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The Development Context of Sustainable Derivatives

The first stage of the development of perpetual derivatives is the reverse perpetual contract, that is, the Bitcoin reverse perpetual contract developed by Bitmex in 2016. Traditional delivery futures have mechanisms such as settlement date, delivery, and contract position transfer. Perpetual derivatives make the perpetual contract shine through the combination of three mechanisms: pledge, funding rate, and price tracking. But it was not until 2020 that a large number of exchanges followed up with perpetual derivatives.

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Figure: The return of the reverse contract is non-linear

Source: The Block

Source: The Block

The third stage is that with the launch of Layer 2, the limitation of the underlying performance of the perpetual contract has been broken through, and the order book has become an optional direction for the project again, and the centralized liquidity of Uniswap V3 has its own order book feature, allowing professional market makers Merchants and traders enter. Derivatives are not just speculation, complex on-chain derivative strategy combinations have begun to be adopted.

We believe that the fourth stage of perpetual derivatives is that perpetual options will become a recognized tool for new traders in 2022-23. With Paradigm's discussion on everlasting options and some projects implementing on-chain perpetual options, more protocols will participate in this non-linear game. In the fourth stage, the market will begin to understand the Greeks trading opportunities and combination opportunities brought by non-linear derivatives. Perpetual options solve the dilemma that the liquidity of delivery options is divided on a two-dimensional plane. Long-tail assets will get more attention. And because of the relatively large volatility, they will become the favorite varieties of traders.

Perpetual derivatives will eventually coexist with other delivery derivatives, and more strategies will be derived for non-perpetual contracts to arbitrage cross-term derivatives. The market will return to a multi-product state, and liquidity will increase significantly, and this will enter the stage where the derivatives market talked about by optimists is much larger than the spot market (that is, the estimation method of TAM is applied). Another important feature of the fourth stage is that fixed-income derivatives have become popular, and this has truly entered a very institutionalized era. The interest rate, a product that has not been traded before, is completed.

We believe that perpetual derivatives have the following functions:

• A tool that facilitates the direction of the game. The existing perpetual derivatives in the market continue to prove the applicability of perpetual contracts

• A management portfolio tool. It can be combined with spot, delivery futures and delivery options. Professional traders can construct more types of portfolios. Singular combinations can be constructed between perpetual contracts, expiring contracts, perpetual options and expiring options

• way of providing fixed income. Due to the special way of perpetual contracts to maintain price stability, purely fund rate transactions must prevail in the circle of professional traders, similar to carry trade in foreign exchange. In addition to the combinations constructed by professional traders, some contracts have begun to template such combinations.

• A way to provide decentralized volatility trading. Use perpetual options to dilute the properties of delta and theta.

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Pricing of Perpetual Derivatives

The differential form of general options:

S is the underlying asset, σ is the implied volatility, t is time, z is a Gaussian process, and f is the option price.

Futures can be thought of as sections that contain only one-time items:

Both futures and options can be regarded as leverage on future targets. If boundary conditions are not included, options also include the quadratic term for price changes (ie fluctuations) and the value of time. Options can be viewed as including primary, secondary, and time items. Futures can be regarded as an option with only delta items, while option currency futures have more gamma items and theta items. The logic of futures is relatively simple, and both buyers and sellers have rights and obligations. The option has a payoff function due to the existence of the strike price, which is determined by the existence of the option premium. The buyer of the option has only the right and no obligation. The assignment of this obligation is represented by the premium. When the seller sells the premium , acquires an obligation to deliver on the due date.

The funding rate is the most delicate point of the perpetual futures contract, and all derivatives are expanding around their own rate. That is, the buyer or seller of funds pays the funding rate to the other party to maintain the balance between the futures price and the underlying price (index). However, due to the increased possibility of high-leverage perpetual contracts being liquidated, perpetual options provide another solution: 1. It will not be liquidated, and the option buyer has only rights but no obligations; 2. Without liquidation, the Leverage is enlarged.

The main problem to be solved by options is pricing. Because of the introduction of quadratic terms and time, the price shows convexity. The difference between option pricing (selling options) and the actual transaction price is the source of profit for option trading.

