Presenting Divergence v1

TL;DR

Options are powerful tools that can help protect against volatility in assets. In DeFi, thus far, options have been tricky to price, inflexible with terms, and capital intensive to trade. Quite often, trade-offs have been made in decentralization and utility. For all the technicalities, it comes down to:

How to enable everyone to efficiently buy and sell options of customizable terms, at their preferred prices and times, from self-custodied wallets?

The answer is Divergence v1. A noncustodial automated market-maker (AMM) for digital options. A simple-to-use, chain-agnostic decentralized application that puts everyone in the divers’ seat, irrespective of their background.

Our solution addresses a vital gap in decentralized financial derivatives infrastructure. It facilitates the tokenization, transactions and settlement of digital options on a broad spectrum of DeFi-native and real-world assets. It also serves as a prediction market for both on- and off-chain events, among various other use cases.

Divergence v1 AMM offers a full suite of derivatives market functionalities, entirely on-chain. Anyone can create an options pool at preferred strikes and expiries. A single collateral asset is needed — a fungible token from any layer of the DeFi stack. This collateral asset is also used to trade and settle the options from the same pool. From a self-custodied wallet:

• A trader can market buy calls or puts at a preferred time.
• A liquidity provider (LP) can passively sell calls or puts while earning fees, at a custom price range.
• Anyone can enjoy freedom of expression, and generate a return up to 99x per option.

The Decentralized Option

Divergence was conceived in the wake of the 2020 DeFi summer, as assets proliferated across various layers of decentralized protocols. Our founding vision is to empower the ecosystem participants, who face the constant challenges of unpredictable price movements, changing interest rates, and fluctuating staking rewards. We built a beta version, and went through multiple iterations to dramatically improve customization, capital efficiency, and composability.

Throughout every code update, our commitment to decentralization remains unchanged: Divergence v1 is to enable options price discovery through peer-to-peer transactions from user-custodied wallets, without centralized intermediaries.

Fundamentally, Divergence v1 AMM employs put-call parity within a constant product market maker for digital options. It leans on Uniswap V3' decentralized architecture and logic to tackle the intricacies of options trading. Its innovative use of the constant product reserve equation for collateralizing options is unprecedented.

At the heart of our solution is convertible liquidity:

• LPs can passively sell options of chosen specifications at custom price ranges. Unlike traditional orderbooks, a liquidity position on Divergence v1 can sell unlimited number of options, achieving auto risk-reduction by offsetting short call and put exposures.
• A position has a predetermined cap on short exposures in either calls or puts. Using just one asset as seed collateral, a liquidity position avoids impermanent loss due to changing asset ratios. Instead it can take on impermanent optionality: an LP’s short interest in options becomes permanent only if liquidity is withdrawn.
• Fees accrue from notional sales volume, providing the opportunity to earn fees multiple times to seed liquidity, with lessened or even zero short options exposures.
• Options tokens can also be provided as liquidity to earn fees before expiry. This type of liquidity position is similar to a “limit close” order for longs, without needing more collateral.

A Deep Dive into Divergence v1 AMM

Divergence v1 provides an extensive selection of options pools, each with its unique underlying, collateral, strike, and expiry. An options pool is a decentralized, peer-to-peer infrastructure, combining traditional roles of an issuer, a secondary market and a clearinghouse. The options are fully collateralized before they are tokenized, transacted, and settled.

Tokenize

A pool tokenizes European digital options of a chosen specification. A digital option has limited risk and pre-determined payoff. It differs from a standard option, which has a variable payoff.

An European digital call (or put)
🔹costs from 0.01 to 0.99 collateral;
🔹pays 1 collateral if the underlying asset settles above or equal (or below) the strike price.
🔹otherwise, it expires worthless.

The calls and puts are minted as Spear and Shield tokens, respectively. When you buy a call, your expect a return equal to the value of a put, and vice versa. According to put-call parity:

Digital Call Price + Digital Put Price = 1 Collateral
🔹Expected return for a Call = 1 - Call Price = Put Price
🔹Expected return for a Put = 1 - Put Price = Call Price

As an example:

💡Suppose a digital call costs 0.01 DAI. Its underlying is ETHUSD. Its strike is $2,000.
📈 If ETH settles at or above $2,000, it pays 1 DAI. Its buyer earns 1–0.01 = 0.99 DAI less fees, i.e., a 99x return. Its seller loses 0.99 DAI.
📉Otherwise it expires worthless. Its seller keeps the premium of 0.01 collateral.

