Collateral-Health Factor

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223

/** Dependency-free reference calculations for D25-F02. */
export type JsonObject = Record<string, any>;

function finite(value: unknown, name: string, minimum?: number, maximum?: number): number {
  if (typeof value !== "number" || !Number.isFinite(value)) throw new Error(`${name} must be a finite number`);
  if (minimum !== undefined && value < minimum) throw new Error(`${name} must be at least ${minimum}`);
  if (maximum !== undefined && value > maximum) throw new Error(`${name} must be at most ${maximum}`);
  return value;
}

function rounded(value: any, digits = 10): any {
  if (typeof value === "number") return Number(value.toFixed(digits));
  if (Array.isArray(value)) return value.map(item => rounded(item, digits));
  if (value && typeof value === "object") return Object.fromEntries(Object.entries(value).map(([key, item]) => [key, rounded(item, digits)]));
  return value;
}

export function impermanentLoss(data: JsonObject, config: JsonObject): JsonObject {
  const initialValue = finite(data.initial_pool_value, "initial_pool_value", 1e-9);
  const ratio = finite(data.price_ratio, "price_ratio", 1e-9);
  const feeFraction = finite(config.fee_return_fraction ?? 0, "fee_return_fraction", 0);
  const holdValue = initialValue * (1 + ratio) / 2;
  const poolValue = initialValue * Math.sqrt(ratio);
  const relativeValue = poolValue / holdValue;
  const fees = initialValue * feeFraction;
  const trace = Array.from({ length: 241 }, (_, index) => {
    const logRatio = Math.log(0.2) + index * (Math.log(5) - Math.log(0.2)) / 240;
    const r = Math.exp(logRatio);
    const hv = initialValue * (1 + r) / 2;
    const pv = initialValue * Math.sqrt(r);
    return { price_ratio: r, impermanent_loss: pv / hv - 1, hold_value: hv, pool_value: pv, net_pool_value: pv + fees };
  });
  return rounded({
    initial_pool_value: initialValue,
    price_ratio: ratio,
    hold_value: holdValue,
    pool_value_excluding_fees: poolValue,
    impermanent_loss_fraction: relativeValue - 1,
    impermanent_loss_amount: poolValue - holdValue,
    fee_income: fees,
    net_pool_value: poolValue + fees,
    net_vs_hold_fraction: (poolValue + fees) / holdValue - 1,
    trace,
  });
}

export function feeApr(data: JsonObject, config: JsonObject): JsonObject {
  if (!Array.isArray(data.rows) || data.rows.length === 0) throw new Error("rows must be a non-empty list");
  const annualization = finite(config.annualization_days ?? 365, "annualization_days", 1e-9);
  const protocolShare = finite(config.protocol_fee_share ?? 0, "protocol_fee_share", 0, 1);
  const basis = config.capital_basis ?? "time_weighted";
  if (!["time_weighted", "ending"].includes(basis)) throw new Error("capital_basis must be time_weighted or ending");
  let elapsed = 0, capitalTime = 0, cumulative = 0, cumulativeVolume = 0;
  const trace: JsonObject[] = [];
  data.rows.forEach((row: JsonObject, index: number) => {
    const duration = finite(row.duration_days ?? 1, `rows[${index}].duration_days`, 1e-9);
    const volume = finite(row.volume, `rows[${index}].volume`, 0);
    const feeRate = finite(row.fee_rate, `rows[${index}].fee_rate`, 0, 1);
    const share = finite(row.lp_share, `rows[${index}].lp_share`, 0, 1);
    const capital = finite(row.lp_capital, `rows[${index}].lp_capital`, 1e-9);
    const fees = volume * feeRate * share * (1 - protocolShare);
    elapsed += duration; capitalTime += capital * duration; cumulative += fees; cumulativeVolume += volume;
    const denominator = basis === "time_weighted" ? capitalTime / elapsed : capital;
    trace.push({
      index, timestamp: row.timestamp, volume, lp_capital: capital, daily_fee_income: fees,
      cumulative_fee_income: cumulative, running_apr: cumulative / denominator * annualization / elapsed,
    });
  });
  const averageCapital = capitalTime / elapsed;
  const denominator = basis === "time_weighted" ? averageCapital : finite(data.rows.at(-1).lp_capital, "ending lp_capital", 1e-9);
  return rounded({
    elapsed_days: elapsed,
    gross_volume: cumulativeVolume,
    lp_fee_income: cumulative,
    time_weighted_average_capital: averageCapital,
    capital_denominator: denominator,
    capital_basis: basis,
    protocol_fee_share: protocolShare,
    simple_fee_apr: cumulative / denominator * annualization / elapsed,
    period_fee_return: cumulative / denominator,
    annualization_days: annualization,
    trace,
  });
}

