Contract Name:
VolatilitySurfaceOracle
Contract Source Code:
// SPDX-License-Identifier: BUSL-1.1
// For further clarification please see https://license.premia.legal
pragma solidity ^0.8.0;
import {OwnableInternal, OwnableStorage} from "@solidstate/contracts/access/OwnableInternal.sol";
import {EnumerableSet} from "@solidstate/contracts/utils/EnumerableSet.sol";
import {ABDKMath64x64} from "abdk-libraries-solidity/ABDKMath64x64.sol";
import {OptionMath} from "../libraries/OptionMath.sol";
import {VolatilitySurfaceOracleStorage} from "./VolatilitySurfaceOracleStorage.sol";
import {IVolatilitySurfaceOracle} from "./IVolatilitySurfaceOracle.sol";
/**
* @title Premia volatility surface oracle contract
*/
contract VolatilitySurfaceOracle is IVolatilitySurfaceOracle, OwnableInternal {
using VolatilitySurfaceOracleStorage for VolatilitySurfaceOracleStorage.Layout;
using EnumerableSet for EnumerableSet.AddressSet;
using ABDKMath64x64 for int128;
uint256 internal constant DECIMALS = 12;
event UpdateCoefficients(
address indexed baseToken,
address indexed underlyingToken,
bytes32 callCoefficients, // Coefficients must be packed using formatVolatilitySurfaceCoefficients
bytes32 putCoefficients // Coefficients must be packed using formatVolatilitySurfaceCoefficients
);
/**
* @notice Add relayer to the whitelist so that they can add oracle surfaces.
* @param _addr The addresses to add to the whitelist
*/
function addWhitelistedRelayer(address[] memory _addr) external onlyOwner {
VolatilitySurfaceOracleStorage.Layout
storage l = VolatilitySurfaceOracleStorage.layout();
for (uint256 i = 0; i < _addr.length; i++) {
l.whitelistedRelayers.add(_addr[i]);
}
}
/**
* @notice Remove relayer from the whitelist so that they cannot add oracle surfaces.
* @param _addr The addresses to remove the whitelist
*/
function removeWhitelistedRelayer(address[] memory _addr)
external
onlyOwner
{
VolatilitySurfaceOracleStorage.Layout
storage l = VolatilitySurfaceOracleStorage.layout();
for (uint256 i = 0; i < _addr.length; i++) {
l.whitelistedRelayers.remove(_addr[i]);
}
}
/**
* @notice Get the list of whitelisted relayers
* @return The list of whitelisted relayers
*/
function getWhitelistedRelayers()
external
view
override
returns (address[] memory)
{
VolatilitySurfaceOracleStorage.Layout
storage l = VolatilitySurfaceOracleStorage.layout();
uint256 length = l.whitelistedRelayers.length();
address[] memory result = new address[](length);
for (uint256 i = 0; i < length; i++) {
result[i] = l.whitelistedRelayers.at(i);
}
return result;
}
/**
* @notice Get the volatility surface data of a token pair
* @param baseToken The base token of the pair
* @param underlyingToken The underlying token of the pair
* @return The volatility surface data
*/
function getVolatilitySurface(address baseToken, address underlyingToken)
external
view
override
returns (VolatilitySurfaceOracleStorage.Update memory)
{
VolatilitySurfaceOracleStorage.Layout
storage l = VolatilitySurfaceOracleStorage.layout();
return l.volatilitySurfaces[baseToken][underlyingToken];
}
/**
* @notice Get unpacked volatility surface coefficients
* @param baseToken The base token of the pair
* @param underlyingToken The underlying token of the pair
* @param isCall whether it is for call or put
* @return The unpacked coefficients of the volatility surface
*/
function getVolatilitySurfaceCoefficientsUnpacked(
address baseToken,
address underlyingToken,
bool isCall
) external view override returns (int256[] memory) {
VolatilitySurfaceOracleStorage.Layout
storage l = VolatilitySurfaceOracleStorage.layout();
bytes32 valuePacked = l.getCoefficients(
baseToken,
underlyingToken,
isCall
);
return
VolatilitySurfaceOracleStorage.parseVolatilitySurfaceCoefficients(
valuePacked
);
}
/**
* @notice Get time to maturity in years, as a 64x64 fixed point representation
* @param maturity Maturity timestamp
* @return Time to maturity (in years), as a 64x64 fixed point representation
*/
function getTimeToMaturity64x64(uint64 maturity)
external
view
override
returns (int128)
{
return ABDKMath64x64.divu(maturity - block.timestamp, 365 days);
}
/**
* @notice Get annualized volatility as a 64x64 fixed point representation
* @param baseToken The base token of the pair
* @param underlyingToken The underlying token of the pair
* @param spot64x64 The spot, as a 64x64 fixed point representation
* @param strike64x64 The strike, as a 64x64 fixed point representation
* @param timeToMaturity64x64 Time to maturity (in years), as a 64x64 fixed point representation
* @param isCall whether it is for call or put
* @return Annualized volatility, as a 64x64 fixed point representation. 1 = 100%
*/
function getAnnualizedVolatility64x64(
address baseToken,
address underlyingToken,
int128 spot64x64,
int128 strike64x64,
int128 timeToMaturity64x64,
bool isCall
) public view override returns (int128) {
VolatilitySurfaceOracleStorage.Layout
storage l = VolatilitySurfaceOracleStorage.layout();
int256[] memory volatilitySurface = VolatilitySurfaceOracleStorage
.parseVolatilitySurfaceCoefficients(
l.getCoefficients(baseToken, underlyingToken, isCall)
);
return
_getAnnualizedVolatility64x64(
spot64x64,
strike64x64,
timeToMaturity64x64,
volatilitySurface
);
}
function _getAnnualizedVolatility64x64(
int128 spot64x64,
int128 strike64x64,
int128 timeToMaturity64x64,
int256[] memory volatilitySurface
) internal pure returns (int128) {
require(volatilitySurface.length == 5, "Invalid vol surface");
// Time adjusted log moneyness
int128 adjustedLogMoneyness64x64 = spot64x64.div(strike64x64).ln().div(
timeToMaturity64x64.sqrt()
);
return
_toCoefficient64x64(volatilitySurface[0]) +
_toCoefficient64x64(volatilitySurface[1]).mul(
adjustedLogMoneyness64x64
) +
_toCoefficient64x64(volatilitySurface[2]).mul(
adjustedLogMoneyness64x64.mul(adjustedLogMoneyness64x64)
