For the crypto enthusiasts this may not be new, but I'll try to gloss over some of the basics for others, perhaps skip ahead if you know the background. Long read, hope it's fun to think about at least.
Automated Market Makers
In the crypto space folks have developed decentralized exchanges (DEXes); ways of submitting orders to the blockchain such that no central entity controls the transaction.
Originally, some typical order books were attempted. This is costly and illiquid; every interaction with the blockchain costs fees; putting up an order let alone taking it down would all cost fees, so you can imagine it would be difficult to "trade" this way.
Automated Market Makers, known academically, were utilized by the most popular DEX Uniswap. AMMs price algorithmically using liquidity pooled by individual Liquidity Providers (LPs), with a particularly simple algorithm: XY=K. X being the units of one asset in the pool, and Y being the units of the other, and K being a constant (only updated when new X and Y are added).
For example: TSLA is at 600$. I provide 60000 USD and 100 shares of TSLA into a pool, making K 6,000,000.
Should any trader want to take USD or TSLA from the pool, they must replenish the other variable such that K remains constant. If I want to buy 10 shares, then I will need to give 6,000,000/(100-90) - 60000 = 6666, or 666 per share.
The astute will note that this creates asymptotic pricing; you can never buy all the liquidity in the pool before price climbs to infinity. But that slippage is mitigated the more liquidity exists in the pool and the larger K gets; as of now folks are trading millions of crypto with (relatively) low slippage.
LPs are also exposed to risk from "Impermanent Loss," which is essentially the opportunity cost of starting the LP. Any change in the ratio of X:Y from the start will be worth less than the starting values: going back to the previous example, assuming 666$ is the market price, the starting values of 60K +100 shares would be worth 126666$. While the post-trade value would be 66666+90*666 = 126606. On Uniswap, LPs are incentivized with .3% of every trade to continue providing liquidity (and this .3% is added directly into the pool, compounding the size of the pool)
Problematic "Automated" Options Market Makers
This brings me to a relatively burgeoning field of crypto development, people attempting to apply similar concepts to Options markets. As of now, development of decentralized options is relatively slim. There is one example I can provide called Hegic.
Hegic LPs pool their coins and essentially sell covered calls. Except instead of offering individual options, buyers may specify the expiry, strike, and volume. IV is manually updated by Hegic's "owner", and underlying price feeds are obtained algorithmically on-chain, I believe. This provides most all the necessary variables for pricing options.
There is no direct mechanism to sell back options before expiry, although there are secondary markets, with a literal handful of liquidity on a good day.
The program stops allowing new purchases if the collateral for the short options reaches 80% utilization. Their protocol also currently only allows expiries up to 28 days.
They can sell puts as well; options are cash-settled (except the cash is, obviously, crypto)
Premiums go directly into the pool, allowing profit if the pool grows from unexercised options.
There is a host of issues with this approach, but I bring myself here now because I want to understand how to solve some of these issues, and their relationship to understanding Black-Scholes and options pricing.
1. Underpricing IV leads to all the collateral becoming locked up; crypto volatility easily outpaces a manual update. Then they have to wait for expiry unable to make more premium (and likely losing collateral due to overly cheap options)
2. Why only 28 days is a mystery to me, but I imagine there could be pricing issues with long-dated options.
3. Especially because the risk-free rate I am not sure where they get it. Manually? Coded in? Is it "necessary" for BS pricing in this scenario?
4. Requiring a manual update is not a decentralized exchange.
My aims
I am moderately math-y and still learning Solidity (the coding language for Ethereum) and want to see if I could possibly develop something better using something like Uniswap's algorithmic pricing model of instantly scaling price. However, since options are not uniform in expiry or strike, it cannot be that simple. But, I thought to myself, perhaps the one variable that is most dynamic, the IV, can be somehow tied algorithmically to the utilization of the pool! Buyers can provide the other Black-Scholes variables and get any option they want, theoretically. But this is where my understanding of Black-Scholes ends.
1. How important is the risk-free rate here theoretically, or practically, in the world of crypto? It would be feasible to allow it to be set by a weighted vote from all participating LPs since this is least likely to be "found" on-chain.
2. If I were to set IV = (Minimum IV)/(Remaining Collateral Percentage), the minimum would need to be also set algorithmically, perhaps by weighted vote. I am also unsure about how this price curve would look and whether it can be "straightened" with an exponent somewhere. It would be silly if this algorithmically underpriced everything but the last 1% of collateral. But then again, this system acknowledges that there must be an equilibrium price where the options suddenly become priced correctly. Adding collateral (or taking it away) would also affect the IV pricing instantly, but that can be addressed programatically...
3. Did Hegic set their expiries to 28 maximum for good reason? Is there something I'm missing about a singular IV being used to price both near and long-term options? Is there a recommended way to scale IV along time?
4. Put-Call parity; someone suggested to me when I was sketching out this idea that Puts or Calls could perhaps become weighted based on the Delta of the pool. I thought this maybe would be too complicated to truly start weighting options based on the greeks.
5. I would love to somehow be able to close contracts with the pool, perhaps pricing with a 1% spread. Or even they deposit collateral and the pool buys an option off of them. I'm worried however, that this may be gameable in some way, which is really one of the dangers of algorithmic contracts, that somehow someone could buy up the options, drive the price up, and sell them for a profit to the program until it was drained.
Anyways, this was a long type, but hopefully some entertaining food for thought. I'd probably try to make this just to use it as an LP, as there is no "good" way so far to sell covered calls on my crypto
6.
