LP Position
Learn about LP positions, margining, LP Health, and the conditions leading to liquidation.
Once liquidity provider (LP) adds liquidity to a Vol-range AMM, he receives an LP position in return. He can monitor, manage or close his LP position at any time.
In addition to monitoring profit and risk factors, an essential aspect of the LP position is LP Health. If the LP Health falls below a predefined threshold, similar to the process of user account liquidation, the LP position becomes susceptible to liquidation.
Let's start with what's inside of LP position.
Structure
Adding liquidity consists of borrowing funds from the Margin Pool and providing available cash ($USD) from the Margin Account to the LP position.
For call markets, borrowed funds (ETH) are divided into long option and short option tokens where the following formula is always true:
For put markets, $USD is borrowed and divided to long option and short option tokens using the formula:
Longs, shorts, and cash is added to LP position, and their balances are tracked by the AMM. Debt created by the opening of LP position is part of the margin account.
Dynamics
On each new trade, long and cash balances are updated, while the short balance remains the same. When a trader buys options, the LP position's long balance decreases and the cash balance increases. When a trader sells options, the long balance increases, while the cash balance decreases. The LP position serves as a counterparty to a trader.
It's important to note that when the LP position is opened, the delta remains at 0 until a trade occurs. The LP position incurs some negative theta from borrowing the funds in the form of an interest rate.
Before we delve into the details of how the LP position is margined, let's compare the two most commonly used margin systems: cross-margin and isolated.
Cross-margin vs. Isolated Margin
When a user opens a short option position or a futures position, they can borrow funds from the Margin pool to gain leverage. All of the user’s positions are cross-margined, meaning they can offset each other. For example, if a user sells 1600 call option and buys 2000 call option, their risk is limited, and if they maintain enough assets in their margin account, their account can never be liquidated. In another scenario, a single short position could wipe out their entire margin account. Cross-margining means that all their positions and assets, such as USD and ETH, are netted out.
In contrast, when dealing with isolated margin, assets are allocated to cover each specific position. Multiple positions aren't offset against each other. Isolated margin allows users to isolate risky positions and protect the rest of their margin account assets and positions from liquidation.
LP Position Margining
LP positions are part of the account margin and are cross-margined with all the other longs, shorts, and LP positions. However, they are also isolated, meaning that assets are allocated specifically for each LP position, which is subject to LP position liquidation.
Asset allocation provides LPs with an easy to way to limit the risk exposure associated with LP positions, and protect the rest of their margin account.
To understand when can LP position be liquidated, we first need to understand LP Health.
LP Health
The key to understanding LP position is the term LP health, expressed using the following formula:
where Required represents the cash ($USD) needed to buy all the options in the range, and Actual is the sum of available cash in the LP position and cash that LP would receive if he would sold all the options in their sell-side subrange.
LP Health is the ratio between Actual cash and Required cash, expressed as a percentage. LP Health must always be maintained above a 125% threshold; otherwise, the LP position becomes eligible for liquidation.
Let's delve deeper into how LP Health is calculated and its implications.
Price Above Range
Let's take a look at the following example:
- Options in range: 10 options,
- Range: 40% - 42%,
- Current volatility: 42%, above range,
- Cash reserves: $1000,
- Option price: $50.
In the above example, the LP is buying 10 options within the 40% to 42% volatility range, and they have $1000 available for this purpose, while the required amount is $500. The LP Health calculation in this case is as follows:
LP Health = $1000 / $500 x 100% = 200%
In this scenario, the LP position has sufficient cash, and therefore, it cannot be liquidated.
The example provided was straightforward, where the current volatility was above the specified range, indicating that the LP was only buying options. Now, let's explore how to calculate LP Health when the current volatility is within the specified range.
Price In Range or Below Range
Let's examine another example:
- Options in range: 10 options,
- Range: 40% - 42%,
- Current volatility: 41%, in range,
- Cash reserves: $750,
- Option price: $50.
In this example, given that the current volatility falls within the middle of the specified range, the LP is doing the following:
Buying 5 options within the [40%, 41%] subrange.
Selling 5 options within the [41%, 42%] subrange.
Once again, the required amount is (10 x $50) = $500, and the actual amount is the sum of available cash and the cash that would be received if 5 options were sold on the sell side. The actual amount is calculated as follows: $750 + (5 x $50) = $1000. As a result, the LP Health remains unchanged at 200%, computed as:
LP Health = $1000 / (10 x $50) x 100% = 200%.
A key takeaway from this example is that LP Health doesn't fluctuate significantly with changes in volatility; it primarily changes when other parameters of the Black-Scholes formula change. The primary driver for potential LP position liquidation is the underlying price, and we can determine it using the LP Health formula in combination with the Black-Scholes model.
Before we explore when LP positions are liquidated, let's understand what happens during the liquidation process.
LP Liquidation
When an LP position is liquidated, it is withdrawn from the AMM market, and it ceases to be a part of the liquidity pool. The LP user incurs a $300 penalty, which is credited to the liquidator's account.
As for the balances within the liquidated LP position:
All balances are transferred back to the LP's margin account.
Long option and short option tokens are merged back into the underlying asset.
Any outstanding debt is repaid.
If the LP user had existing long or short positions in their margin account, these positions are netted out with the remaining longs and shorts from the LP position. Again, any remaining debt is repaid in this process.
Following the closure or liquidation of the LP position, the LP user is either left with a long or short option position, but not both, as everything is netted out.
In summary, after LP liquidation:
Delta, Gamma, and Vega of the margin account remain unchanged.
Theta is reduced due to the repayment of debt.
Liquidation Price
The liquidation price is the underlying price at which an LP position can be liquidated. To determine this price, we first identify the option price at which the LP Health falls below 125%. Then, we perform a reverse Black-Scholes calculation to find the corresponding underlying price.
Let's revisit our first example: the option price that would reduce LP Health to 125% is $80, because:
LP Health = $1000 / (10 x $80) x 100% = 125%.
Next, we can calculate the underlying price at which the option price is $80. This calculated value represents the LP Position's liquidation price. For call options, the liquidation price should be higher than the current underlying price, while for put options, it should be lower.
Even before opening an LP position, you can easily find the liquidation price on the chart (indicated by the red dashed line) using our app:
The LP Liquidation penalty is just one of the risks associated with maintaining an LP position. In our next post, we'll delve further into the various other risks involved in being an LP on Gamma Options.
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