) +
_toCoefficient64x64(volatilitySurface[3]).mul(timeToMaturity64x64) +
_toCoefficient64x64(volatilitySurface[4])
.mul(adjustedLogMoneyness64x64)
.mul(timeToMaturity64x64);
}
function _toCoefficient64x64(int256 value) internal pure returns (int128) {
return ABDKMath64x64.divi(value, int256(10**DECIMALS));
}
function _getBlackScholesPrice64x64(
address baseToken,
address underlyingToken,
int128 strike64x64,
int128 spot64x64,
int128 timeToMaturity64x64,
bool isCall
) internal view returns (int128) {
int128 annualizedVolatility = getAnnualizedVolatility64x64(
baseToken,
underlyingToken,
strike64x64,
spot64x64,
timeToMaturity64x64,
isCall
);
int128 annualizedVariance = annualizedVolatility.mul(
annualizedVolatility
);
return
OptionMath._blackScholesPrice(
annualizedVariance,
strike64x64,
spot64x64,
timeToMaturity64x64,
isCall
);
}
/**
* @notice Get Black Scholes price as a 64x64 fixed point representation
* @param baseToken The base token of the pair
* @param underlyingToken The underlying token of the pair
* @param strike64x64 Strike, as a64x64 fixed point representation
* @param spot64x64 Spot price, as a 64x64 fixed point representation
* @param timeToMaturity64x64 Time to maturity (in years), as a 64x64 fixed point representation
* @param isCall Whether it is for call or put
* @return Black scholes price, as a 64x64 fixed point representation
*/
function getBlackScholesPrice64x64(
address baseToken,
address underlyingToken,
int128 strike64x64,
int128 spot64x64,
int128 timeToMaturity64x64,
bool isCall
) external view override returns (int128) {
return
_getBlackScholesPrice64x64(
baseToken,
underlyingToken,
strike64x64,
spot64x64,
timeToMaturity64x64,
isCall
);
}
/**
* @notice Get Black Scholes price as an uint256 with 18 decimals
* @param baseToken The base token of the pair
* @param underlyingToken The underlying token of the pair
* @param strike64x64 Strike, as a64x64 fixed point representation
* @param spot64x64 Spot price, as a 64x64 fixed point representation
* @param timeToMaturity64x64 Time to maturity (in years), as a 64x64 fixed point representation
* @param isCall Whether it is for call or put
* @return Black scholes price, as an uint256 with 18 decimals
*/
function getBlackScholesPrice(
address baseToken,
address underlyingToken,
int128 strike64x64,
int128 spot64x64,
int128 timeToMaturity64x64,
bool isCall
) external view override returns (uint256) {
return
_getBlackScholesPrice64x64(
baseToken,
underlyingToken,
strike64x64,
spot64x64,
timeToMaturity64x64,
isCall
).mulu(10**18);
}
/**
* @notice Update a list of volatility surfaces
* @param baseTokens List of base tokens
* @param underlyingTokens List of underlying tokens
* @param callCoefficients List of call coefficients
* @param putCoefficients List of put coefficients
*/
function updateVolatilitySurfaces(
address[] memory baseTokens,
address[] memory underlyingTokens,
bytes32[] memory callCoefficients,
bytes32[] memory putCoefficients
) external {
uint256 length = baseTokens.length;
require(
length == underlyingTokens.length &&
length == callCoefficients.length &&
length == putCoefficients.length,
"Wrong array length"
);
VolatilitySurfaceOracleStorage.Layout
storage l = VolatilitySurfaceOracleStorage.layout();
require(
l.whitelistedRelayers.contains(msg.sender),
"Relayer not whitelisted"
);
for (uint256 i = 0; i < length; i++) {
l.volatilitySurfaces[baseTokens[i]][
underlyingTokens[i]
] = VolatilitySurfaceOracleStorage.Update({
updatedAt: block.timestamp,
callCoefficients: callCoefficients[i],
putCoefficients: putCoefficients[i]
});
emit UpdateCoefficients(
baseTokens[i],
underlyingTokens[i],
callCoefficients[i],
putCoefficients[i]
);
}
}
/**
* @notice Unpack volatility surface coefficients from a bytes43
* @param input Packed volatility surface coefficients to unpack
* @return coefficients The unpacked coefficients of the volatility surface
*/
function parseVolatilitySurfaceCoefficients(bytes32 input)
external
pure
returns (int256[] memory coefficients)
{
return
VolatilitySurfaceOracleStorage.parseVolatilitySurfaceCoefficients(
input
);
}
/**
* @notice Pack volatility surface coefficients into a single bytes32
* @dev This function is used to pack the coefficients into a single variable, which is then used as input in `updateVolatilitySurfaces`
* @param coefficients Coefficients of the volatility surface to pack
* @return result The packed coefficients of the volatility surface
*/
function formatVolatilitySurfaceCoefficients(int256[5] memory coefficients)
external
pure
returns (bytes32 result)
{
return
VolatilitySurfaceOracleStorage.formatVolatilitySurfaceCoefficients(
coefficients
);
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
import { OwnableStorage } from './OwnableStorage.sol';
abstract contract OwnableInternal {
using OwnableStorage for OwnableStorage.Layout;
modifier onlyOwner() {
require(
msg.sender == OwnableStorage.layout().owner,
'Ownable: sender must be owner'
);
_;
}
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
/**
* @title Set implementation with enumeration functions
* @dev derived from https://github.com/OpenZeppelin/openzeppelin-contracts (MIT license)
*/
library EnumerableSet {
struct Set {
bytes32[] _values;
// 1-indexed to allow 0 to signify nonexistence
mapping(bytes32 => uint256) _indexes;
}
struct Bytes32Set {
Set _inner;
}
struct AddressSet {
Set _inner;
}
struct UintSet {
Set _inner;
}
function at(Bytes32Set storage set, uint256 index)
internal
view
returns (bytes32)
{
return _at(set._inner, index);
}
function at(AddressSet storage set, uint256 index)
internal
view
returns (address)
{
return address(uint160(uint256(_at(set._inner, index))));
}
function at(UintSet storage set, uint256 index)
internal
view
returns (uint256)
{
return uint256(_at(set._inner, index));