Perpetual options have been discussed a lot in academia, such as the non-right of American call option, the analytical solution of put option, etc. However, for users of options, the biggest threshold is: 1. Understanding the relationship between options and the underlying object; 2. Compared with futures, what additional benefits are provided by options, allowing users to at least make an equivalent choice between the two. Due to historical reasons and product complexity, most users started their business with futures.

Paradigm provides a representation of perpetual option pricing in terms of rates:

Deri protocol launched the perpetual option product on August 11. They used the model of the paradigm to price options, and introduced another expression of the perpetual model:

And C (t) and P (t) are represented by the general general BS model

The on-chain perpetual option agreement Shield protocol goes a step further and solves the analytical solution of the perpetual option:

The analytical solution of Shield Protocol is based on the empirical results of 3-year historical data dynamic hedging verification and OTC option pricing theory research.
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dYdX

Founded in 2017, dYdX provides cryptocurrency derivatives business products including: perpetual contracts, spot and leveraged transactions, lending, etc. dYdX's perpetual contract uses USDC as collateral, and crossmargin is possible, that is, multiple contracts use the same collateral. The funding rate of the perpetual contract is settled every hour. The fund rate of dydx also takes into account the interest rate difference between the two proportions of direct lending. His funding rate formula is:

Funding Rate = (Premium Component / 8) + Interest Rate Component

dYdX's perpetual contract is built on zk-rollup designed by Starkware. zk rollup completes customer transactions off the chain and transmits the transaction results to the chain. rollup is responsible for transaction packaging, and zk is responsible for providing zero-knowledge proofs to prove that depositing in layer2 is valid. The interaction process is as follows:

• Ethereum to Layer2: dYdX monitors relevant Ethereum transactions, namely deposits, forced withdrawals and forced transactions. Once such transactions are received on Ethereum, related operations such as adding funds will take place on the second layer.

• Layer 2 to Ethereum: After a batch of transactions are executed off-chain, proof of their validity is generated and verified by STARK verifiers on-chain. After the STARK validator approves the state transition, the state transition takes effect, such as depositing or withdrawing from the second layer to change the user's Ethereum balance.

dYdX uses an order book system, and the order book can provide limit orders, so it is more suitable for derivatives. Injective, a perpetual derivatives agreement, once compared the two mechanisms of order book and AMM.

The advantage of the order book system is that it can provide many complex order types, but it still relies on market makers. For example, dYdX uses market makers like Wintermute, so the order book and market makers are essentially a system. In addition to professional market makers, general liquidity providers can add USDC to the liquidity pool, and then professional market makers can apply this part of USDC, making a distinction between liquidity and market making, which is further beneficial to having funds but no transactions Ability to engage users.

dYdX is very similar to the traditional trading market. The biggest innovation lies in the API, which can already be provided to a level similar to that of a centralized exchange. That is, such an API completely removes the logic of the blockchain, and only the remaining ones are suitable for market makers. . For example, 1.25ETH is 1.25, not the most basic wei representation. According to Wintermute's feedback, cross margin is very friendly to market makers and can save a lot of capital.

After dYdX launched layer2, the transaction volume increased significantly.

The daily trading volume can reach 7 billion US dollars, but with the decline of the market, it has already entered the downturn. The three largest trading pairs are BTC/ETH/SOL/COMP and so on.

Layer 2 engine

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Source: Starkware

The user's funds are transferred to the StarkEX contract to achieve decentralized self-custody, and then they can be traded on dYdX. The off-chain components of StarkEX will manage all transaction orders and send status updates to the on-chain components after execution.

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Perpetual Protocol

Perpetual is the on-chain perpetual futures market (currently second) with the largest trading volume on the entire network. The V1 version of Perpetual uses a vAMM-type trading pool, which is an extended type of AMM. According to the statistics of trading volume, Perpetual, dYdX and Futureswap are the top three perpetual derivatives.

vAMM adopts the calculation method of AMM, but does not adopt the liquidation method of AMM. The K value can be adjusted. The larger the K value, the lower the slippage, and the K value should also match the OTC market. vAMM can use almost unlimited liquidity, so according to the constant product formula k=x*y, there will be almost no transaction slippage, and all AMM pools with low liquidity will face insufficient liquidity and excessive transaction slippage question. The real clearing and settlement of vAMM is at the bottom of Perpetual, and the insurance fund assumes the role of liquidity provider. Perpetual's v1 adopts xDai as the second layer solution.

