position-tracker/src/ai/greeks.ts

/**
 * Black-Scholes IV solver + Greeks calculator for European options.
 *
 * Why Black-Scholes for SENSEX weeklies (European, no dividends mid-week)?
 *  - Closed-form, fast (~5ms per position)
 *  - Standard model; bid-ask spreads dominate any model error on weeklies
 *
 * Inputs use IST conventions:
 *  - dte: days to expiry (integer or fractional). Expiry assumed at 15:30 IST.
 *  - rfr: 6.5% (RBI repo, default — can be overridden via env)
 *  - dy:  1.2% SENSEX trailing dividend yield (default)
 */
export interface GreeksInput {
  spot:    number;   // Underlying spot price
  strike:  number;   // Option strike
  dte:     number;   // Days to expiry (fractional ok, e.g. 2.3)
  ltp:     number;   // Current option premium
  type:    'CE' | 'PE';
  rfr?:    number;   // Annualised risk-free rate, default 0.065
  dy?:     number;   // Annualised dividend yield, default 0.012
}

export interface Greeks {
  iv:    number;   // Implied vol, annualised (e.g. 0.16 = 16%)
  delta: number;   // ∂price/∂spot (per 1.0 spot move)
  gamma: number;   // ∂delta/∂spot
  theta: number;   // ∂price/∂t (per day, NOT per year — we divide by 365)
  vega:  number;   // ∂price/∂vol (per 1.0 vol point, i.e. 100%)
  rho:   number;   // ∂price/∂rfr (per 1.0 rate point)
  ok:    boolean;  // false if IV solver failed (deep OTM, illiquid, etc)
}

const SQRT_2PI = Math.sqrt(2 * Math.PI);

// Standard normal PDF
const pdf = (x: number) => Math.exp(-0.5 * x * x) / SQRT_2PI;

// Standard normal CDF — Abramowitz & Stegun approximation, |err| < 7.5e-8
function cdf(x: number): number {
  const sign = x < 0 ? -1 : 1;
  x = Math.abs(x) / Math.SQRT2;
  // A&S formula 7.1.26
  const a1 =  0.254829592, a2 = -0.284496736, a3 =  1.421413741;
  const a4 = -1.453152027, a5 =  1.061405429, p  =  0.3275911;
  const t  = 1.0 / (1.0 + p * x);
  const y  = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1) * t * Math.exp(-x * x);
  return 0.5 * (1.0 + sign * y);
}

/**
 * Black-Scholes price for European call or put with continuous dividend yield.
 * Returns price; helper used by IV solver.
 */
function bsPrice(spot: number, strike: number, t: number, rfr: number, dy: number, vol: number, type: 'CE' | 'PE'): number {
  if (t <= 0 || vol <= 0) {
    // At-expiry intrinsic value
    return type === 'CE' ? Math.max(spot - strike, 0) : Math.max(strike - spot, 0);
  }
  const sqrtT = Math.sqrt(t);
  const d1 = (Math.log(spot / strike) + (rfr - dy + 0.5 * vol * vol) * t) / (vol * sqrtT);
  const d2 = d1 - vol * sqrtT;
  const discS = spot   * Math.exp(-dy  * t);
  const discK = strike * Math.exp(-rfr * t);
  if (type === 'CE') return discS * cdf(d1) - discK * cdf(d2);
  return discK * cdf(-d2) - discS * cdf(-d1);
}

/**
 * Solve for implied vol via Newton-Raphson (vega-based), with bisection fallback.
 *
 * Returns IV in annualised decimal form (e.g. 0.16 = 16% annualised).
 * Returns NaN if no convergence — caller should treat as "Greeks unavailable".
 */
export function solveIV(input: GreeksInput): number {
  const { spot, strike, dte, ltp, type } = input;
  const rfr = input.rfr ?? 0.065;
  const dy  = input.dy  ?? 0.012;
  const t   = dte / 365;

  if (t <= 0 || ltp <= 0) return NaN;