}
function contains(Bytes32Set storage set, bytes32 value)
internal
view
returns (bool)
{
return _contains(set._inner, value);
}
function contains(AddressSet storage set, address value)
internal
view
returns (bool)
{
return _contains(set._inner, bytes32(uint256(uint160(value))));
}
function contains(UintSet storage set, uint256 value)
internal
view
returns (bool)
{
return _contains(set._inner, bytes32(value));
}
function indexOf(Bytes32Set storage set, bytes32 value)
internal
view
returns (uint256)
{
return _indexOf(set._inner, value);
}
function indexOf(AddressSet storage set, address value)
internal
view
returns (uint256)
{
return _indexOf(set._inner, bytes32(uint256(uint160(value))));
}
function indexOf(UintSet storage set, uint256 value)
internal
view
returns (uint256)
{
return _indexOf(set._inner, bytes32(value));
}
function length(Bytes32Set storage set) internal view returns (uint256) {
return _length(set._inner);
}
function length(AddressSet storage set) internal view returns (uint256) {
return _length(set._inner);
}
function length(UintSet storage set) internal view returns (uint256) {
return _length(set._inner);
}
function add(Bytes32Set storage set, bytes32 value)
internal
returns (bool)
{
return _add(set._inner, value);
}
function add(AddressSet storage set, address value)
internal
returns (bool)
{
return _add(set._inner, bytes32(uint256(uint160(value))));
}
function add(UintSet storage set, uint256 value) internal returns (bool) {
return _add(set._inner, bytes32(value));
}
function remove(Bytes32Set storage set, bytes32 value)
internal
returns (bool)
{
return _remove(set._inner, value);
}
function remove(AddressSet storage set, address value)
internal
returns (bool)
{
return _remove(set._inner, bytes32(uint256(uint160(value))));
}
function remove(UintSet storage set, uint256 value)
internal
returns (bool)
{
return _remove(set._inner, bytes32(value));
}
function _at(Set storage set, uint256 index)
private
view
returns (bytes32)
{
require(
set._values.length > index,
'EnumerableSet: index out of bounds'
);
return set._values[index];
}
function _contains(Set storage set, bytes32 value)
private
view
returns (bool)
{
return set._indexes[value] != 0;
}
function _indexOf(Set storage set, bytes32 value)
private
view
returns (uint256)
{
unchecked {
return set._indexes[value] - 1;
}
}
function _length(Set storage set) private view returns (uint256) {
return set._values.length;
}
function _add(Set storage set, bytes32 value) private returns (bool) {
if (!_contains(set, value)) {
set._values.push(value);
set._indexes[value] = set._values.length;
return true;
} else {
return false;
}
}
function _remove(Set storage set, bytes32 value) private returns (bool) {
uint256 valueIndex = set._indexes[value];
if (valueIndex != 0) {
uint256 index = valueIndex - 1;
bytes32 last = set._values[set._values.length - 1];
// move last value to now-vacant index
set._values[index] = last;
set._indexes[last] = index + 1;
// clear last index
set._values.pop();
delete set._indexes[value];
return true;
} else {
return false;
}
}
}
// SPDX-License-Identifier: BSD-4-Clause
/*
* ABDK Math 64.64 Smart Contract Library. Copyright © 2019 by ABDK Consulting.
* Author: Mikhail Vladimirov <[email protected]>
*/
pragma solidity ^0.8.0;
/**
* Smart contract library of mathematical functions operating with signed
* 64.64-bit fixed point numbers. Signed 64.64-bit fixed point number is
* basically a simple fraction whose numerator is signed 128-bit integer and
* denominator is 2^64. As long as denominator is always the same, there is no
* need to store it, thus in Solidity signed 64.64-bit fixed point numbers are
* represented by int128 type holding only the numerator.
*/
library ABDKMath64x64 {
/*
* Minimum value signed 64.64-bit fixed point number may have.
*/
int128 private constant MIN_64x64 = -0x80000000000000000000000000000000;
/*
* Maximum value signed 64.64-bit fixed point number may have.
*/
int128 private constant MAX_64x64 = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF;
/**
* Convert signed 256-bit integer number into signed 64.64-bit fixed point
* number. Revert on overflow.
*
* @param x signed 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function fromInt (int256 x) internal pure returns (int128) {
unchecked {
require (x >= -0x8000000000000000 && x <= 0x7FFFFFFFFFFFFFFF);
return int128 (x << 64);
}
}
/**
* Convert signed 64.64 fixed point number into signed 64-bit integer number
* rounding down.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64-bit integer number
*/
function toInt (int128 x) internal pure returns (int64) {
unchecked {
return int64 (x >> 64);
}
}
/**
* Convert unsigned 256-bit integer number into signed 64.64-bit fixed point
* number. Revert on overflow.
*
* @param x unsigned 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function fromUInt (uint256 x) internal pure returns (int128) {
unchecked {
require (x <= 0x7FFFFFFFFFFFFFFF);
return int128 (int256 (x << 64));
}
}
/**
* Convert signed 64.64 fixed point number into unsigned 64-bit integer
* number rounding down. Revert on underflow.
*
* @param x signed 64.64-bit fixed point number
* @return unsigned 64-bit integer number
*/
function toUInt (int128 x) internal pure returns (uint64) {
unchecked {
require (x >= 0);
return uint64 (uint128 (x >> 64));
}
}
/**
* Convert signed 128.128 fixed point number into signed 64.64-bit fixed point
* number rounding down. Revert on overflow.
*
* @param x signed 128.128-bin fixed point number
* @return signed 64.64-bit fixed point number
*/
function from128x128 (int256 x) internal pure returns (int128) {
unchecked {
int256 result = x >> 64;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Convert signed 64.64 fixed point number into signed 128.128 fixed point
* number.