export function healthFactor(data: JsonObject, config: JsonObject): JsonObject {
  if (!Array.isArray(data.collateral) || data.collateral.length === 0 || !Array.isArray(data.debts))
    throw new Error("collateral must be non-empty and debts must be a list");
  const cm = finite(config.collateral_price_multiplier ?? 1, "collateral_price_multiplier", 0);
  const dm = finite(config.debt_price_multiplier ?? 1, "debt_price_multiplier", 0);
  let collateralValue = 0, adjusted = 0, debtValue = 0;
  const collateralLedger = data.collateral.map((asset: JsonObject, index: number) => {
    const quantity = finite(asset.quantity, `collateral[${index}].quantity`, 0);
    const price = finite(asset.price, `collateral[${index}].price`, 0) * cm;
    const threshold = finite(asset.liquidation_threshold, `collateral[${index}].liquidation_threshold`, 0, 1);
    const eligible = asset.eligible ?? true;
    const value = quantity * price;
    const contribution = eligible ? value * threshold : 0;
    collateralValue += value; adjusted += contribution;
    return { asset: asset.asset ?? `C${index}`, value, threshold, eligible, adjusted_contribution: contribution };
  });
  const debtLedger = data.debts.map((asset: JsonObject, index: number) => {
    const quantity = finite(asset.quantity, `debts[${index}].quantity`, 0);
    const price = finite(asset.price, `debts[${index}].price`, 0) * dm;
    const value = quantity * price; debtValue += value;
    return { asset: asset.asset ?? `D${index}`, value };
  });
  const hf = debtValue === 0 ? null : adjusted / debtValue;
  const state = hf === null ? "no-debt" : hf < 1 ? "liquidatable" : hf === 1 ? "at-threshold" : "above-threshold";
  const trace = Array.from({ length: 241 }, (_, index) => {
    const multiplier = 0.4 + index / 240;
    const stressed = adjusted * multiplier;
    return { collateral_price_multiplier: multiplier, health_factor: debtValue === 0 ? null : stressed / debtValue, adjusted_collateral_value: stressed };
  });
  return rounded({
    total_collateral_value: collateralValue,
    threshold_adjusted_collateral_value: adjusted,
    total_debt_value: debtValue,
    weighted_average_liquidation_threshold: collateralValue === 0 ? 0 : adjusted / collateralValue,
    health_factor: hf,
    buffer_value: hf === null ? null : adjusted - debtValue,
    state, collateral_ledger: collateralLedger, debt_ledger: debtLedger, trace,
  });
}

export function liquidationPrice(data: JsonObject, config: JsonObject): JsonObject {
  if (!Array.isArray(data.collateral) || data.collateral.length === 0 || !Array.isArray(data.debts) || !data.selected_asset)
    throw new Error("collateral, debts, and selected_asset are required");
  const debtMultiplier = finite(config.debt_multiplier ?? 1, "debt_multiplier", 0);
  const shift = finite(config.threshold_shift ?? 0, "threshold_shift", -1, 1);
  let debtValue = 0;
  data.debts.forEach((asset: JsonObject, index: number) => {
    debtValue += finite(asset.quantity, `debts[${index}].quantity`, 0) * finite(asset.price, `debts[${index}].price`, 0);
  });
  debtValue *= debtMultiplier;
  let otherAdjusted = 0;
  let chosen: JsonObject | null = null;
  data.collateral.forEach((asset: JsonObject, index: number) => {
    const quantity = finite(asset.quantity, `collateral[${index}].quantity`, 0);
    const price = finite(asset.price, `collateral[${index}].price`, 0);
    const threshold = finite(asset.liquidation_threshold, `collateral[${index}].liquidation_threshold`, 0, 1);
    if (asset.asset === data.selected_asset) chosen = { quantity, current_price: price, threshold: Math.max(0, Math.min(1, threshold + shift)) };
    else if (asset.eligible ?? true) otherAdjusted += quantity * price * threshold;
  });
  if (chosen === null) throw new Error("selected_asset is not present in collateral");
  const c = chosen as JsonObject;
  const denominator = c.quantity * c.threshold;
  const required = denominator <= 0 ? null : Math.max(0, (debtValue - otherAdjusted) / denominator);
  const reason = denominator <= 0 ? "selected collateral has zero quantity or zero effective liquidation threshold" : required === 0 ? "other collateral alone covers debt" : "finite break-even price";
  const currentAdjusted = c.quantity * c.current_price * c.threshold;
  const currentHf = debtValue === 0 ? null : (otherAdjusted + currentAdjusted) / debtValue;
  const trace = Array.from({ length: 241 }, (_, index) => {
    const price_multiplier = 0.4 + index / 240;
    const selected_price = c.current_price * price_multiplier;
    const health_factor = debtValue === 0 ? null : (otherAdjusted + c.quantity * selected_price * c.threshold) / debtValue;
    return { price_multiplier, selected_price, health_factor };
  });
  return rounded({
    selected_asset: data.selected_asset,
    selected_quantity: c.quantity,
    current_selected_price: c.current_price,
    effective_selected_liquidation_threshold: c.threshold,
    total_debt_value: debtValue,
    other_adjusted_collateral_value: otherAdjusted,
    liquidation_price: required,
    distance_to_liquidation_fraction: required === null || c.current_price === 0 ? null : (c.current_price - required) / c.current_price,
    current_health_factor: currentHf,
    reason, trace,
  });
}

