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# Arrow Markets Litepaper

Arrow Markets’ name is inspired by the insight from Nobel laureate economist Kenneth Arrow that options contracts can form a basis for the prices of financial assets, making it possible to construct a rich variety of derivatives and structured products from simple options.

# Two Pool System

A dual-pool system underpins Arrow’s option creation and settlement functionality. The first pool holds the net premiums (longs - shorts) from options trading, as well as the collateral from writers. Our AMM sets premia (prices) for buying and selling, and the trading pool’s liabilities are dynamically hedged via an automated hedging engine. The second pool is an insurance pool for the system. Insurance providers are compensated with the residuals from the trading pool plus transaction fees.

# AMM

Our AMM determines option prices for both buy and sell orders. The AMM also determines a hedge for the position with its internal hedging engine. The price relies both on the chosen hedge and the risk assessment of the AMM. The risk assessment is made using a monetary risk measure, specifically, an entropic risk measure. The entropic risk measure is closely related to value at risk, and can intuitively be thought of as measuring the capital required for the system to be considered safe.

The AMM sets the indifference price according to the marginal contribution of each new contract to the risk profile of the trading pool. Specifically, each new contract liability is charged to offset its incremental contribution to the liability distribution's entropic risk.

Formally, suppose that Z represents the sum of current book positions and $\rho$ represents a monetary risk measure. Z is a random variable that is a function of the underlying asset’s prices at various expiration times. Then the expression for the indifference price is

$p_t = \rho_t \; (Z + \text{new position} + \text{new hedges})-\rho_t \; (Z + \text{current hedges})$

For example, in the case of selling a call option with strike K and expiration price $U_T$ the AMM would calculate a quote for adding the position

$\text{new position} = -max \{U_T - K, 0\}$

To reiterate, the intuition behind the indifference price is that it is the amount of extra capital that a market maker would take to make them indifferent between taking or leaving the additional option position on their book.

This monetary risk measure formulation can also account for trading costs such as price impact and slippage by explicitly incorporating them in the risk assessment.

It can be shown that this formulation sets prices in a way that is equivalent to the case where the market maker is optimizing a CARA utility function over future payouts.

# Hedging Engine

The Arrow system runs an automated hedging engine to keep the risk profile of the trading pool insensitive to underlying price movements. This works as follows. Along with prices, the AMM calculates a $\Delta$ (a "delta"), or hedge position, for each new option added or removed from the system. The smart contract that houses the trading pool balances then takes that $\Delta$ and picks up the corresponding balance in the underlying. If the net $\Delta$ is positive, the position is obtained by programmatically swapping stablecoin for the underlying (or vice-versa, depending on the sign of the option $\Delta$) on a DEX such as Pangolin or Trader Joe. If the net $\Delta$ is negative, the position is obtained by programmatically interacting with an on-chain lending protocol such as BenQi or Banker Joe. In the latter case, if the option $\Delta$ is negative, the short position in the underlying is increased, and if the option $\Delta$ is positive, the short position is decreased.

# Risk Stability Circuit

The interaction between the indifference pricing and the insurance pool is designed to keep the primary pool insolvency probabilities very low. This is, in part, accomplished by charging an additional fee when options are traded. This fee is determined by dynamically assessing potential shortfalls in the trading pool’s ability to fund its liabilities, accounting for trading activity on the platform. Trading fees have the desirable countercyclical property: trading activity increases when volatility is high, and this is also when the ability of the trading pool to fund obligations is most uncertain.

Arrow’s protocol incorporates tools from the frontiers of mathematical finance and statistics, including monetary risk measures, fat-tailed distributions, and statistical learning. To accommodate the necessary computational sophistication, Arrow is built with a hybrid on-chain and off-chain architecture. Computations for asset prices and hedging policies are performed off-chain, while settlement, ownership transfers, tokenized option creation, and execution of hedging strategies are performed on-chain.

The off-chain API has been developed to emphasize upgradability and extensibility, so that the computations necessary to deliver cutting edge performance in terms of demand-based option pricing and dynamic hedging policies can adapt as innovations materialize. To see a discussion of how we are thinking about verification for the off-chain computations, check out our talk at IC3.

Arrow’s Decentralized Autonomous Organization (DAO) will consider proposals to upgrade the aforementioned pricing and hedging mechanisms as needed. The DAO will also manage proposals for the addition of new options markets on new underliers. These proposals will be put to a vote among Arrow’s token holders.