*
* @param x signed 64.64-bit fixed point number
* @return signed 128.128 fixed point number
*/
function to128x128 (int128 x) internal pure returns (int256) {
unchecked {
return int256 (x) << 64;
}
}
/**
* Calculate x + y. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function add (int128 x, int128 y) internal pure returns (int128) {
unchecked {
int256 result = int256(x) + y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate x - y. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function sub (int128 x, int128 y) internal pure returns (int128) {
unchecked {
int256 result = int256(x) - y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate x * y rounding down. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function mul (int128 x, int128 y) internal pure returns (int128) {
unchecked {
int256 result = int256(x) * y >> 64;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate x * y rounding towards zero, where x is signed 64.64 fixed point
* number and y is signed 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64 fixed point number
* @param y signed 256-bit integer number
* @return signed 256-bit integer number
*/
function muli (int128 x, int256 y) internal pure returns (int256) {
unchecked {
if (x == MIN_64x64) {
require (y >= -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF &&
y <= 0x1000000000000000000000000000000000000000000000000);
return -y << 63;
} else {
bool negativeResult = false;
if (x < 0) {
x = -x;
negativeResult = true;
}
if (y < 0) {
y = -y; // We rely on overflow behavior here
negativeResult = !negativeResult;
}
uint256 absoluteResult = mulu (x, uint256 (y));
if (negativeResult) {
require (absoluteResult <=
0x8000000000000000000000000000000000000000000000000000000000000000);
return -int256 (absoluteResult); // We rely on overflow behavior here
} else {
require (absoluteResult <=
0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return int256 (absoluteResult);
}
}
}
}
/**
* Calculate x * y rounding down, where x is signed 64.64 fixed point number
* and y is unsigned 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64 fixed point number
* @param y unsigned 256-bit integer number
* @return unsigned 256-bit integer number
*/
function mulu (int128 x, uint256 y) internal pure returns (uint256) {
unchecked {
if (y == 0) return 0;
require (x >= 0);
uint256 lo = (uint256 (int256 (x)) * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)) >> 64;
uint256 hi = uint256 (int256 (x)) * (y >> 128);
require (hi <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
hi <<= 64;
require (hi <=
0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF - lo);
return hi + lo;
}
}
/**
* Calculate x / y rounding towards zero. Revert on overflow or when y is
* zero.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function div (int128 x, int128 y) internal pure returns (int128) {
unchecked {
require (y != 0);
int256 result = (int256 (x) << 64) / y;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate x / y rounding towards zero, where x and y are signed 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x signed 256-bit integer number
* @param y signed 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function divi (int256 x, int256 y) internal pure returns (int128) {
unchecked {
require (y != 0);
bool negativeResult = false;
if (x < 0) {
x = -x; // We rely on overflow behavior here
negativeResult = true;
}
if (y < 0) {
y = -y; // We rely on overflow behavior here
negativeResult = !negativeResult;
}
uint128 absoluteResult = divuu (uint256 (x), uint256 (y));
if (negativeResult) {
require (absoluteResult <= 0x80000000000000000000000000000000);
return -int128 (absoluteResult); // We rely on overflow behavior here
} else {
require (absoluteResult <= 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return int128 (absoluteResult); // We rely on overflow behavior here
}
}
}
/**
* Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x unsigned 256-bit integer number
* @param y unsigned 256-bit integer number
* @return signed 64.64-bit fixed point number
*/
function divu (uint256 x, uint256 y) internal pure returns (int128) {
unchecked {
require (y != 0);
uint128 result = divuu (x, y);
require (result <= uint128 (MAX_64x64));
return int128 (result);
}
}
/**
* Calculate -x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function neg (int128 x) internal pure returns (int128) {
unchecked {
require (x != MIN_64x64);
return -x;
}
}
/**
* Calculate |x|. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function abs (int128 x) internal pure returns (int128) {
unchecked {
require (x != MIN_64x64);
return x < 0 ? -x : x;
}
}
/**
* Calculate 1 / x rounding towards zero. Revert on overflow or when x is
* zero.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function inv (int128 x) internal pure returns (int128) {
unchecked {
require (x != 0);
int256 result = int256 (0x100000000000000000000000000000000) / x;
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate arithmetics average of x and y, i.e. (x + y) / 2 rounding down.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function avg (int128 x, int128 y) internal pure returns (int128) {
unchecked {
return int128 ((int256 (x) + int256 (y)) >> 1);
}
}
/**
* Calculate geometric average of x and y, i.e. sqrt (x * y) rounding down.
* Revert on overflow or in case x * y is negative.
*
* @param x signed 64.64-bit fixed point number
* @param y signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function gavg (int128 x, int128 y) internal pure returns (int128) {
unchecked {
int256 m = int256 (x) * int256 (y);
require (m >= 0);
require (m <
0x4000000000000000000000000000000000000000000000000000000000000000);
return int128 (sqrtu (uint256 (m)));
}
}
/**
* Calculate x^y assuming 0^0 is 1, where x is signed 64.64 fixed point number
* and y is unsigned 256-bit integer number. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @param y uint256 value
* @return signed 64.64-bit fixed point number
*/
