Moby Preview(4): Risk Premium, The Mother of Tight Spread and Risk Hedging
1. Intro: Options, Order Book and AMM
Options are a critical derivative in financial markets, providing the right, but not the obligation, to buy (Call Options) or sell (Put Options) an underlying asset at a predetermined price (Strike Price) at a specific future date (Expiry). The options buyers pay the option seller a premium for this right, with the sellers obligated to settle the difference between the strike price and the price at expiration if the option is exercised.
Investors utilize options for hedging against price volatility or for speculative purposes. Buyers can leverage options to bet on market directions or mitigate potential losses on their existing spot/futures positions by paying only a fraction of the underlying asset’s price. On the other hand, sellers can earn fixed premiums with relatively lower risk than buyers. Unlike futures and forwards, where both parties have contractual obligations, options offer only the right to exercise, leaving the decision entirely with the option buyer.
Options are highly leveraged instruments with an insurance-like nature, making them a favorite among institutional investors in traditional financial markets. This significance extends beyond traditional markets, as evidenced by the increasing trading volume of options in the cryptocurrency market, driven by the popularity of 0DTE (Zero Days to Expiry) options.
However, crypto options markets remain challenging for institutions and individual traders due to high inefficiencies from low liquidity. In leading crypto options exchanges like Deribit, trades are executed using an order book system (like in TradFi), where buyers list their maximum bid price and quantity, and sellers list their minimum ask price and quantity. The highest bid price is the Best Bid Price, and the lowest ask price is the Best Ask Price.
To execute an immediate trade, buyers must use the Best Ask Price, and sellers use the Best Bid Price. For short-term profitability, the Best Bid Price at the position closing should be higher than the Best Ask Price at entry. However, the Best Ask Price is always equal to or higher than the Best Bid Price, with cryptocurrency options often having a larger Bid-Ask Spread compared to traditional financial markets due to lower liquidity. This large spread hinders short-term profit potential and deters individual and institutional investors.
Efforts to improve the Bid-Ask Spread in order book systems and address liquidity issues have largely focused on decentralized finance (DeFi) environments, leveraging Automated Market Maker (AMM) mechanisms. AMM-based exchanges eliminate the need for matching engines by acting as counterparties themselves, offering immediate position openings at calculated prices. This approach provides capital-efficient spreads compared to order book-based exchanges.
Despite the advantages, AMM-based exchanges require substantial liquidity pools to support the counterparty roles for both buy and sell positions, exposing them to various risks associated with holding option positions.
This article introduces methods to minimize risk exposure for AMM-based exchanges while offering competitive Bid-Ask Spreads. We start by analyzing existing AMM-based models and then introduce the “Risk Premium” model. This model will quantitatively analyze the factors affecting Bid-Ask Spreads in crypto options markets and conduct simulations to optimize parameters that balance risk and spread competitiveness.
2. Existing AMM-based models
Leading DeFi options exchanges like Premia v2 and Lyra Finance pioneered using AMM models for crypto options trading. This section will analyze how these projects implemented their AMM models and managed the risks associated with liquidity pools.
2.1 Premia v2
Premia v2, operating on Arbitrum, a Layer 2 solution on Ethereum, offers Call/Put options for assets like BTC, ETH, and ARB. Options traders can only take buy positions, with the liquidity pool acting as the counterparty, thus taking sell positions. Users can indirectly take sell positions by providing liquidity to the pool.
Premia v2 determines the fair option price using the Black-Scholes model, adjusted by a coefficient C* (reflecting the price impact of the option size on the pool). Parameters for Black-Scholes include spot price, strike price, DTE, IV, and risk-free rate, with IV sourced from their IVOL Surface Oracle.
The fair price is linearly adjusted by the initial price level coefficient, ‘C.’ When fair price*C deviates from the actual option price, it influences the pool’s supply-demand balance, adjusting the C level to converge the fair price with the market price. Additionally, Premia v2 applies a slippage coefficient, g(x), to manage the marginal cost of large trades and prevent sudden pool supply reductions.
2.2 Lyra Finance v1
Lyra Finance v1, based on Arbitrum and Optimism, offers both buy and sell positions for BTC and ETH options. Similar to Premia v2, its liquidity pool acts as the counterparty, exposing it to multiple risks.
Lyra Finance v1 categorizes these risks primarily as Delta Risk and Vega Risk, each with specific management mechanisms. Delta Risk is managed by ensuring the pool remains delta-neutral through spot/futures positions on other exchanges.
At the same time, Vega Risk is controlled by adjusting premiums based on the pool’s Vega exposure. However, Lyra Finance v1 does not address other Greeks Risks like Theta Risk and incurs additional costs for hedging Delta Risk.
3. Risk Premium Model and its mechanism
In the case of Premia v2, it prevents options tradings that can have a sudden impact on the Liquidity Pool based on the slippage coefficient; there is a problem that it cannot properly hedge the risk that occurs when the Liquidity Pool takes an option selling position. Furthermore, in the case of Lyra Finance v1, the Liquidity Pool exposure risk is divided into Delta Risk and Vega Risk. It has a mechanism to adjust the risk of these two. Still, it has limitations in that the Liquidity Pool is defenseless against other types of Greeks Risk such as Theta (sensitivity of option price according to time change) Risk, and additional transaction costs are incurred according to the current/futures position to hedge the Delta Risk.
Thus, Moby introduces the “Risk Premium Model” that further develops the methodology of existing AMM-based projects. The Risk Premium is calculated based on the direction and level of impact of the new option position on the Delta, Vega, and Theta Risk of the Liquidity Pool. The specific calculation method of the Risk Premium can be organized through the formula and calculation order below.
