# THEO Protocol - v1.1

Abstract: This litepaper introduces a conceptual framework as to how Hxro Network’s options liquidity protocol, THEO, can build institutional exchange grade liquidity in a standardized on-chain options market. With theoretical volatility surface data aggregated from independent pricing nodes, THEO utilizes portfolio optimization with advanced risk management to efficiently build options liquidity across digital assets.

## Introduction

Options markets are more dynamic than traditional spot and futures markets. They exhibit more complex, non-linear risk characteristics. From each underlying asset derives a countless number of listed options contracts: there are several expiration dates that span weeks, months, and years into the future, all containing a wide range of strike prices.

The leading options liquidity providers (market makers) are tasked with continuously pricing hundreds (even thousands) of options on one underlying asset and streaming automated two-sided price quotes to the market, while managing the multidimensional risk of a dynamic options portfolio.

Each proprietary options pricing model is different from the next, generating theoretical values (commonly referred to as "theos") that vary between market participants. The trade execution price is where theoretical value meets real value, as the best liquid bid and offer in the order books represent the prices that can actually be traded, determining the real value of risk that transfers from one participant account to another.

The fundamental goal of the options market maker is to consistently buy options below their theo values and sell options above their theo values, accruing theoretical edge in the options portfolio. With sufficient trade volume (market liquidity) and proper risk management, accrued theoretical edge can become realized profits as positions are closed through trading and/or contract expiration. The best market makers are extremely successful at converting theoretical edge to realized profits while reducing the overall risk of the options portfolio.

## Decentralized Options

It is our belief that DeFi has proven its product/market fit and decentralized exchanges will become a leading form of exchanging assets and risk in the future. Decentralized options liquidity and trade volume will grow multiples from where it stands today.

Disintermediation and self-custody of one’s digital assets are foundational pillars of decentralized finance, expanding the limits and efficiencies of asset exchange. Participants in the Hxro Network will have access to institutional grade options liquidity with instant settlement while maintaining control of their assets.

Decentralized options markets face several obstacles as they currently stand: liquidity consistency issues, capital inefficiency, prohibitive fee structures, and high latency. Most blockchain networks are not built to support an advanced, low latency derivatives marketplace. High fees and latency have plagued the on-chain options offerings to date.

Hxro Network is building THEO on Solana, a blockchain network that supports high performance with low fees. Solana can process 50,000 transactions per second with 400 millisecond block times (with potential for sub-200 millisecond block times in the future). Fees on the Solana network are extremely low, making high transaction volume applications possible without the need for layer two solutions.

## Liquidity

THEO protocol addresses the liquidity consistency problem with a hybrid AMM / Order Book (via Serum) design for standardized cash-settled european call and put options. These standardized contracts can be managed in a portfolio with the most actively traded crypto options on centralized exchanges, enabling simpler cross-exchange arbitrage, which greatly improves price competitiveness and overall liquidity.

Although standardized or “vanilla” options will be the first listed contracts, THEO protocol is designed to manage the mint/burn, valuation, collateralization, settlement, and liquidation of derivatives with a variety of settlement specifications. Other option contract types will be listed in the future, adding incremental liquidity to the network.

THEO AMM will provide bids and offers across all strikes and expiries while other market makers inject quotes in the same order books, competing for order flow. Hxro Network composes with Serum to utilize the most powerful on-chain central limit order books as a robust secondary market for the token contracts minted by THEO protocol.

There is a Liquidity Pool for each underlying asset with listed options contracts. Participants that contribute capital to liquidity pools earn a significant share of all trading fees collected and also share in additional pool-specific reward distributions. As more capital enters the liquidity pools, THEO AMM’s options markets become deeper and more competitive.

## THEO Automated Market Maker (AMM)

THEO AMM is designed to optimize how capital is used in its liquidity pools, with dynamic pricing and quote sizing to balance return on capital with risk.

Serving as a primary liquidity provider to the protocol, THEO AMM streams automated two-sided price quotes to the order books of all listed options markets in the network.

A theoretical volatility surface is aggregated from independent Surface Provider nodes in the Hxro Network. The Surface Provider nodes stream theoretical values (theos) for listed options across all strikes and expirations. This zero-preference THEO volatility surface is the foundation for generating two-sided price quotes for all listed options. Quote sizes, widths, and value adjustments to THEO are based on different risk factors, including the amount of capital in the LP, the portfolio inventory of the LP, the volatility of volatility (vol of vol), and the state of liquidity in the options market and underlying market.