The insurance fund assumes the counterparty risk of vAMM (for example, when it is consistent long and consistent short). If the business does not continue to develop steadily, the growth of insurance funds should not be sustainable. Large negative swings can offset weeks of increases in insurance funds.

In the new V2 version, Perpetual utilizes the liquidity of Uniswap V3, introduces counterparties, and reduces liquidity risk. The V2 version has made many other improvements and designs, and the V2 version will be divided into four steps: V2.1: Utilize the centralized liquidity of the V3 version, market-making based on Arbitrium; V2.2: Launch the current price list system and staking of PERP; V2.3 : multi-collateral system other than USDC; V2.4: private market without permission. In version V2.2 this will become a limit order system like dYdX. Offchain Lab believes that Arbitrium can pack 4,200 transactions per second, which is 300 times higher than the Ethereum mainnet.

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Perpetual swap DerivaDEX

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Source: DerivaDEX

DerivaDEX uses an order book, and DerivaDEX also designed an insurance fund similar to the Perpetual Protocol to protect the agreement when a certain loss occurs (such as the loss of the counterparty exceeds their mortgage). There is no special solution to liquidation, it needs to rely on insurance fund to solve it, which is another mechanism created by Bitmex perpetual contract.

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Perpetual Options Shield Protocol

Shield Protocol is an on-chain perpetual derivatives agreement, and its economic logic is non-cooperative game logic. Its first version of the product is an on-chain perpetual option product, after which it will develop perpetual contract products, OTC options and structured products. It has the characteristics of non-mortgage, transparency, no intermediary fees, trustless and easy to use. The formal logic of perpetual option products is similar to that of perpetual futures, that is, the payoff of option prices is determined by price changes, funding fees and transaction fees:

Payoff= (No. Of Contracts*Price Change) - Funding Fee - Trading Fee

Compared with futures, options have no concept of liquidation. The biggest loss per day is the funding rate. Its liquidity is supported by two pools, the private pool and the public pool. The core innovation of Shield lies in the analytical solution of the pricing formula of perpetual options, which is in the form of BS model, as mentioned above.

The main problem of options at the market fit level is that they are not very suitable for retail investors because of the complicated operation, and the T-quote board is the biggest obstacle. The trading volume of the largest options exchange Deribit is relatively small, and the options field is more suitable for professional traders. Shield's solution to this problem is: 1. So the role of broker is introduced. Broker helps users understand options and provides trading/investment consultation. The whole process takes place on the chain, and the broker can get a commission. Like traditional finance, the commission comes from the transaction commission of the recommender. 2. The traditional delivery option is transformed into a perpetual option, and users can only buy at-value options, which greatly reduces the threshold and risk for users.

Unique to Shield is the public pool and private pool system. The private pool serves as the main transaction pool, and the public pool serves as a supplement. Private pools are for professional traders who can transfer risk through external hedging. The public pool has a low threshold and is suitable for retail investors and risk-averse people to participate. At T=0, the private pool is equivalent to the seller of the option, and the trader is the seller of the option. All transactions are peer to pool, and the liquidity comes from the pool. The distribution of newly opened orders is determined by random numbers, one is the hash of the block, and the other is the time of the block. Orders are randomly matched into private pools. The provider of the private pool obtains transaction fees based on SLD (governance token), and the fee income of the private pool is relatively high. Liquidators get rewards by providing liquidation services. The five roles of Shield maintain the stability of the protocol through non-cooperative games.

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Persistent Templating and Composability - Ribbon and OPYN

The story of Ribbon and OPYN shows an interesting phenomenon. The creativity of complex products often relies on extremely simple front-ends to achieve expansion, which just reflects the advantages of DeFi composability. Ribbon Finance uses the perpetual option template provided by OPYN to create a fund pool similar to regular savings. The bottom is supported by the option selling strategy of put selling and covered call strategies, which can provide users with fixed-income collection products.