function pow (int128 x, uint256 y) internal pure returns (int128) {
unchecked {
bool negative = x < 0 && y & 1 == 1;
uint256 absX = uint128 (x < 0 ? -x : x);
uint256 absResult;
absResult = 0x100000000000000000000000000000000;
if (absX <= 0x10000000000000000) {
absX <<= 63;
while (y != 0) {
if (y & 0x1 != 0) {
absResult = absResult * absX >> 127;
}
absX = absX * absX >> 127;
if (y & 0x2 != 0) {
absResult = absResult * absX >> 127;
}
absX = absX * absX >> 127;
if (y & 0x4 != 0) {
absResult = absResult * absX >> 127;
}
absX = absX * absX >> 127;
if (y & 0x8 != 0) {
absResult = absResult * absX >> 127;
}
absX = absX * absX >> 127;
y >>= 4;
}
absResult >>= 64;
} else {
uint256 absXShift = 63;
if (absX < 0x1000000000000000000000000) { absX <<= 32; absXShift -= 32; }
if (absX < 0x10000000000000000000000000000) { absX <<= 16; absXShift -= 16; }
if (absX < 0x1000000000000000000000000000000) { absX <<= 8; absXShift -= 8; }
if (absX < 0x10000000000000000000000000000000) { absX <<= 4; absXShift -= 4; }
if (absX < 0x40000000000000000000000000000000) { absX <<= 2; absXShift -= 2; }
if (absX < 0x80000000000000000000000000000000) { absX <<= 1; absXShift -= 1; }
uint256 resultShift = 0;
while (y != 0) {
require (absXShift < 64);
if (y & 0x1 != 0) {
absResult = absResult * absX >> 127;
resultShift += absXShift;
if (absResult > 0x100000000000000000000000000000000) {
absResult >>= 1;
resultShift += 1;
}
}
absX = absX * absX >> 127;
absXShift <<= 1;
if (absX >= 0x100000000000000000000000000000000) {
absX >>= 1;
absXShift += 1;
}
y >>= 1;
}
require (resultShift < 64);
absResult >>= 64 - resultShift;
}
int256 result = negative ? -int256 (absResult) : int256 (absResult);
require (result >= MIN_64x64 && result <= MAX_64x64);
return int128 (result);
}
}
/**
* Calculate sqrt (x) rounding down. Revert if x < 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function sqrt (int128 x) internal pure returns (int128) {
unchecked {
require (x >= 0);
return int128 (sqrtu (uint256 (int256 (x)) << 64));
}
}
/**
* Calculate binary logarithm of x. Revert if x <= 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function log_2 (int128 x) internal pure returns (int128) {
unchecked {
require (x > 0);
int256 msb = 0;
int256 xc = x;
if (xc >= 0x10000000000000000) { xc >>= 64; msb += 64; }
if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
if (xc >= 0x10000) { xc >>= 16; msb += 16; }
if (xc >= 0x100) { xc >>= 8; msb += 8; }
if (xc >= 0x10) { xc >>= 4; msb += 4; }
if (xc >= 0x4) { xc >>= 2; msb += 2; }
if (xc >= 0x2) msb += 1; // No need to shift xc anymore
int256 result = msb - 64 << 64;
uint256 ux = uint256 (int256 (x)) << uint256 (127 - msb);
for (int256 bit = 0x8000000000000000; bit > 0; bit >>= 1) {
ux *= ux;
uint256 b = ux >> 255;
ux >>= 127 + b;
result += bit * int256 (b);
}
return int128 (result);
}
}
/**
* Calculate natural logarithm of x. Revert if x <= 0.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function ln (int128 x) internal pure returns (int128) {
unchecked {
require (x > 0);
return int128 (int256 (
uint256 (int256 (log_2 (x))) * 0xB17217F7D1CF79ABC9E3B39803F2F6AF >> 128));
}
}
/**
* Calculate binary exponent of x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function exp_2 (int128 x) internal pure returns (int128) {
unchecked {
require (x < 0x400000000000000000); // Overflow
if (x < -0x400000000000000000) return 0; // Underflow
uint256 result = 0x80000000000000000000000000000000;
if (x & 0x8000000000000000 > 0)
result = result * 0x16A09E667F3BCC908B2FB1366EA957D3E >> 128;
if (x & 0x4000000000000000 > 0)
result = result * 0x1306FE0A31B7152DE8D5A46305C85EDEC >> 128;
if (x & 0x2000000000000000 > 0)
result = result * 0x1172B83C7D517ADCDF7C8C50EB14A791F >> 128;
if (x & 0x1000000000000000 > 0)
result = result * 0x10B5586CF9890F6298B92B71842A98363 >> 128;
if (x & 0x800000000000000 > 0)
result = result * 0x1059B0D31585743AE7C548EB68CA417FD >> 128;
if (x & 0x400000000000000 > 0)
result = result * 0x102C9A3E778060EE6F7CACA4F7A29BDE8 >> 128;
if (x & 0x200000000000000 > 0)
result = result * 0x10163DA9FB33356D84A66AE336DCDFA3F >> 128;
if (x & 0x100000000000000 > 0)
result = result * 0x100B1AFA5ABCBED6129AB13EC11DC9543 >> 128;
if (x & 0x80000000000000 > 0)
result = result * 0x10058C86DA1C09EA1FF19D294CF2F679B >> 128;
if (x & 0x40000000000000 > 0)
result = result * 0x1002C605E2E8CEC506D21BFC89A23A00F >> 128;
if (x & 0x20000000000000 > 0)
result = result * 0x100162F3904051FA128BCA9C55C31E5DF >> 128;
if (x & 0x10000000000000 > 0)
result = result * 0x1000B175EFFDC76BA38E31671CA939725 >> 128;
if (x & 0x8000000000000 > 0)
result = result * 0x100058BA01FB9F96D6CACD4B180917C3D >> 128;
if (x & 0x4000000000000 > 0)
result = result * 0x10002C5CC37DA9491D0985C348C68E7B3 >> 128;
if (x & 0x2000000000000 > 0)
result = result * 0x1000162E525EE054754457D5995292026 >> 128;
if (x & 0x1000000000000 > 0)
result = result * 0x10000B17255775C040618BF4A4ADE83FC >> 128;
if (x & 0x800000000000 > 0)
result = result * 0x1000058B91B5BC9AE2EED81E9B7D4CFAB >> 128;
if (x & 0x400000000000 > 0)
result = result * 0x100002C5C89D5EC6CA4D7C8ACC017B7C9 >> 128;
if (x & 0x200000000000 > 0)
result = result * 0x10000162E43F4F831060E02D839A9D16D >> 128;
if (x & 0x100000000000 > 0)
result = result * 0x100000B1721BCFC99D9F890EA06911763 >> 128;
if (x & 0x80000000000 > 0)
result = result * 0x10000058B90CF1E6D97F9CA14DBCC1628 >> 128;
if (x & 0x40000000000 > 0)
result = result * 0x1000002C5C863B73F016468F6BAC5CA2B >> 128;
if (x & 0x20000000000 > 0)
result = result * 0x100000162E430E5A18F6119E3C02282A5 >> 128;
if (x & 0x10000000000 > 0)
result = result * 0x1000000B1721835514B86E6D96EFD1BFE >> 128;
if (x & 0x8000000000 > 0)
result = result * 0x100000058B90C0B48C6BE5DF846C5B2EF >> 128;
if (x & 0x4000000000 > 0)
result = result * 0x10000002C5C8601CC6B9E94213C72737A >> 128;
if (x & 0x2000000000 > 0)
result = result * 0x1000000162E42FFF037DF38AA2B219F06 >> 128;
if (x & 0x1000000000 > 0)
result = result * 0x10000000B17217FBA9C739AA5819F44F9 >> 128;
if (x & 0x800000000 > 0)