THEO uses automated delta-hedging with the underlying asset to manage the directional risk of the LP. For example, when BTC options trades are executed, THEO buys or sells spot BTC or BTC futures, composing with Solana network protocols to remain “delta-neutral.” If THEO sells 10 BTC calls that have a 50-delta, it will buy 5 BTC in the futures or spot market to hedge the directional risk of the options trade. As the price of the underlying asset changes over time, THEO continues to manage the overall directional risk of the portfolio by hedging residual deltas from open positions.

## Network Liquidity Incentives

Solving for liquidity consistency problems is not unique to on-chain markets. In traditional markets, exchanges set out to enlist several market makers who agree to continuously provide deep liquidity with a competitive bid/ask spread for hedgers and speculators to execute against. These market makers are often compensated by the exchange based on factors such as volume traded, time in market and quote width. With enough market maker liquidity and hedger/speculator activity, this creates a positive feedback loop where more market participants transact because of the ability to access deeper liquidity and enter/exit larger positions with tighter market spreads. In return, these enlisted market makers are incentivized with various monetary rewards, including fee discounts, maker/taker rebates, and lucrative volume-based rebates.

Hxro Network incentives are designed to attract active participation from strong liquidity providers and hedgers/speculators resulting in competitive two-sided quotes in all listed options markets.

All network trading fees flow to staked HXRO token holders. Incentives are designed so the most active network participants earn an increased share of the distributed fees and rewards. This creates a powerful incentive structure for strong liquidity providers in the options markets to become active in the markets and liquidity pools.

There are four stakeholders in the options liquidity model, all of whom are incentivized to act in the best interest of the network. All transaction fees are shared among stakeholders, with 10% going to the Hxro Network treasury (this amount can be changed through governance).

The first stakeholder is the market taker (hedger and/or speculator) who takes directional views on the market, paying trading fees while often crossing the bid/ask spread. All else equal, hedgers and speculators prefer competitive price quotes (tighter markets) and consistently deep liquidity where they can enter and exit positions with speed and efficiency. While individual market taker results will vary, on average, the expected value of each taker transaction is negative after fees. This is because most taker orders cross the bid/ask spread and the executed price is above or below the market’s implied theoretical value, often referred to as theoretical edge for market makers. Takers that stake HXRO benefit from reduced transaction fees and a share in network transaction fees.

The second stakeholder is the Liquidity Pool participant which contributes capital (liquidity) to the pool for a given underlier. The LP does not pay the trading fees for any markets in which THEO AMM provides liquidity. The LP captures value from sharing in the network trading fees collected and any theoretical edge accrued in the market by THEO AMM. As more capital is contributed to the liquidity pools, the options markets become deeper and tighter, creating more efficient trading conditions for all market participants. In turn, this increases network trading fees collected, enhancing fee share to the LP and other stakeholders.

THEO employs a delta-neutral strategy to manage directional risk while quote pricing and sizing is dictated by its portfolio optimization utility function.

The third stakeholder is the SP (Surface Provider) - nodes that provide real-time theoretical volatility surface values to the network. We envision several independent oracle-type nodes that submit volatility surfaces (theoretical prices) directly to THEO for a given underlying asset. The SPs are incentivized by earning a portion of the trading fees.

The fourth and last stakeholder is the GT, made up of the Governance Token Holders. HXRO token holders who stake their tokens have voting rights in the governance of the Hxro Network. The GT sets and periodically adjusts certain parameters of the protocol to ensure that it remains in a state of equilibrium i.e. LPs are generating sufficient return on capital, speculators aren’t paying excessive fees and a competitive SP market exists. The GTs would further control the protocol treasury and use this for future developments to THEO and on-chain options liquidity.

## Capital Efficiency

One of the main challenges in options markets comes from the dynamic nature of the contract values that vary over time in relation to both the price and volatility of the underlying asset. Sellers of options contracts (also called writers) are often required to commit significant capital as collateral for long periods of time (until contract expiration or the closing/liquidation of the open positions).

The most advanced options markets utilize different variations of risk-based margin systems to allow for improved capital efficiency among liquidity providers and market participants. This is not an exact science and is difficult to achieve without including sufficient margins of error.

In Hxro Network, the listed options for each underlying asset have pooled risk across strikes and expirations. This allows for improved capital efficiency when a market participant’s short positions are partially or fully offset by correlated long positions in the same underlying asset pool.