# The Avalanche Web3 Ecosystem

Arrow’s technology will enable the next generation of derivatives markets by delivering decentralized options creation and settlement to Avalanche. A key advantage of building asset creation and settlement capabilities on blockchains is that users of the transaction application comprise the transaction infrastructure, greatly reducing barriers to innovation and access. On blockchains like Ethereum and Avalanche, balances of financial assets are associated with an address and transfer approvals are under control of the user who has a cryptographic key associated with their address. Often, secure wallet applications interact with financial applications to automate this approval process.

Avalanche is the natural base layer for Arrow because of high throughput, near-instant finality, near-zero transaction fees, and front-runner resistance, all of which are enabled by its unique random-sampling consensus algorithm. Avalanche’s average transaction costs are lower than Ethereum despite running the Ethereum virtual machine (EVM) on its C-chain, and is home to a rapidly growing Defi ecosystem.

While Arrow’s option contracts and settlement mechanism are deployed on Avalanche's C-Chain network, a subset of the calculations the protocol makes are handled by specialized nodes. For price oracles, we use Chainlink price feeds, which can be setup for any price reference with a public API. For our pricing and hedging calculations, we use our own custom oracles that run reproducible computations using the pool data and the monetary risk measure. Our oracles are called to generate the indifference prices and updated hedging requirements for new contracts.

Future versions of the Arrow protocol will be extended to incorporate streamlined virtual machines (VMs) like the Avalanche X- chain and custom VMs that target oracalization of underlier data. The protocol can also be implemented in private networks.

# UX and Structured Products

User-friendly options trading tools are at the forefront of Arrow’s vision for empowering users to customize strategies for their market outlooks. Complex trading strategies for speculation and hedging will be precompiled into easy to buy portfolios of options via an intuitive user interface. Specifically, our option recommendation system assumes no prior options trading experience. For speculation, users specify their price forecast and an expiry date, and are presented with a call or put option that maximizes payoff for that expectation. For hedging, users specify an underlier and risk tolerance and are presented with a put option to provide commensurate coverage. We also have a "pro" trading interface that displays the option chain familiar to experienced option traders. Together, these will help options trading break into the DeFi user community.

# Arrow Tokenomics

Arrow's platform token gives owners access to the Insurance Pool, where they can participate as liquidity providers. Being an LP for the insurance pool grants access to the residual premia from the primary pools, including surplus from the hedging portfolios, as well as option creation and transaction fees. In addition, 40% of the platform token fixed total supply will be distributed to token owners actively LPing in the insurance pool over the first two years.

The cost of providing liquidity to the insurance pool is positively related to the overall health of the system, introducing a market mechanism for the cost of providing insurance. When there is more activity in the trading pools, more trading pools, and low insolvency rates for the trading pools, the rewards to providing insurance are high so the value of the platform token is high. The primary pools have a low cost of capital in this case. Conversely, when the trading pools have less activity or higher insolvency rates, the expected rewards to insurance provision are lower, reducing the platform token value and hence reducing the cost of buying into the insurance pool.

Arrow’s platform token also provides access to participation in the DAO voting. The DAO is responsible for updating the Arrow pricing mechanism as improvements materialize and for adding new underlying markets.

# Vision and Pipeline

The Arrow team is working on several important initiatives that will play a role in later versions of the deployment:

1. Performing off-chain computations in a verifiable and trustless manner using SGX, Avalanche’s custom Virtual Machines or another side chain service designed to carry out computations for a variety of applications. See our recent work at IC3 on an SGX implementation.
2. Deep reinforcement learning techniques that optimize the risk stability circuit. We expect this to further optimize prices and improve hedges. Similar techniques are currently being used by sophisticated market makers in traditional options markets like JPM and we are currently developing and backtesting them!
3. Stablecoin-settled options for assets not natively available on Avalanche such as off-chain, cross-chain underliers, or even weather events.
4. Providing a social channel for users to share and follow trading strategies. Web3 technology naturally enables such features and some of their basic forms will show up as early as our trading competition in December!
5. Allowing and incentivizing competition among several pricing algorithms. We are currently working with economists at the University of Chicago to develop such a system.

Disclaimer: Nothing in this document should be construed as a market investment recommendation or as accounting, legal or tax advice. This document is a description of technological capabilities and a vision of how these capabilities can flourish. Specific capabilities or reference outcomes may be subject to regulatory and/or licensing constraints. The designs reflected herein are subject to change.