A standard call of the same specification costs a different amount, and does not pay a fixed amount.
📈If ETH settles at $2,001, a standard call pays $2,001 — $2,000 = $1.
📉If ETH settles below $2,000, it expires worthless. Its seller keeps the premium.

With their predictable, non-linear returns, digital options provide a cost-effective hedge for a DeFi portfolio. If preferred, digital options can also be used as building blocks to compose a standard option.

Transact

At an options pool, a trader swaps collateral tokens for call or put tokens. This process uses a virtual curve inspired by Uniswap v3, which swaps two spot assets.

A Divergence v1 pool, in contrast, handles three assets: a call, a put, and a collateral token. If the put-call parity is broken, it generates triangular arbitrage within a pool. So, a “juggling” is performed to:

1️⃣ receive a collateral value of calls (or puts) as payment

2️⃣ combine with a collateral value of puts (or calls) to reserve for settlement

3️⃣ mint call (or put) tokens for the buyer

In effect, a trader swaps in collateral premiums for a matching return, which is not payable until settlement. Call and put options are valued relative to each other. Their relative prices change when collateral is swapped for either calls or puts, and a new market price for both options is found.

Settle

A v1 pool settles options by fetching an underlying price from an external decentralized oracle network. The options are settled with the pool in this logical order:

1️⃣ A long call and a long put settle each other, regardless of the outcome.

2️⃣ Any remaining longs in calls or puts in the pool are then squared with the LPs.

💡 Alice buys a call and Bob buys a put from Chad’s liquidity position. At settlement, 1 DAI is paid out:
📈If the underlying price settles at or above the strike, Bob’s premium ends up with Alice.
📉Otherwise, Alice’s premium goes to Bob as his return.
🤑Chad pockets all fees with no options exposure.

Convertible Liquidity

Divergence v1 liquidity providers passively sell options at custom price ranges to those who swap in collateral. LPs can not only concentrate liquidity within custom ranges, but also convert liquidity — in calls, puts or collateral — to take on or off options exposures.

Concentrate

LPs can concentrate their liquidity within custom price ranges. They can set up multiple positions in a single pool, tailoring exposures to suit their needs. At any time, liquidity can be removed to finalize a position’s exposures.

A position either sell more calls than puts, or more puts than calls, depending on its price range. When the price exits its range, a position stops selling options, capping its net shorts. This ensures that a position’s seed liquidity can always meet payout obligations to these net shorts, in case they settle profitably.

A liquidity position on Divergence v1 has:

🚀unlimited gross shorts in calls AND puts;

🛑️limited net shorts in calls OR puts

To naked short a call (or put), an LP selects a price range above the current call (or put) price.

The seed collateral of a liquidity position is the required return for its maximum net shorts:
🔹Short 1 Call = 1 - Call Price
🔹Short 1 put = 1 - Put Price

In effect, an LP is a fee-earning trader. Per put-call parity, an LP’s risk-reward works out as follows:

For the same liquidity range:
🔹Short 1 Call = Long 1 Put
🔹Short 1 Put = Long 1 Call

For example:

💡 Chad deposits ~0.20 DAI of seed collateral to short 1 call. Alice buys a call at ~0.80 DAI. Chad now net shorts 1 call, which works out similarly to long 1 put at ~0.20 DAI:
🔹If Alice’s call settles profitably, Chad loses ~0.20 DAI.
🔹Otherwise, he can withdraw 1 DAI plus fees, and keep Alice’s premium as profit.
Chad can also buy back 1 call, and send to the pool before expiry to redeem 1 DAI. This is similar to a traditional order to “market close” shorts.

💡Suppose Bob buys a put at ~0.20 DAI afterward. Chad’s options exposure is reduced to zero. He can collect his seed collateral of ~0.20 DAI, and fees from Alice and Bob. At settlement, Alice and Bob settle each other.

In contrast to a conventional limit sell order, a liquidity position can potentially have zero open shorts and unlimited fee income. Consider:

💡 Chad seeds collateral to open short a single call. Alice buys a call, fully crossing his position. Then Bob buys a put, undoing Chad’s short call exposure. Alice buys another call and Bob buys another put. They trade back and forth until Alice ends up with 1 million calls and Bob has 1 million puts.