  // Intrinsic value floor — if premium ≤ intrinsic, IV is effectively 0
  const intrinsic = type === 'CE' ? Math.max(spot - strike, 0) : Math.max(strike - spot, 0);
  if (ltp <= intrinsic + 0.01) return 0;

  // Newton-Raphson: start with reasonable IV guess
  let vol = 0.20; // start 20% annualised
  for (let i = 0; i < 50; i++) {
    const price = bsPrice(spot, strike, t, rfr, dy, vol, type);
    const diff  = price - ltp;
    if (Math.abs(diff) < 0.01) return vol;
    // Vega in per-1.0-vol terms
    const sqrtT = Math.sqrt(t);
    const d1 = (Math.log(spot / strike) + (rfr - dy + 0.5 * vol * vol) * t) / (vol * sqrtT);
    const vega = spot * Math.exp(-dy * t) * pdf(d1) * sqrtT;
    if (vega < 1e-6) break;  // dead zone — bail to bisection
    vol = vol - diff / vega;
    // Sanity guard
    if (vol < 0.001) vol = 0.001;
    if (vol > 5)     vol = 5;
  }

  // Bisection fallback (slower but always converges within bracket)
  let lo = 0.001, hi = 5;
  for (let i = 0; i < 60; i++) {
    const mid = (lo + hi) / 2;
    const price = bsPrice(spot, strike, t, rfr, dy, mid, type);
    if (Math.abs(price - ltp) < 0.01) return mid;
    if (price < ltp) lo = mid; else hi = mid;
  }
  return NaN;
}

/**
 * Compute full Greeks pack for an option position.
 *
 * Notes on units:
 *   - delta: per 1 unit move in spot (multiply by qty for position delta)
 *   - gamma: per 1 unit move in spot
 *   - theta: per day (already converted from per-year)
 *   - vega:  per 1 vol-point (i.e. price change if IV moves from 0.20 to 0.21 = vega/100)
 *
 * Sign convention: position-level (qty applied externally for portfolio aggregation)
 */
export function calcGreeks(input: GreeksInput): Greeks {
  const { spot, strike, dte, type } = input;
  const rfr = input.rfr ?? 0.065;
  const dy  = input.dy  ?? 0.012;
  const t   = dte / 365;

  const iv = solveIV(input);

  if (!isFinite(iv) || iv <= 0 || t <= 0) {
    return { iv: NaN, delta: 0, gamma: 0, theta: 0, vega: 0, rho: 0, ok: false };
  }

  const sqrtT = Math.sqrt(t);
  const d1 = (Math.log(spot / strike) + (rfr - dy + 0.5 * iv * iv) * t) / (iv * sqrtT);
  const d2 = d1 - iv * sqrtT;
  const discS = spot   * Math.exp(-dy  * t);
  const discK = strike * Math.exp(-rfr * t);

  const delta = type === 'CE'
    ? Math.exp(-dy * t) * cdf(d1)
    : Math.exp(-dy * t) * (cdf(d1) - 1);

  const gamma = (Math.exp(-dy * t) * pdf(d1)) / (spot * iv * sqrtT);

  // Theta per year then convert to per-day
  const thetaPerYear = type === 'CE'
    ? -(discS * pdf(d1) * iv) / (2 * sqrtT)
      - rfr * discK * cdf(d2)
      + dy  * discS * cdf(d1)
    : -(discS * pdf(d1) * iv) / (2 * sqrtT)
      + rfr * discK * cdf(-d2)
      - dy  * discS * cdf(-d1);
  const theta = thetaPerYear / 365;

  // Vega per 1 vol-point (decimal); divide by 100 if you want per 1% vol
  const vega = discS * pdf(d1) * sqrtT;

  const rho = type === 'CE'
    ? strike * t * Math.exp(-rfr * t) * cdf(d2) / 100
    : -strike * t * Math.exp(-rfr * t) * cdf(-d2) / 100;

  return { iv, delta, gamma, theta, vega, rho, ok: true };
}

const MONTH_MAP: Record<string, string> = {
  JAN:'01',FEB:'02',MAR:'03',APR:'04',MAY:'05',JUN:'06',
  JUL:'07',AUG:'08',SEP:'09',OCT:'10',NOV:'11',DEC:'12',
};