A market participant that is long or short a vertical put spread (long one put and short one put) should not be required to post full collateral on both individual options positions. Combined, this position has limited risk. Long options positions can offset the unlimited risk profile of short options positions.

A market participant that is long or short a 5-month / 6-month calendar call spread should not be required to post full collateral on both individual options positions. At the current point in time, the 5-month option is very highly correlated with the 6-month option, so the risk of maintaining the calendar spread position is relatively small - much smaller than maintaining full collateral on the short-leg. As the 5-month expiration approaches, the two options become less and less correlated, so the risk of the calendar spread position increases in most cases, depending on the price of the underlying.

THEO’s risk-based collateral system uses a set of two-dimensional market shocks to help calculate a range of real-time collateral values - shocks that would significantly change the net liquidation value of any open positions. Extreme movements in both underlying price and implied volatility levels determine hypothetical profit/loss scenarios, which dictate the collateral requirements for maintaining the open positions along with expected liquidation levels.

## Automated Market Maker (AMM) Background

In traditional finance, automated market making systems have been operational in the options markets for decades. The Chicago Board Options Exchange (CBOE) became the first marketplace for listed options almost 50 years ago, in 1973. Into the early 2000’s, there was an “Auto-quote” terminal in each trading pit that housed a standard options pricing model and disseminated automated quotes for all of the options listed in the pit. For years the auto-quote terminal was managed by the independent market makers in each pit - typically the strongest or most vocal market makers would manually update system parameters at the terminal throughout the trading day. Market makers could also call out specific bid/ask markets to the pit’s quote reporters who would then take those markets off “auto-quote” for a period of time and post the open outcry markets instead.

In 1999, the exchange began awarding control of quote dissemination to a “Designated Primary Market Maker” (DPM) for each trading pit. The DPM was the one entity responsible for guaranteeing automated two-sided quotes in all of the options markets listed in the pit - similar to a back-stop liquidity provider. This model existed at all the largest exchanges: at the AMEX they were called “Lead Market Makers” and at the NYSE they were called “Specialists.”

A critical function of any exchange is to ensure that there are liquid, executable markets available at all times. By awarding a leadership role to one well-capitalized market making entity for each pit (group of assets), the exchanges sought to guarantee consistent, competitive and reliable liquidity provisioning for all listed assets.

In the following years, with the advancement of electronic trading technology, a new “hybrid” automated market making system took shape allowing for all of the individual market makers to submit streaming automated price quotes to the exchange from their own servers. There was still a DPM or lead market maker in each pit that served as the backstop liquidity provider, but there were several liquidity providers streaming automated quotes to the order books in all markets. (https://www.cboe.com/about/history/)

# Markowitz Portfolio Utility Function for THEO AMM

## Single option case

Consider the following utility function which balances returns on capital with risk, $M=G-0.5*\lambda*V$ where G is expected gain in capital, is a risk aversion parameter and V is the variance of G. We seek to maximize M.

For a given option, since we expect to close the position for theoretical value, $G=E(theo-p0)*q=(E(theo)-p0)*q$, where theo is the theoretical value, p0 is our original trade price and q is our position size. Over a short enough time duration where we can ignore the effect of theta and with a delta-hedged position, $E(theo)=theo$, therefore $G=theo-p0*q$ .

Next, assuming a delta-hedged position and negligible effect of theta, $dTheo=dIv*(dpnl/dIv)$ and , therefore, $dCapital=dIv*vega*q$ . Assuming implied volatility is normally distributed, the variance of capital is then $Variv*vega^2*q^2 = vov^2*vega^2*q^2$ , where iv is the annualized implied vol of the option and vov is the annualized vol of implied vol of the option.

## Numerical example

You have a capital pool of $1,000,000. Consider option BTC-24SEP21-32000-P with mark iv of 109.59, mark theo of 0.15 btc ($5,830) and vega of 73.68. Assume annualized vol of vol is 200. You want to trade this option with the intention of holding this position for 24 hours. How much should you buy if you want less than 15% probability of losing no more than 1% of your capital on this trade?

## Multiple Instruments

We can extend the above result to multiple instruments by replacing q with a vector of quantities for each instrument q, edge theo-p0 with a vector of edges e, and Var with a covariance matrix $\sum$ , s.t $\sum=[v_1^2 ... v_n*p_n*v_1 v_1*p_1n*vn ... v_n^2]$ We then get that $q=1/\lambda*\sum^-1*e$ .