Alice and Bob collectively paid 1 million collateral, which is reserved to pay off either calls or puts. Chad, with no options exposure, reclaims his seed collateral in full plus fees for every trade. 🤑

Convert

Options tokens, once purchased, can be used to create liquidity positions. This type of liquidity position resembles a traditional “limit close” order. Except, its liquidity must be removed to finalize. If not, premiums from option sales will later effectively become liquidity for new option purchases. This makes the position function like one seeded with collateral.

💡 Bob decides to exit his long put before expiration. He creates a liquidity position using 1 put, at a put price range of [0.30, 0.31]. Once the put price cross above 0.31, he removes liquidity to receive ~0.30 collateral. He makes 0.30–0.20 = 0.10 collateral, a 50% return.

This type of positions enables options holders to generate fee income, while enhancing a pool’s liquidity.

💡 Bob is unconcerned about his long 1 put exposure. He expects back-and-forth price moves, and uses his put-funded liquidity position to collect fees. When the put price cross back below 0.30. The put he seeded is sold. His position effectively uses the ~0.30 put premium to sell a call.
If Bob remove liquidity now, he retains this short 1 call (aka long 1 put) exposure. Otherwise, he can wait until the put price to cross back above 0.31 again to collect a ~0.30 put premium plus fees.

Exploring the Uncharted Territories

The DeFi options market is in its early stages. Divergence v1 presents an intuitive and instantly scalable solution that pushes the conventional boundaries. It is designed to embrace a broad range of underlying assets, collateral, strikes and expiries, opening up new realms of trading possibilities. It caters not only to options traders but also participants of prediction markets and insurance. Furthermore, it lays the groundwork for integrating digital options into structured products, potentially redefining DeFi yield farming.

Customization

Users of Divergence v1 have the freedom to price options, creating, entering and exiting markets with minimal friction. Departing from DeFi conventions, the protocol eliminates the use of theoretical models, such as the Black-Scholes, for pricing options. In doing so, it avoids a universal cost for such model computations, which may not suit every participant at all times. As market participants collectively price options, rational players will likely enhance pricing efficiency over time.

The protocol’s creative mechanism for collateralizing options minimizes market friction. Users get to decide their trading times. LPs enjoy the flexibility to remove liquidity at will, without concerns of over-collateralizing options.

Composability

The protocol can support an extensive range of underlying assets, from crypto assets, to on- and off-chain events:

• Interest rates and staking APRs for major crypto assets
• Price of mid-to-long tail assets, including wrapped assets and decentralized stable coins
• Ethereum gas price
• NFT floor prices
• Fed interest rate decisions

Users can choose from stable coin or asset tokens as collateral to create cash-or-nothing and asset-or-nothing, which are building blocks of a standard option. It would be also possible to use borrowed funds or wrapped tokens from other protocols to create exotic structures. There are many opportunities add optionality to a portfolio, using DeFi-native assets.

💡 Chad provides liquidity for the DIVER-WETH pool in Uniswap V3, and collects fees in DIVER tokens. Using the DIVER fees, Chad can buy or sell ETH options on Divergence v1. This hedges against ETH price volatility and potentially rewards Chad more DIVERs. If he chooses to sell options (aka provide options liquidity), he can have even more fee income.

Capital Efficiency

The conventional DeFi models require locking up an amount of collateral for a fixed amount of calls and puts, before they circulate in the secondary markets.

Divergence v1 presents unprecedented capital efficiency for DeFi options. Liquidity providers can now allocate collateral specifically for a capped call or put exposure, with the potential to earn fees from offsetting trades within range. This shift towards elastic circulation reduces market barriers and arbitrage risks, giving LPs the flexibility to finalize options exposures as needed throughout the trading process.

Liquidity supplied to Divergence v1 also has a multiplier effect. The notional value of a position’s net shorts in calls or puts could be up to 99x its seed capital. The overall notional value of option sales, from which fees are collected, can dwarf this net short interest. Once sold, the option tokens can add to liquidity depth, increasing the turnover of a pool’s circulating options.

💡 A single trade across a liquidity position can yield a fee income up to 21% of the upfront seed collateral. 🤿

Upcoming Tides

Divergence v1 smart contracts are deployed to the Göerli testnet of Arbitrum, so our community can experiment with the protocol before its official launch. Our mainnet contracts have been deployed and going through final checks, and we expect a formal release on 21st December. Prior to that, we will open source the code, and release an extensive technical reference in our docs. We welcome collaborations in security, and are happy to work with the whitehat community as always.
For questions or comments, please head to our discord or telegram channels, and we are ready to help.

Diver Team🤿

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