result = result * 0x1000000058B90BFCDEE5ACD3C1CEDC823 >> 128;
if (x & 0x400000000 > 0)
result = result * 0x100000002C5C85FE31F35A6A30DA1BE50 >> 128;
if (x & 0x200000000 > 0)
result = result * 0x10000000162E42FF0999CE3541B9FFFCF >> 128;
if (x & 0x100000000 > 0)
result = result * 0x100000000B17217F80F4EF5AADDA45554 >> 128;
if (x & 0x80000000 > 0)
result = result * 0x10000000058B90BFBF8479BD5A81B51AD >> 128;
if (x & 0x40000000 > 0)
result = result * 0x1000000002C5C85FDF84BD62AE30A74CC >> 128;
if (x & 0x20000000 > 0)
result = result * 0x100000000162E42FEFB2FED257559BDAA >> 128;
if (x & 0x10000000 > 0)
result = result * 0x1000000000B17217F7D5A7716BBA4A9AE >> 128;
if (x & 0x8000000 > 0)
result = result * 0x100000000058B90BFBE9DDBAC5E109CCE >> 128;
if (x & 0x4000000 > 0)
result = result * 0x10000000002C5C85FDF4B15DE6F17EB0D >> 128;
if (x & 0x2000000 > 0)
result = result * 0x1000000000162E42FEFA494F1478FDE05 >> 128;
if (x & 0x1000000 > 0)
result = result * 0x10000000000B17217F7D20CF927C8E94C >> 128;
if (x & 0x800000 > 0)
result = result * 0x1000000000058B90BFBE8F71CB4E4B33D >> 128;
if (x & 0x400000 > 0)
result = result * 0x100000000002C5C85FDF477B662B26945 >> 128;
if (x & 0x200000 > 0)
result = result * 0x10000000000162E42FEFA3AE53369388C >> 128;
if (x & 0x100000 > 0)
result = result * 0x100000000000B17217F7D1D351A389D40 >> 128;
if (x & 0x80000 > 0)
result = result * 0x10000000000058B90BFBE8E8B2D3D4EDE >> 128;
if (x & 0x40000 > 0)
result = result * 0x1000000000002C5C85FDF4741BEA6E77E >> 128;
if (x & 0x20000 > 0)
result = result * 0x100000000000162E42FEFA39FE95583C2 >> 128;
if (x & 0x10000 > 0)
result = result * 0x1000000000000B17217F7D1CFB72B45E1 >> 128;
if (x & 0x8000 > 0)
result = result * 0x100000000000058B90BFBE8E7CC35C3F0 >> 128;
if (x & 0x4000 > 0)
result = result * 0x10000000000002C5C85FDF473E242EA38 >> 128;
if (x & 0x2000 > 0)
result = result * 0x1000000000000162E42FEFA39F02B772C >> 128;
if (x & 0x1000 > 0)
result = result * 0x10000000000000B17217F7D1CF7D83C1A >> 128;
if (x & 0x800 > 0)
result = result * 0x1000000000000058B90BFBE8E7BDCBE2E >> 128;
if (x & 0x400 > 0)
result = result * 0x100000000000002C5C85FDF473DEA871F >> 128;
if (x & 0x200 > 0)
result = result * 0x10000000000000162E42FEFA39EF44D91 >> 128;
if (x & 0x100 > 0)
result = result * 0x100000000000000B17217F7D1CF79E949 >> 128;
if (x & 0x80 > 0)
result = result * 0x10000000000000058B90BFBE8E7BCE544 >> 128;
if (x & 0x40 > 0)
result = result * 0x1000000000000002C5C85FDF473DE6ECA >> 128;
if (x & 0x20 > 0)
result = result * 0x100000000000000162E42FEFA39EF366F >> 128;
if (x & 0x10 > 0)
result = result * 0x1000000000000000B17217F7D1CF79AFA >> 128;
if (x & 0x8 > 0)
result = result * 0x100000000000000058B90BFBE8E7BCD6D >> 128;
if (x & 0x4 > 0)
result = result * 0x10000000000000002C5C85FDF473DE6B2 >> 128;
if (x & 0x2 > 0)
result = result * 0x1000000000000000162E42FEFA39EF358 >> 128;
if (x & 0x1 > 0)
result = result * 0x10000000000000000B17217F7D1CF79AB >> 128;
result >>= uint256 (int256 (63 - (x >> 64)));
require (result <= uint256 (int256 (MAX_64x64)));
return int128 (int256 (result));
}
}
/**
* Calculate natural exponent of x. Revert on overflow.
*
* @param x signed 64.64-bit fixed point number
* @return signed 64.64-bit fixed point number
*/
function exp (int128 x) internal pure returns (int128) {
unchecked {
require (x < 0x400000000000000000); // Overflow
if (x < -0x400000000000000000) return 0; // Underflow
return exp_2 (
int128 (int256 (x) * 0x171547652B82FE1777D0FFDA0D23A7D12 >> 128));
}
}
/**
* Calculate x / y rounding towards zero, where x and y are unsigned 256-bit
* integer numbers. Revert on overflow or when y is zero.
*
* @param x unsigned 256-bit integer number
* @param y unsigned 256-bit integer number
* @return unsigned 64.64-bit fixed point number
*/
function divuu (uint256 x, uint256 y) private pure returns (uint128) {
unchecked {
require (y != 0);
uint256 result;
if (x <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF)
result = (x << 64) / y;
else {
uint256 msb = 192;
uint256 xc = x >> 192;
if (xc >= 0x100000000) { xc >>= 32; msb += 32; }
if (xc >= 0x10000) { xc >>= 16; msb += 16; }
if (xc >= 0x100) { xc >>= 8; msb += 8; }
if (xc >= 0x10) { xc >>= 4; msb += 4; }
if (xc >= 0x4) { xc >>= 2; msb += 2; }
if (xc >= 0x2) msb += 1; // No need to shift xc anymore
result = (x << 255 - msb) / ((y - 1 >> msb - 191) + 1);
require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
uint256 hi = result * (y >> 128);
uint256 lo = result * (y & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
uint256 xh = x >> 192;
uint256 xl = x << 64;
if (xl < lo) xh -= 1;
xl -= lo; // We rely on overflow behavior here
lo = hi << 128;
if (xl < lo) xh -= 1;
xl -= lo; // We rely on overflow behavior here
assert (xh == hi >> 128);
result += xl / y;
}
require (result <= 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF);
return uint128 (result);
}
}
/**
* Calculate sqrt (x) rounding down, where x is unsigned 256-bit integer
* number.
*
* @param x unsigned 256-bit integer number
* @return unsigned 128-bit integer number
*/
function sqrtu (uint256 x) private pure returns (uint128) {
unchecked {
if (x == 0) return 0;
else {
uint256 xx = x;
uint256 r = 1;
if (xx >= 0x100000000000000000000000000000000) { xx >>= 128; r <<= 64; }
if (xx >= 0x10000000000000000) { xx >>= 64; r <<= 32; }
if (xx >= 0x100000000) { xx >>= 32; r <<= 16; }
if (xx >= 0x10000) { xx >>= 16; r <<= 8; }
if (xx >= 0x100) { xx >>= 8; r <<= 4; }
if (xx >= 0x10) { xx >>= 4; r <<= 2; }
if (xx >= 0x8) { r <<= 1; }
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1;
r = (r + x / r) >> 1; // Seven iterations should be enough
uint256 r1 = x / r;
return uint128 (r < r1 ? r : r1);
}
}
}
}
// SPDX-License-Identifier: BUSL-1.1
// For further clarification please see https://license.premia.legal
pragma solidity ^0.8.0;
import {ABDKMath64x64} from "abdk-libraries-solidity/ABDKMath64x64.sol";
library OptionMath {
using ABDKMath64x64 for int128;
struct QuoteArgs {