Automated Market Makers
In the crypto space folks have developed decentralized exchanges (DEXes); ways of submitting orders to the blockchain such that no central entity controls the transaction.
Originally, some typical order books were attempted. This is costly and illiquid; every interaction with the blockchain costs fees; putting up an order let alone taking it down would all cost fees, so you can imagine it would be difficult to "trade" this way.
Automated Market Makers, known academically, were utilized by the most popular DEX Uniswap. AMMs price algorithmically using liquidity pooled by individual Liquidity Providers (LPs), with a particularly simple algorithm: XY=K. X being the units of one asset in the pool, and Y being the units of the other, and K being a constant (only updated when new X and Y are added).
For example: TSLA is at 600$. I provide 60000 USD and 100 shares of TSLA into a pool, making K 6,000,000.
Should any trader want to take USD or TSLA from the pool, they must replenish the other variable such that K remains constant. If I want to buy 10 shares, then I will need to give 6,000,000/(100-90) - 60000 = 6666, or 666 per share.
The astute will note that this creates asymptotic pricing; you can never buy all the liquidity in the pool before price climbs to infinity. But that slippage is mitigated the more liquidity exists in the pool and the larger K gets; as of now folks are trading millions of crypto with (relatively) low slippage.
LPs are also exposed to risk from "Impermanent Loss," which is essentially the opportunity cost of starting the LP. Any change in the ratio of X:Y from the start will be worth less than the starting values: going back to the previous example, assuming 666$ is the market price, the starting values of 60K +100 shares would be worth 126666$. While the post-trade value would be 66666+90*666 = 126606. On Uniswap, LPs are incentivized with .3% of every trade to continue providing liquidity (and this .3% is added directly into the pool, compounding the size of the pool)
Problematic "Automated" Options Market Makers
This brings me to a relatively burgeoning field of crypto development, people attempting to apply similar concepts to Options markets. As of now, development of decentralized options is relatively slim. There is one example I can provide called Hegic.
Hegic LPs pool their coins and essentially sell covered calls. Except instead of offering individual options, buyers may specify the expiry, strike, and volume. IV is manually updated by Hegic's "owner", and underlying price feeds are obtained algorithmically on-chain, I believe. This provides most all the necessary variables for pricing options.
There is no direct mechanism to sell back options before expiry, although there are secondary markets, with a literal handful of liquidity on a good day.
The program stops allowing new purchases if the collateral for the short options reaches 80% utilization. Their protocol also currently only allows expiries up to 28 days.
They can sell puts as well; options are cash-settled (except the cash is, obviously, crypto)
Premiums go directly into the pool, allowing profit if the pool grows from unexercised options.
There is a host of issues with this approach, but I bring myself here now because I want to understand how to solve some of these issues, and their relationship to understanding Black-Scholes and options pricing.
1. Underpricing IV leads to all the collateral becoming locked up; crypto volatility easily outpaces a manual update. Then they have to wait for expiry unable to make more premium (and likely losing collateral due to overly cheap options)
2. Why only 28 days is a mystery to me, but I imagine there could be pricing issues with long-dated options.
3. Especially because the risk-free rate I am not sure where they get it. Manually? Coded in? Is it "necessary" for BS pricing in this scenario?
4. Requiring a manual update is not a decentralized exchange.
My aims
I am moderately math-y and still learning Solidity (the coding language for Ethereum) and want to see if I could possibly develop something better using something like Uniswap's algorithmic pricing model of instantly scaling price. However, since options are not uniform in expiry or strike, it cannot be that simple. But, I thought to myself, perhaps the one variable that is most dynamic, the IV, can be somehow tied algorithmically to the utilization of the pool! Buyers can provide the other Black-Scholes variables and get any option they want, theoretically. But this is where my understanding of Black-Scholes ends.
1. How important is the risk-free rate here theoretically, or practically, in the world of crypto? It would be feasible to allow it to be set by a weighted vote from all participating LPs since this is least likely to be "found" on-chain.
2. If I were to set IV = (Minimum IV)/(Remaining Collateral Percentage), the minimum would need to be also set algorithmically, perhaps by weighted vote. I am also unsure about how this price curve would look and whether it can be "straightened" with an exponent somewhere. It would be silly if this algorithmically underpriced everything but the last 1% of collateral. But then again, this system acknowledges that there must be an equilibrium price where the options suddenly become priced correctly. Adding collateral (or taking it away) would also affect the IV pricing instantly, but that can be addressed programatically...
3. Did Hegic set their expiries to 28 maximum for good reason? Is there something I'm missing about a singular IV being used to price both near and long-term options? Is there a recommended way to scale IV along time?
4. Put-Call parity; someone suggested to me when I was sketching out this idea that Puts or Calls could perhaps become weighted based on the Delta of the pool. I thought this maybe would be too complicated to truly start weighting options based on the greeks.
5. I would love to somehow be able to close contracts with the pool, perhaps pricing with a 1% spread. Or even they deposit collateral and the pool buys an option off of them. I'm worried however, that this may be gameable in some way, which is really one of the dangers of algorithmic contracts, that somehow someone could buy up the options, drive the price up, and sell them for a profit to the program until it was drained.
Anyways, this was a long type, but hopefully some entertaining food for thought. I'd probably try to make this just to use it as an LP, as there is no "good" way so far to sell covered calls on my crypto
6.
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