserves like we did in our initial uh initial design where we had a set of uh we gave a choice and then whatever left we claimed and this is exactly what we do. Whatever left is there for for them to claim.

Now um thanks to this we can always um take the following way to resolve uh uh to settle any position. Obviously the the first abandoned best way probably is to sell the position because if if me and some counterparty uh are having opposite positions one can buy from the other if we agree on the current price and on the value and then we don't even need a settlement. process. Um, this is the easiest one. Doesn't require any uh game theory.

But now if we do uh we already know how to replicate uh shapes using these fundamental options. We can always increase the payoff, decrease the payoff uh and add uh numerator. So what we do is if we have a certain payoff uh we just try to replicate it using a set of options and then we see how high does it have to be and we deposit that much numeric or speculative however many uh much we we need and split them into the options and then we exercise those which we can and then we're left uh with uh with short options and this perfectly settles but we can do some optimizations for example if I think the price is going to be somewhere in spike um I know all the other spikes are not um are not going to bring bring me any value. So for simplicity or uh even not to need so much capital to deposit at settlement only uh I can limit myself to a single spike and then simply add a um put option here a two shorts here and a put option here and that's it. um I only need to increase it a little bit to settle it uh using our our initial options.

Now um well okay that's a cool story but uh how do we exactly know that the short options can really that there is enough reserves for short options to claim? That's the only caveat, right? Uh everything else seems to work. Uh well I wonder if we have time. I don't think we do.

Uh but I'm going to go through it very quickly. Uh so um uh this is not a don't get scared of this graph. It's going to be okay. Uh the uh green line, the green continuous line is uh the sum of all short options of the payers of these options. Now we also know that all the reserves the payoffs of the reserves are the sum of payoffs of all payoff functions that we created.

That is our initial the first assumption. We can only increase the total sum by depositing more assets. So uh the payoff of all the reserves is here and we know that the payoff sum of payoffs of a subset of short options uh has to be strictly uh non- strictly less than uh our reserves and there's a point at which we equalize um the slope. Now this is a very special point uh because we want to split these uh all these short options into two types of um options. The uh the ones that we cover with speculative so where we give the speculative asset and the ones where we give the numerator.

And uh how do we do that? We prioritize the highest strike. So, whenever I have the two short options, for example, one is $200, $2,000 strike and the other is $5,000 strike. Obviously, I'd rather give one ETH to the $5,000 strike first before thinking about the other because if I don't have enough ETH, then I'd rather pay $2,000 than $5,000. And this is actually uh a feasible strategy and it's the best strategy.

Um so what I can do is I can take uh from this point on I can take all the slope changes and take the take them as uh as the short option and this is the red her. So the sum of all short option which are uh which can claim uh enough speculative are here because as we know uh short options have slope of one exactly one at zero. So uh we know that uh we're going to um uh that how much speculative here the red dotted line is going to be be below uh above not not strictly above the uh the red line which refers to the derivatives settled with with speculative. Now what we're left with is um is something like this. And how do we know that we have enough uh numerator for settlement?

First um let's note that um this point is at a height of uh how much numerator we have plus how much specular we have times times this coordinate. So we can think of it as ax plus b. And then uh it turns out that because we took the high strike prices uh until this point these two lines the red lines are perfectly aligned which means that what we've taken out is exactly exactly the uh the ax component. So we're actually left with just uh just b which is the amount amount of numeric that's left. Uh, I hope that wasn't uh too complicated.

I'd be happy to explain it better later, but unfortunately we don't have time for that. So, uh, it works. Now, what do we get out of it? Why why is it so interesting and cool? Well, first of all, we can get liquidation as debt.

And liquidation is that is simply you know I get the upside and then if if um if the price goes down at some point uh the value should be negative but we can't convey debt and we don't liquidate so we just stay at a constant zero price and this is a call option. If I purchase a call option for uh ETH at $2,000, I effectively I kind of borrow $2,000 for the duration of the option and earn on ETH in the uh in the meantime. As long as it's it's above 2,000, then I I don't lose anymore, which is also cool. For speculation, practically all of these shapes can be used for speculation, but there are some that are very very uh interesting to think about. um at the money calls and puts uh calls and puts that are very close to the current price whose whose strike price is very close to the current price spreads.

Here we can replicate insanely huge negative leverage without liquidations simply by defining uh such a function. Um but every shape is useful in speculation yield. uh we can underwrite uh calls and puts uh like in here I want to have some exposure the price let's say in here but then I can also lend some of some of my funds um some of the numerator funds for other people to uh uh well to cover some losses so my losses are going to be greater if the price goes very very much down I'm also going to give up some of the upside but this way I can earn a lot of yield uh mic Micro Strategy also has a strategy uh that is very uh relevant to this and I think uh it's not a signal that micro strategy is aligned uh I think it's a strategy that micro strategy has thought about what do they really want and whenever someone does that uh this is probably the best way to express what someone wants so they want uh increased BTC um uh leverage and to to do that they they purchase something of a call but then uh this lending and the optionality value that is being given um is costly. So in in order not to pay too much for it, they also underwrite calls out of the money calls uh which acts like a uh which slightly decrease their BTC exposure if BTC per performs very well which is fine. So effectively with their lenders uh they they say hey uh please lend me some money u and if BTC is going to rise very very sharply you're going to get some of the upside.

