wip

foundry.toml

@@ -2,6 +2,7 @@
 remappings = [
   "solmate/=lib/solstat/lib/solmate/src/",
   "solstat/=lib/solstat/src/",
+  "pendle/=lib/pendle-core-v2-public/contracts/"
 ]
 solc_version = "0.8.22"
 

src/CoveredCall/CoveredCall.sol

@@ -17,7 +17,7 @@ import {
     decodeControllerUpdate
 } from "src/CoveredCall/CoveredCallUtils.sol";
 import { EPSILON } from "src/lib/StrategyLib.sol";
-import "forge-std/console2.sol";
+import { IStandardizedYield } from "pendle/interfaces/IStandardizedYield.sol";
 
 enum UpdateCode {
     Invalid,
@@ -191,8 +191,6 @@ contract CoveredCall is PairStrategy {
         int256 computedInvariant =
             tradingFunction(pool.reserves, computedL, params);
 
-        console2.log("Computed Invariant: {}", computedInvariant);
-
         if (computedInvariant < 0 || computedInvariant > EPSILON) {
             revert InvalidComputedLiquidity(computedInvariant);
         }

src/SYCoveredCall/README.md

@@ -0,0 +1,172 @@
+# Log Normal Market Maker
+This will be all the background needed to understand the `LogNormal` DFMM.
+
+## Conceptual Overview
+The `LogNormal` DFMM provides the LP with a a log-normal shaped liquidity distribution centered around a price $\mu$ with a width given by $\sigma$.
+
+Note that this strategy can be made time-dependent by an additional $\tau$ parameter that is the time til the pool will "expire".
+In this case, the LN trading function provides the LP with a payoff that is equivalent to a Black-Scholes covered call option with strike $K = \mu$, implied volatility $\sigma$, and time to expiration $\tau$. 
+We do not cover this explicitly here.
+
+## Core
+We mark reserves as:
+- $x \equiv \mathtt{rX}$
+- $y \equiv \mathtt{rY}$
+
+`LogNormal` has two variable parameters:
+- $\mu \equiv \mathtt{mean}$
+- $\sigma \equiv \mathtt{width}$
+- These parameters must satisfy:
+$$\mu > 0\\
+\sigma > 0$$
+
+The trading function for this DFMM is given by
+$$\begin{equation}
+\boxed{\varphi(x,y,L;\mu,\sigma) = \Phi^{-1}\left(\frac{x}{L}\right)+\Phi^{-1}\left(\frac{y}{\mu L}\right)+\sigma}
+\end{equation}$$
+where $L$ is the **liquidity** of the pool.
+
+Given the domain of $\Phi^{-1}$ ([inverse Gaussian CDF](https://en.wikipedia.org/wiki/Normal_distribution)) we can see that $x\in [0,L]$ and $y\in [0,\mu L]$.
+As the pool's liquidity increases, the maximal amount of each reserve increases and both are scaled by the same factor, which is also how we decide how to compute fees.
+
+## Useful Notation
+We will use the following notation:
+$$\begin{equation}
+d_1(S;\mu,\sigma) = \frac{\ln\frac{S}{\mu}+\frac{1}{2}\sigma^2 }{\sigma}
+\end{equation}
+$$
+$$
+\begin{equation}
+d_2(S;\mu,\sigma) = \frac{\ln\frac{S}{\mu}-\frac{1}{2}\sigma^2 }{\sigma}
+\end{equation}
+$$
+
+## Price
+We can provide the price of the pool given either of the reserves:
+$$\begin{equation}
+\boxed{P_X(x, L; \mu, \sigma) = \mu \exp\left(\Phi^{-1} \left(1 - \frac{x}{L}\right) \sigma  - \frac{1}{2} \sigma^2 \right)} 
+\end{equation}$$
+
+$$\begin{equation}
+\boxed{P_Y(y, L; \mu, \sigma) = \mu \exp\left(\Phi^{-1} \left(\frac{y}{\mu L}\right) \sigma + \frac{1}{2} \sigma^2 \right)}
+\end{equation}$$
+
+Note that other DFMMs such as the `GeometricMean` have a price that can be determined from both reserves at once, so we typically do not write $P_X$ and $P_Y$.
+
+## Pool initialization
+When the pool is initialized, we need to determine the value of $L$ and the other reserve.
+The user will provide a price $S_0$ and an amount $x_0$ or an amount of $y_0$ that they wish to tender and we can get the other reserve and $L$ from the trading function.
+
+We can recall that get that:
+$$\begin{equation}
+\frac{x}{L} = 1-\Phi((d_1(S;\mu,\sigma))
+\end{equation}$$
+and
+$$\begin{equation}
+\frac{y}{\mu L} = \Phi(d_2(S;\mu,\sigma))
+\end{equation}$$
+
+### Given $x$ and price
+Suppose that the user specifies the amount $x_0$ they wish to allocate and they also choose a price $S_0$.