- Determine UG: Calculate Unit Greeks based on the size and risk of the options position held by OLP before and after each trade
- Determine Direction: Calculate the direction of risk by comparing the magnitude and symbol of the OLP’s risk before and after each trade
- Determine Weight: Determine the weight of the Greeks based on the type of Greeks and the timeframe of the OLP
- Determine UR Mul: Calculate the UR Mul that causes the Risk Premium to increase rapidly when the Utility Ratio of OLP exceeds a certain threshold
- Determine Market Factor: Calculate a set of factors such that the Risk Premium may have a tendency similar to the market spread (from CEXs). Those factors are determined based on each option position’s spec, including Moneynes, DTE, Underlying Asset, Call/Put, etc
Meanwhile, the Fair Options Price in the Risk Premium is calculated based on the Black-76 equation that uses futures as the price of the underlying asset, unlike the Black-Scholes equation, which calculates the Greeks of each option and the Greeks of the entire Liquidity Pool. The same is true when. In this case, the price provided to the Long Position (Ask Price) is the Fair Options Price plus the Risk Premium, and in the case of the price provided to the Short Position (Bid Price), the Fair Options Price minus the Risk Premium is used to form an artificial Bid/Ask Spread.
The Fair Options Price is not applied to the Long/Short Position, and the Risk Premium is used to create a gap to prevent the Greeks Risk of the Liquidity Pool from being biased to one side. In other words, in the case of an option position that increases the Greeks Risk of the Liquidity Pool, the Risk Premium is calculated significantly, which increases the size of the paid premium in the case of a buy position and decreases the size of the received premium in the case of a sell position, thereby inducing traders to avoid option transactions that increase the Greeks Risk.
In addition to increasing the Greeks’ Risk of the Liquidity Pool as described above, the goal that the Risk Premium should achieve is to provide a competitive spread compared to the market’s Bid/Ask Spread or the Bid/Ask Spread of a centralized exchange such as Deribit. The risk premium model aims to achieve this by applying a coefficient such as the market factor or by adjusting the Greeks weight, which is the main parameter of the risk premium.
First, the Market Factor is calculated based on the trader’s position and market conditions, not the Greeks’ Risk of the Liquidity Pool. By applying the Coefficient, the Risk Premium can hedge the Risk of the Liquidity Pool. By reflecting the characteristics of the actual market’s Bid/Ask Spread, the Risk Premium contributes to providing a cheaper Spread than competitors with a high probability.
The elements that make up the Market Factor can be summarized as follows.
- RP Mul: The Multiplier that allows Risk Premium to be calculated differently depending on Moneynes and DTE of a specific options position
- Underlying Ratio: Factor to reflect the tendency that the Market Spread to appear differently depending on the Underlying Asset
- Call/Put Ratio: Factor to reflect the tendency that Market spread to appear differently depending on the Call/Put
- Market Volatility Ratio: Factor that reflects the tendency that Market Spread can be changed significantly when the Underlying Asset’s Real Volatility increases rapidly
RP Mul, which plays the most important role in deriving the Market Factor, is a factor that reflects the general tendency that market spreads become tighter when the DTE of an option is long. When checking actual data, it is observed that the spread becomes narrower as the Date-To-Expiry gets longer, not only for 50 Delta options but also for 25 Delta options.
In addition, to analyze the correlation between Moneyness and market spread when Date-To-Expiry is fixed, the study performed a polynomial regression analysis on the past market spreads of centralized exchanges such as Deribit, OKX, and Bybit against Moneyness. As a result, as shown in Figure (1) below, the market spread could be approximated using a second-order polynomial for Moneyness at a confidence level of 50% or higher, and the RP Mul function for individual DTEs could be derived based on this. Furthermore, the final risk premium sufficiently reflected the increasing moneyness as it moved away from 0.5 (ATM situation).
Next, a simulation was conducted to adjust the Greeks Weight, the main parameter of Risk Premium, based on the Market Factor determined as above. The simulation was conducted using a random transaction sample based on Historical Data and Random Walk data of the price of the underlying asset and option trading tendencies.
- L/S: Long/Short Preference (Preference for option position direction)
- C/P: Call/Put option preference
- A/O: Moneyness preference (Near ATM / Far OTM preference)
- D/W/M: Date-To-Expiry related preference
Afterward, we set the objective function for Target Spread and Risk Premium according to transaction preference. We conducted Greek weight estimation based on GMM (Generalized Method of Moments), which adjusts the objective function to be close to 0. As a result of the simulation, as shown in Figure (3), it was confirmed that it is possible to stably maintain the Greeks Risk of the Liquidity Pool while providing a narrow spread compared to the Bid-Ask Spread of the comparison group (centralized exchange) in 50–80% of the total executions, as shown in Figure (4).
Moby Preview Series:
(1) Why Crypto Options and How Moby Changes the Market
(2) Synchronized-Liquidity-Engine(SLE), The Core Engine of Moby
(3) Options Pricing Model & Greeks
(4) Risk Premium, The Mother of Tight Spread and Risk Hedging
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Moby: The Next Options Protocol with Maximized Liquidity
• More than 1,000x leverage without liquidation for traders
• Accurate options price based on real-time IV and Futures data
• Dynamic risk premium based on LPs’ real time Greeks risk to provide narrow spread
• Tokenized options positions to integrate with other DeFi, RWA and structured products
• TradFi style infra (Prime Brokerage, Clearing House) to boost capital efficiency