Then there's hedging. Uh if I'm uncertain about some asset I can purchase a hedge which is a put. Uh but you probably won't hold as a put for too long because it's better to exercise it first one way and then you get to withdraw the collateral for the put. uh use it for whatever time you have and then before expiry turn it back if the asset hasn't failed. Liquidity provision this one is extremely interesting.

Uh so by choosing uh the right uh the right shape we can replicate any non- degenerate AMM uh it can be curve it can be unis swap uh v2 v3 any general uh weighted pools as long as they have two tokens we can replicate anything simply by stating uh the payoff curve and all the properties all the math behind them uh is encoded in this curve. So and the the uh liquidity provision effectively how it works is we underwrite two um two options. We create two options. We deposit some numerator and some speculative uh we have one option that I showed earlier as an unis swap b2 lp and this is the second one. The first one is something we're going to be left with after we finish.

But this one is the one we use for LPing. And whenever the price diverges, we simply exercise it and then we get some of the profit. And then when the price diverges the other way around, we again exercise it. And we exercise it as many times as we can and gather some profit in the meantime. And this is this is the strategy.

Now because of this protocol what we can do is we can underwrite the payoff of for example a unis swap v2 position uh we can create it and then we can give it to someone else instead and someone can use an any arbitrary strategy that is in line with uni v2 math they can change the fees however you want they can use their own smart contracts we don't care how they can even not use their for liquidity just maybe up underwriting some other options or or hedging some of their positions. It doesn't really matter. Uh but the option seller, someone who has a unis swap v2 like payoff uh gets to be paid a constant value and sell the ability to uh to provide this liquidity without without taking any risks of smart contract that someone is going to use without taking any risks uh operational risks model risks because now a lot of strategies uh LP strategies are opinionated and because of that they get really really bad or use use oracles which can be dangerous can be a good idea as well. Uh depends. Yeah.

So in terms of uh providing liquidity this is this is uh very very very interesting and then uh risk stratification uh whenever we have uh that we can have some senior debt and this is a short option that very unlikely is is going to go into these uh these fields where someone loses and most likely will be at par with dollar. Then we have can have mezzanine or junior trenches um which are more risky and will pay uh pay more and then equity um uh which is a uh call option on on the value of the firm. Uh we can also use this we can also uh for riskification this is very useful when it comes to um um securization. We can take a lot of different uh positions, a lot of for example uh um depth obligations and we can basket them directly on chain to see what is in there. That's the problem with TFI.

They don't do that. But we can actually see what's in there. We can basket them and then on top of that using this protocol we can underwrite certain trenches and have exactly define uh what exposure does someone want to have and soundly and this this wouldn't wouldn't cause any uh um economic problems if if if this was used instead. So uh to summarize we now have complete payoff control complete control of the future price uh payoff uh we can design any function that we interested in and the design space is so large that I don't think this is a product in itself I'm not pitching a product I'm pitching a piece of infrastructure in order for users to actually get it we have to constrain these functions heavily and create an interface for a very constrained version so that users will understand uh and then it can implement uh dozens of products simply by by by this very simple and powerful protocol. It is fully oracleless.

It does not depend does not require any um any certain price to be determined. every single participant can have a different perceived price and it still works perfectly for everyone. So we don't want we don't need the oracles we don't have to care about markup manipulation and for assets which do not have the price defined we can still create these so we can have options for example on on stocks and just describe them on chain or like company stocks and then investing for for new startups and then it's perfectly capital efficient. uh there always has to be a zero of the function. Um and you can always withdraw whenever uh for all prices the value is going to be uh at least that.

Um and that's all. [Applause]

Thanks for listening.

Do we have questions? I have a question. How far are you from P? Are you Do you have P already? So this is about 20% of the thoughts I have on the topic.

Um there is an implementation of simple uh simple sound options. So the three options and it's 20 lines of code. So we can see how utterly simple this is. Usually options protocol are like 500 lines of code, thousand lines of code. This is 20 lines of code and it's it's not offset to libraries.

I I not using any libraries. uh uh just just some helpers maybe but that's irrelevant. Um when it comes to the full protocol there are a lot of other things to consider like a payoff function representation. So in uh real implementations uh we we can't really draw any function say it's a sign plus a constant value plus square root uh because programs don't usually don't operate on arbitrary functions. we have to constrain this and create a representation that is satisfying.

So one of these representations is just a piewise linear function and then we can approximate all other functions from that. Um but it um then we cannot have like these smooth functions smoothly changing so uh always differentiable for example. Uh what we can do is we can add for example a square root uh of the price. So say it's it's not a x plus b, it's a x plus b square roots of price or a * price times b time square of price plus c. And uh this is actually very really nice representation because it's symmetrical when it comes to which token is the numerator and the speculative and the symmetries.

I haven't gone into them but they're beautiful. uh um and it's also great. Then uh a problem emerges which is how do we settle uh short uh square root options because they're ranges and then when they're concave functions it's more difficult to find the point on chain uh the point here this point this point where the uh uh the uh the slope at which the slope uh goes achieves or goes beyond the speculative Um so it's it's a little bit tricky in these cases. There are ways to deal with that but then and there is a whole side of uh settlement when it comes to determining this point as you know what algorithm algorithms to use. Is it ZK?

Is it some other magic uh so when it comes to the implementation there's actually a lot more to consider.

Got it. This is what I wanted to hear. This is what I wanted. There is still a lot to consider. I I love how passionate you are about this.

Uh thank you so much. Thank you so much, guys, for your attention.