int128 varianceAnnualized64x64; // 64x64 fixed point representation of annualized variance
int128 strike64x64; // 64x64 fixed point representation of strike price
int128 spot64x64; // 64x64 fixed point representation of spot price
int128 timeToMaturity64x64; // 64x64 fixed point representation of duration of option contract (in years)
int128 oldCLevel64x64; // 64x64 fixed point representation of C-Level of Pool before purchase
int128 oldPoolState; // 64x64 fixed point representation of current state of the pool
int128 newPoolState; // 64x64 fixed point representation of state of the pool after trade
int128 steepness64x64; // 64x64 fixed point representation of Pool state delta multiplier
int128 minAPY64x64; // 64x64 fixed point representation of minimum APY for capital locked up to underwrite options
bool isCall; // whether to price "call" or "put" option
}
struct CalculateCLevelDecayArgs {
int128 timeIntervalsElapsed64x64; // 64x64 fixed point representation of quantity of discrete arbitrary intervals elapsed since last update
int128 oldCLevel64x64; // 64x64 fixed point representation of C-Level prior to accounting for decay
int128 utilization64x64; // 64x64 fixed point representation of pool capital utilization rate
int128 utilizationLowerBound64x64;
int128 utilizationUpperBound64x64;
int128 cLevelLowerBound64x64;
int128 cLevelUpperBound64x64;
int128 cConvergenceULowerBound64x64;
int128 cConvergenceUUpperBound64x64;
}
// 64x64 fixed point integer constants
int128 internal constant ONE_64x64 = 0x10000000000000000;
int128 internal constant THREE_64x64 = 0x30000000000000000;
// 64x64 fixed point constants used in Choudhury’s approximation of the Black-Scholes CDF
int128 private constant CDF_CONST_0 = 0x09109f285df452394; // 2260 / 3989
int128 private constant CDF_CONST_1 = 0x19abac0ea1da65036; // 6400 / 3989
int128 private constant CDF_CONST_2 = 0x0d3c84b78b749bd6b; // 3300 / 3989
/**
* @notice recalculate C-Level based on change in liquidity
* @param initialCLevel64x64 64x64 fixed point representation of C-Level of Pool before update
* @param oldPoolState64x64 64x64 fixed point representation of liquidity in pool before update
* @param newPoolState64x64 64x64 fixed point representation of liquidity in pool after update
* @param steepness64x64 64x64 fixed point representation of steepness coefficient
* @return 64x64 fixed point representation of new C-Level
*/
function calculateCLevel(
int128 initialCLevel64x64,
int128 oldPoolState64x64,
int128 newPoolState64x64,
int128 steepness64x64
) external pure returns (int128) {
return
newPoolState64x64
.sub(oldPoolState64x64)
.div(
oldPoolState64x64 > newPoolState64x64
? oldPoolState64x64
: newPoolState64x64
)
.mul(steepness64x64)
.neg()
.exp()
.mul(initialCLevel64x64);
}
/**
* @notice calculate the price of an option using the Premia Finance model
* @param args arguments of quotePrice
* @return premiaPrice64x64 64x64 fixed point representation of Premia option price
* @return cLevel64x64 64x64 fixed point representation of C-Level of Pool after purchase
*/
function quotePrice(QuoteArgs memory args)
external
pure
returns (
int128 premiaPrice64x64,
int128 cLevel64x64,
int128 slippageCoefficient64x64
)
{
int128 deltaPoolState64x64 = args
.newPoolState
.sub(args.oldPoolState)
.div(args.oldPoolState)
.mul(args.steepness64x64);
int128 tradingDelta64x64 = deltaPoolState64x64.neg().exp();
int128 blackScholesPrice64x64 = _blackScholesPrice(
args.varianceAnnualized64x64,
args.strike64x64,
args.spot64x64,
args.timeToMaturity64x64,
args.isCall
);
cLevel64x64 = tradingDelta64x64.mul(args.oldCLevel64x64);
slippageCoefficient64x64 = ONE_64x64.sub(tradingDelta64x64).div(
deltaPoolState64x64
);
premiaPrice64x64 = blackScholesPrice64x64.mul(cLevel64x64).mul(
slippageCoefficient64x64
);
int128 intrinsicValue64x64;
if (args.isCall && args.strike64x64 < args.spot64x64) {
intrinsicValue64x64 = args.spot64x64.sub(args.strike64x64);
} else if (!args.isCall && args.strike64x64 > args.spot64x64) {
intrinsicValue64x64 = args.strike64x64.sub(args.spot64x64);
}
int128 collateralValue64x64 = args.isCall
? args.spot64x64
: args.strike64x64;
int128 minPrice64x64 = intrinsicValue64x64.add(
collateralValue64x64.mul(args.minAPY64x64).mul(
args.timeToMaturity64x64
)
);
if (minPrice64x64 > premiaPrice64x64) {
premiaPrice64x64 = minPrice64x64;
}
}
/**
* @notice calculate the decay of C-Level based on heat diffusion function
* @param args structured CalculateCLevelDecayArgs
* @return cLevelDecayed64x64 C-Level after accounting for decay
*/
function calculateCLevelDecay(CalculateCLevelDecayArgs memory args)
external
pure
returns (int128 cLevelDecayed64x64)
{
int128 convFHighU64x64 = (args.utilization64x64 >=
args.utilizationUpperBound64x64 &&
args.oldCLevel64x64 <= args.cLevelLowerBound64x64)
? ONE_64x64
: int128(0);
int128 convFLowU64x64 = (args.utilization64x64 <=
args.utilizationLowerBound64x64 &&
args.oldCLevel64x64 >= args.cLevelUpperBound64x64)
? ONE_64x64
: int128(0);
cLevelDecayed64x64 = args
.oldCLevel64x64
.sub(args.cConvergenceULowerBound64x64.mul(convFLowU64x64))
.sub(args.cConvergenceUUpperBound64x64.mul(convFHighU64x64))
.mul(
convFLowU64x64
.mul(ONE_64x64.sub(args.utilization64x64))
.add(convFHighU64x64.mul(args.utilization64x64))
.mul(args.timeIntervalsElapsed64x64)
.neg()
.exp()
)
.add(
args.cConvergenceULowerBound64x64.mul(convFLowU64x64).add(
args.cConvergenceUUpperBound64x64.mul(convFHighU64x64)
)
);
}
/**
* @notice calculate the exponential decay coefficient for a given interval
* @param oldTimestamp timestamp of previous update
* @param newTimestamp current timestamp
* @return 64x64 fixed point representation of exponential decay coefficient
*/
function _decay(uint256 oldTimestamp, uint256 newTimestamp)
internal
pure
returns (int128)
{
return
ONE_64x64.sub(
(-ABDKMath64x64.divu(newTimestamp - oldTimestamp, 7 days)).exp()
);
}
/**
* @notice calculate Choudhury’s approximation of the Black-Scholes CDF
* @param input64x64 64x64 fixed point representation of random variable
