CLAMM Series 4: Composition of a Tick

CLAMM Series 4: Composition of a Tick

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CLAMM Series 4: Composition of a Tick

Last article we covered the “tick'' which is the smallest functional unit of a CLAMM price range. One of the key takeaways is that a price range can be constructed exactly by depositing equivalent liquidity into a price range’s underlying ticks.

Using this logic, it is more appropriate to discuss CLAMM positions using ticks (which can be generalized for a pool, e.g. ETH/USDC) rather than price ranges (which are specific to an LP e.g. Nutoro has deposited $10,000 in ETH/USDC for $1,800-1,900). Calculations regarding a single tick can simply be repeated for every tick within a given range.

Now onto our next lesson - composition at the tick!

Wot mean Composition?

Liquidity in a tick is used to facilitate swaps for trades that occur within the tick’s range. The composition refers to the combination of assets a tick holds depending on its relationship to the prevailing trading price.

For ETH-USDC, a tick may be composed of $ETH, $USDC, or a combination of both.

Composition of a Tick

In-Range Composition

While $ETH’s price remains within a tick’s range, for example $1,776.50 price for the $1,775-1,780 tick, the composition of the tick will be both $ETH and $USDC.

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If $ETH increases in price the tick will be composed of more and more $USDC since users are swapping it for $ETH.

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This means the composition of a tick will change as the price of $ETH also changes!

Out-of-Range Composition

Above we have outlined that as the price of $ETH increases within a tick, the $USDC composition will increase as traders swap their $USDC for the tick’s $ETH. Intuitively, as the price of $ETH decreases within a tick, the $ETH composition will increase as traders swap their $ETH for the tick’s $USDC.

Now let’s see what happens when the price of $ETH increases or decreases beyond the range of a tick.

Spot Price > Tick

Now let’s say that the price of $ETH has increased to $1,825 which is above the upper bound of the $1,775-1,780 tick.

This can be represented as follows:

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Since the spot price is greater than the upper tick bound of $1,780, the $ETH from the tick has been fully swapped to $USDC as traders are purchasing $ETH.

Now let’s say the price of $ETH is now $1,875.

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Same story - since the spot price is greater than the tick price, the $1,775-$1,780 tick is still 100% $USDC!

Spot Price < Tick

Now let’s take the opposite scenario where the price of $ETH has now fallen to $1,725 which is below the lower bound of the $1,775-1,780 tick:

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Since the spot price is now lower than the lower tick bound of $1,775, the tick has been fully converted into $ETH!

If we move the price to $1,675 we get the same story.

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Spot price lower than tick bounds - we are now 100% $ETH.

Composition of a Range

From our previous lesson we learned that a price range is simply the sum of all individual ticks within the range put together. This means that we can extrapolate the logic above and extrapolate it to the range!

Spot Price > Price Range

As the price of $ETH increases, traders are swapping their $USDC for $ETH across the entire range.

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If the spot price exceeds the upper bound of the range, the position will be 100% $USDC.

Spot Price < Price Range

As the price of $ETH decreases, traders are swapping their $ETH for $USDC across the entire range.

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The opposite happens - if the spot price is lower than the lower bound of the range, the position will be 100% $ETH.

Spot Price is within Price Range

Now let’s take the spot price and put it inside the price range.

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As we discussed in In-Range Composition, the price range will be composed in parts $ETH and parts $USDC.

Now as we know, the functional unit of the price range is the tick so it should really be an assessment of composition of ticks within that range:

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As you can see, the position can be broken down into three overarching compositions:

  1. Ticks where Spot Price < Tick are 100% $ETH
  2. TIcks where Spot Price is within Tick are composed of both $ETH and $USDC
  3. Ticks where Spot Price > Tick are 100% $USDC

Absolutely incredible!

Closing Comments

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This lesson we covered the composition of a tick as its relationship with the spot price changes. Important takeaways are:

  1. Composition of the tick depends on the relationship between spot price and the tick
  2. If the spot price is within the tick (i.e. in-range), the composition will be both $ETH and $USDC
  3. If the spot price < tick, the composition is 100% $ETH
  4. If the spot price > tick, the composition is 100% $USDC
  5. The above logic can be extrapolated to a price range by comparing each tick with the spot price

How fascinating indeed.

Next lesson we will introduce the mythical beast of impermanent loss and mayhaps finally tie it all back to what in Nutoro’s name this all has to do with Dopex v2.

Until next time, my beloved readers.

Warm regards,

CEO

About Stryke

Stryke is a decentralised options protocol that focuses on maximising liquidity and enhancing gains for option buyers while minimising losses for option writers—all in a passive approach.Stryke employs option pools that enable anyone to effortlessly earn yield. The protocol provides value to both option sellers and buyers by ensuring equitable and optimised prices for options at various strike prices and expiries, achieved through our proprietary, cutting-edge option pricing model designed to mirror volatility smiles.

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