+We first get $L_0$ using (6):
+$$\begin{equation}
+\boxed{L_0 = \frac{x}{1-\Phi(d_1(S;\mu,\sigma))}}
+\end{equation}$$
+From this, we can get the amount $y_0$ 
+$$
+\boxed{y_0 = \mu L_0 \Phi(d_2(S;\mu,\sigma, \tau))}
+$$
+
+
+### Given $y$ and price
+The work here is basically a mirrored image of the above.
+We get $L_0$:
+$$\begin{equation}
+\boxed{L_0 = \frac{y}{\mu\Phi(d_2(S;\mu,\sigma))}}
+\end{equation}$$
+Suppose that the user specifies the amount $y$ they wish to allocate and they also choose a price $S$.
+Now we need to get $x$:
+$$\boxed{x_0 = L_0 \left(1-\Phi\left(d_1(S;\mu,\sigma)\right)\right)}$$
+
+## Allocations and Deallocations
+Allocations and deallocations should not change the price of a pool, and hence the ratio of reserves cannot change while increasing liquidity the correct amount.
+
+**Input $\Delta_X$:** If a user wants to allocate a specific amount of $\Delta_X$, then it must be that:
+$$
+\frac{x}{L} = \frac{x+\Delta_X}{L+\Delta_L}
+$$
+which yields:
+$$
+\boxed{\Delta_L = L \frac{\Delta_X}{x}}
+$$
+Then it must be that
+$$
+\boxed{\Delta_Y = y\frac{\Delta_X}{x}}
+$$
+
+**Input $\Delta_Y$:** To allocate a specific amount of $\Delta_Y$, then it must be that:
+$$
+\frac{y}{\mu L} = \frac{y+\Delta_Y}{\mu(L+\Delta_L)}
+$$
+which yields:
+$$
+\boxed{\Delta_L = L \frac{\Delta_Y}{y}}
+$$
+and we likewise get
+$$
+\boxed{\Delta_X = x\frac{\Delta_Y}{y}}
+$$
+
+## Swaps
+We require that the trading function remain invariant when a swap is applied, that is:
+$$\Phi^{-1}\left(\frac{x+\Delta_X}{L + \Delta_L}\right)+\Phi^{-1}\left(\frac{y}{\mu (L + \Delta_L)}\right)+\sigma = 0$$
+where either $\Delta_X$ or $\Delta_Y$ is given by user input and the $\Delta_L$ comes from fees.
+
+### Trade in $\Delta_X$ for $\Delta_Y$
+If we want to trade in $\Delta_X$ for $\Delta_Y$, 
+we first accumulate fees by taking 
+$$
+\textrm{Fees} = (1-\gamma) \Delta_X.
+$$
+Then, we treat these fees as an allocation, therefore:
+$$
+\boxed{\Delta_L = \frac{P}{Px +y}L\frac{(1-\gamma)\Delta_X}{x}}
+$$
+where $P$ is the price of token $X$ quoted by the pool itself (i.e., using $P_X$ or $P_Y$ in Eq. (4) or (5) above).
+Then we can use our invariant equation and solve for $\Delta_Y$ in terms of $\Delta_X$ to get:
+$$\boxed{\Delta_Y = \mu (L+\Delta_L)\cdot\Phi\left(-\sigma-\Phi^{-1}\left(\frac{x+\Delta_X}{L+\Delta_L}\right)\right)-y}$$
+
+### Trade in $\Delta_Y$ for $\Delta_X$
+If we want to trade in $\Delta_X$ for $\Delta_Y$, 
+we first accumulate fees by taking 
+$$
+\boxed{\Delta_L = L\frac{(1-\gamma)\Delta_X}{Px +y}}
+$$
+Then we can use our invariant equation and solve for $\Delta_X$ in terms of $\Delta_Y$ to get:
+$$
+\boxed{\Delta_X = (L+\Delta_L)\cdot\Phi\left(-\sigma-\Phi^{-1}\left(\frac{y+\Delta_Y}{\mu(L+\Delta_L)}\right)\right)-x}
+$$
+
+## Value Function on $L(S)$
+Relate to value on $V(L,S)$ and $V(x,y)$. 
+Then we can use this to tokenize. We have $L_X(x, S)$ and $L_Y(y, S)$.
+We know that:
+$$V = Sx + y$$
+We can get the following from the trading function:
+$$
+x = LS\cdot\left(1-\Phi\left(\frac{\ln\frac{S}{\mu}+\frac{1}{2}\sigma^2}{\sigma}\right)\right)\\
+y = \mu\cdot L\cdot \Phi\left(\frac{\ln\frac{S}{\mu}-\frac{1}{2}\sigma^2}{\sigma}\right)
+$$
+Therefore:
+$$
+\boxed{V(L,S) = L\left( S\cdot\left(1-\Phi\left(\frac{\ln\frac{S}{\mu}+\frac{1}{2}\sigma^2}{\sigma}\right)\right) + \mu\cdot \Phi\left(\frac{\ln\frac{S}{\mu}-\frac{1}{2}\sigma^2}{\sigma}\right)\right)}
+$$
+
+### Time Dependence
+Note that $L$ effectively changes as parameters of the trading function change.
+To see this, note that the trading function must always satisfy:
+$$\Phi^{-1}\left(\frac{x}{L}\right)+\Phi^{-1}\left(\frac{y}{
+\mu L}\right) + \sigma  = 0.$$
+For new parameters $\mu'$ and $\sigma'$ we must find an $L'$ so that the trading function is satisfied:
+$$\Phi^{-1}\left(\frac{x}{L'}\right)+\Phi^{-1}\left(\frac{y}{\mu'L'}\right) + \sigma' = 0.$$
+We can find this new $L'$ using a root finding algorithm.