Ribbon is equivalent to establishing a strategy aggregation income front-end for OPYN, helping users to execute the selling option strategy on a weekly basis, which is similar to the derivatives of perpetual options. The realization principle is that Theta Vault (the capital pool on the Ribbon) casts 90% of the investor's deposited funds in OPYN to cast a coverd call, and sells it to the market with oToken (the token representing the option in OPYN), and the parameter setting of the option Determined by Theta Vault, users don't need to think about it, and generally choose out-of-the-money options, which can earn premiums. The disadvantage is that if the underlying price rises to the strike price within a unit period, users will suffer losses.

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Source: Delphidigital

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Looking at Perpetual Derivatives from the Development of Options

The development of options in ancient and modern times can be traced back to the Middle East and the tulip bubble era, both appearing in the form of an agreed transaction contract. For example, the buyer pays the seller a deposit of 3.5%-10%. If the tulip price is lower than the contract price on the due date, the seller can be exempted from the obligation to buy. Modern options are based in the United States, both in theory and practice. Commodity options originated in crops and animal husbandry. Financial options (represented by stock options) were all decentralized models at the beginning, and they were all off-exchange options. 1973 was a turning point in the development of the options market. The Chicago Board Options Exchange invited Nansen Company to complete a "Nansen Report". In the same year, Fisher Black, Myron Sholes and Robert Merton published two papers respectively, and proposed an option pricing model with similar conclusions, which is later called the option pricing model of BSM.

The 1974 US Securities Regulatory Commission report heavily cited the contents of the Nansen Report. Four conclusions are very important: 1. Exchange options help reduce the volatility of spot stocks on the exchange; 2. Options on the exchange increase spot liquidity; 3. Options will not divert liquidity, and 4 on-market options allow investors to mature and face complex markets. In 1985, the four major regulatory agencies in the United States launched the "Research on the Impact of Futures and Option Trading on the Economy". This publication, commonly known as the Quartet Report, put the development of options on the right track.

The development history of options is very long, which is the result of the joint action of the market, theory, traders and supervision. Corresponding to crypto options, we found that the theory is basically unchanged, the market demand exists, the traders are not mature, and the supervision has a very negative attitude, which is in line with the characteristics of the stock option market in the early stage, that is, before 1973. The early stage of the development of derivatives generally has a heavy speculative flavor. It is not until investors mature that the attributes of the instrument slowly reappear. For institutions and individuals, the meaning of options is also obviously different. Therefore, it is worth thinking about the development of the positioning of the crypto option market.

Why are you optimistic about perpetual derivatives at this time:

• Performance improvement: The launch of Layer 2 seems to have solved the performance problem, and more importantly, it has given the derivatives an opportunity to launch a new V. The AMM model in the basic chain begins to transition to the order book. With the emergence of Uniswap V3, the order book, a previously forgotten solution, has come back, and AMM will work together with the order book

• Diverse ways to play: Sustainability is a good direction. Crypto has many retail investors, and many people are not used to operating mature derivatives. It has been proven by the market that perpetual derivatives can be combined into interesting income products.

• The popularity of options is on the rise: The popularity of options is on the rise. Options are very suitable for the emergence of professional market makers. It is common for professional market makers to work in Layer 2. The pricing and time of perpetual and perpetual options have begun to form a trend, which is an important factor that prompts professional traders to enter the market.

• Potential trading factors and non-trading factors: As long as the overall market trading volume increases, the volume of perpetual derivatives will increase very quickly. At present, some other factors have increased the number of DeFi derivatives.

Risks of perpetual derivatives:

• The high leverage of derivative products can attract customers but also put pressure on the agreement

• For the designers of their pools, liquidity providers face losses or are unwilling to actively participate

• Collateral selection is a double-edged sword

• Whether derivatives can bear high throughput has not been verified

• The closer it is to a centralized order book system, the closer it is to competing with centralized exchanges. Users were stimulated through the mining/staking mechanism before, but then there was competition for real products.