export function liquidationWaterfall(data: JsonObject, config: JsonObject): JsonObject {
  const debt = finite(data.debt_value, "debt_value", 0);
  const collateral = finite(data.collateral_sale_proceeds, "collateral_sale_proceeds", 0);
  const reserve = finite(data.protocol_reserve, "protocol_reserve", 0);
  const insurance = finite(data.insurance_fund, "insurance_fund", 0);
  const backstop = finite(data.backstop_capacity, "backstop_capacity", 0);
  const recoveryRate = finite(config.collateral_recovery_rate ?? 1, "collateral_recovery_rate", 0, 1);
  const enabled = config.backstop_enabled ?? true;
  const capacities: Array<[string, number]> = [
    ["collateral-recovery", collateral * recoveryRate],
    ["protocol-reserve", reserve],
    ["insurance-fund", insurance],
    ["backstop", enabled ? backstop : 0],
  ];
  let remaining = debt, cumulative = 0;
  const ledger = capacities.map(([layer, capacity]) => {
    const absorbed = Math.min(remaining, capacity); remaining -= absorbed; cumulative += absorbed;
    return { layer, available_capacity: capacity, absorbed, remaining_debt: remaining, cumulative_absorbed: cumulative };
  });
  ledger.push({ layer: "uncovered-bad-debt", available_capacity: null as any, absorbed: remaining, remaining_debt: 0, cumulative_absorbed: cumulative + remaining });
  const stressTrace = Array.from({ length: 241 }, (_, index) => {
    const collateral_proceeds_multiplier = index * 1.2 / 240;
    const stressed = collateral * recoveryRate * collateral_proceeds_multiplier;
    const capacity = stressed + reserve + insurance + (enabled ? backstop : 0);
    return { collateral_proceeds_multiplier, covered_debt: Math.min(debt, capacity), uncovered_bad_debt: Math.max(0, debt - capacity) };
  });
  return rounded({
    debt_value: debt,
    effective_collateral_proceeds: collateral * recoveryRate,
    total_buffer_capacity: reserve + insurance + (enabled ? backstop : 0),
    covered_debt: debt - remaining,
    uncovered_bad_debt: remaining,
    coverage_fraction: debt === 0 ? 1 : (debt - remaining) / debt,
    backstop_enabled: enabled,
    ledger,
    trace: stressTrace,
  });
}

export function runTopic(kind: string, data: JsonObject, config: JsonObject): JsonObject {
  if (!data || typeof data !== "object" || !config || typeof config !== "object") throw new Error("data and config must be objects");
  const functions: Record<string, (d: JsonObject, c: JsonObject) => JsonObject> = {
    impermanent_loss: impermanentLoss,
    fee_apr: feeApr,
    health_factor: healthFactor,
    liquidation_price: liquidationPrice,
    waterfall: liquidationWaterfall,
  };
  if (!functions[kind]) throw new Error(`unknown topic kind: ${kind}`);
  return functions[kind](data, config);
}