* @return 64x64 fixed point representation of the approximated CDF of x
*/
function _N(int128 input64x64) internal pure returns (int128) {
// squaring via mul is cheaper than via pow
int128 inputSquared64x64 = input64x64.mul(input64x64);
int128 value64x64 = (-inputSquared64x64 >> 1).exp().div(
CDF_CONST_0.add(CDF_CONST_1.mul(input64x64.abs())).add(
CDF_CONST_2.mul(inputSquared64x64.add(THREE_64x64).sqrt())
)
);
return input64x64 > 0 ? ONE_64x64.sub(value64x64) : value64x64;
}
/**
* @notice calculate the price of an option using the Black-Scholes model
* @param varianceAnnualized64x64 64x64 fixed point representation of annualized variance
* @param strike64x64 64x64 fixed point representation of strike price
* @param spot64x64 64x64 fixed point representation of spot price
* @param timeToMaturity64x64 64x64 fixed point representation of duration of option contract (in years)
* @param isCall whether to price "call" or "put" option
* @return 64x64 fixed point representation of Black-Scholes option price
*/
function _blackScholesPrice(
int128 varianceAnnualized64x64,
int128 strike64x64,
int128 spot64x64,
int128 timeToMaturity64x64,
bool isCall
) internal pure returns (int128) {
int128 cumulativeVariance64x64 = timeToMaturity64x64.mul(
varianceAnnualized64x64
);
int128 cumulativeVarianceSqrt64x64 = cumulativeVariance64x64.sqrt();
int128 d1_64x64 = spot64x64
.div(strike64x64)
.ln()
.add(cumulativeVariance64x64 >> 1)
.div(cumulativeVarianceSqrt64x64);
int128 d2_64x64 = d1_64x64.sub(cumulativeVarianceSqrt64x64);
if (isCall) {
return
spot64x64.mul(_N(d1_64x64)).sub(strike64x64.mul(_N(d2_64x64)));
} else {
return
-spot64x64.mul(_N(-d1_64x64)).sub(
strike64x64.mul(_N(-d2_64x64))
);
}
}
}
// SPDX-License-Identifier: BUSL-1.1
// For further clarification please see https://license.premia.legal
pragma solidity ^0.8.0;
import {EnumerableSet} from "@solidstate/contracts/utils/EnumerableSet.sol";
library VolatilitySurfaceOracleStorage {
bytes32 internal constant STORAGE_SLOT =
keccak256("premia.contracts.storage.VolatilitySurfaceOracle");
uint256 internal constant COEFF_BITS = 51;
uint256 internal constant COEFF_BITS_MINUS_ONE = 50;
uint256 internal constant COEFF_AMOUNT = 5;
// START_BIT = COEFF_BITS * (COEFF_AMOUNT - 1)
uint256 internal constant START_BIT = 204;
struct Update {
uint256 updatedAt;
bytes32 callCoefficients;
bytes32 putCoefficients;
}
struct Layout {
// Base token -> Underlying token -> Update
mapping(address => mapping(address => Update)) volatilitySurfaces;
// Relayer addresses which can be trusted to provide accurate option trades
EnumerableSet.AddressSet whitelistedRelayers;
}
function layout() internal pure returns (Layout storage l) {
bytes32 slot = STORAGE_SLOT;
assembly {
l.slot := slot
}
}
function getCoefficients(
Layout storage l,
address baseToken,
address underlyingToken,
bool isCall
) internal view returns (bytes32) {
Update storage u = l.volatilitySurfaces[baseToken][underlyingToken];
return isCall ? u.callCoefficients : u.putCoefficients;
}
function parseVolatilitySurfaceCoefficients(bytes32 input)
internal
pure
returns (int256[] memory coefficients)
{
coefficients = new int256[](COEFF_AMOUNT);
// Value to add to negative numbers to cast them to int256
int256 toAdd = (int256(-1) >> COEFF_BITS) << COEFF_BITS;
assembly {
let i := 0
// Value equal to -1
let mid := shl(COEFF_BITS_MINUS_ONE, 1)
for {
} lt(i, COEFF_AMOUNT) {
} {
let offset := sub(START_BIT, mul(COEFF_BITS, i))
let coeff := shr(
offset,
sub(
input,
shl(
add(offset, COEFF_BITS),
shr(add(offset, COEFF_BITS), input)
)
)
)
// Check if value is a negative number and needs casting
if or(eq(coeff, mid), gt(coeff, mid)) {
coeff := add(coeff, toAdd)
}
// Store result in the coefficients array
mstore(add(coefficients, add(0x20, mul(0x20, i))), coeff)
i := add(i, 1)
}
}
}
function formatVolatilitySurfaceCoefficients(int256[5] memory coefficients)
internal
pure
returns (bytes32 result)
{
for (uint256 i = 0; i < COEFF_AMOUNT; i++) {
int256 max = int256(1 << COEFF_BITS_MINUS_ONE);
require(
coefficients[i] < max && coefficients[i] > -max,
"Out of bounds"
);
}
assembly {
let i := 0
for {
} lt(i, COEFF_AMOUNT) {
} {
let offset := sub(START_BIT, mul(COEFF_BITS, i))
let coeff := mload(add(coefficients, mul(0x20, i)))
result := add(
result,
shl(
offset,
sub(coeff, shl(COEFF_BITS, shr(COEFF_BITS, coeff)))
)
)
i := add(i, 1)
}
}
}
}
// SPDX-License-Identifier: LGPL-3.0-or-later
pragma solidity ^0.8.0;
import {VolatilitySurfaceOracleStorage} from "./VolatilitySurfaceOracleStorage.sol";
interface IVolatilitySurfaceOracle {
function getWhitelistedRelayers() external view returns (address[] memory);
function getVolatilitySurface(address baseToken, address underlyingToken)
external
view
returns (VolatilitySurfaceOracleStorage.Update memory);
function getVolatilitySurfaceCoefficientsUnpacked(
address baseToken,
address underlyingToken,
bool isCall
) external view returns (int256[] memory);
function getTimeToMaturity64x64(uint64 maturity)
external
view
returns (int128);
function getAnnualizedVolatility64x64(
address baseToken,
address underlyingToken,
int128 spot64x64,
int128 strike64x64,
int128 timeToMaturity64x64,
bool isCall
) external view returns (int128);
function getBlackScholesPrice64x64(
address baseToken,
address underlyingToken,
int128 strike64x64,
int128 spot64x64,
int128 timeToMaturity64x64,
bool isCall
) external view returns (int128);
function getBlackScholesPrice(
address baseToken,
address underlyingToken,
int128 strike64x64,
int128 spot64x64,
int128 timeToMaturity64x64,
bool isCall
) external view returns (uint256);
}
// SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
library OwnableStorage {
struct Layout {
address owner;
}
bytes32 internal constant STORAGE_SLOT =
keccak256('solidstate.contracts.storage.Ownable');
function layout() internal pure returns (Layout storage l) {
bytes32 slot = STORAGE_SLOT;
assembly {
l.slot := slot
}
}
function setOwner(Layout storage l, address owner) internal {
l.owner = owner;
}
}