/**
 * Parse Angel One option symbol -> strike/type/expiry.
 * Handles three formats observed in the wild:
 *
 *   Format 1 — YY + M(1-digit) + DD + STRIKE
 *     SENSEX2660475500CE  → 2026-06-04, strike 75500
 *
 *   Format 2 — YY + MON + DD + STRIKE  (NIFTY carry-forward style)
 *     NIFTY28FEB2522500CE → 2025-02-28, strike 22500
 *     (NOTE: regex groups are DD, MON, YY order — Angel puts day first)
 *
 *   Format 3 — DD + MON + STRIKE  (SENSEX weekly, no year in symbol)
 *     SENSEX26JUN77300PE  → 2026-06-26, strike 77300, year inferred
 */
export function parseOptionSymbol(sym: string): { underlying: string; strike: number; type: 'CE' | 'PE'; expiry: Date } | null {
  // Format 1: YY + M(1) + DD + STRIKE
  let m = sym.match(/^([A-Z]+)(\d{2})(\d{1})(\d{2})(\d+)(CE|PE)$/);
  if (m) {
    const yy = m[2], mo = m[3].padStart(2, '0'), dd = m[4];
    const exp = new Date(`20${yy}-${mo}-${dd}T15:30:00+05:30`);
    if (!isNaN(exp.getTime())) {
      return { underlying: m[1], strike: parseInt(m[5]), type: m[6] as 'CE' | 'PE', expiry: exp };
    }
  }
  // Format 2: YY + MON + DD + STRIKE  (kept for backward compat; falls through on invalid dates)
  // Note: SENSEX26JUN77300PE is NOT this format — it falls through to Format 3 below.
  m = sym.match(/^([A-Z]+)(\d{2})(JAN|FEB|MAR|APR|MAY|JUN|JUL|AUG|SEP|OCT|NOV|DEC)(\d{2})(\d+)(CE|PE)$/i);
  if (m) {
    const yy = m[2], mo = MONTH_MAP[m[3].toUpperCase()], dd = m[4];
    const exp = new Date(`20${yy}-${mo}-${dd}T15:30:00+05:30`);
    if (!isNaN(exp.getTime())) {
      return { underlying: m[1], strike: parseInt(m[5]), type: m[6].toUpperCase() as 'CE' | 'PE', expiry: exp };
    }
  }
  // Format 3: DD + MON + STRIKE  (SENSEX weekly — no year, infer from calendar)
  m = sym.match(/^([A-Z]+)(\d{1,2})(JAN|FEB|MAR|APR|MAY|JUN|JUL|AUG|SEP|OCT|NOV|DEC)(\d+)(CE|PE)$/i);
  if (m) {
    const dd = m[2].padStart(2, '0'), mo = MONTH_MAP[m[3].toUpperCase()];
    const thisYear = new Date().getFullYear();
    // Try current year first; if date is already >7 days in the past, try next year
    let exp = new Date(`${thisYear}-${mo}-${dd}T15:30:00+05:30`);
    if (isNaN(exp.getTime()) || exp.getTime() < Date.now() - 7 * 86400000) {
      exp = new Date(`${thisYear + 1}-${mo}-${dd}T15:30:00+05:30`);
    }
    if (!isNaN(exp.getTime())) {
      return { underlying: m[1], strike: parseInt(m[4]), type: m[5].toUpperCase() as 'CE' | 'PE', expiry: exp };
    }
  }
  return null;
}

/**
 * Days-to-expiry as fractional days (using IST 15:30 closing).
 * Returns 0 for expired contracts (clamped).
 */
export function dteFromExpiry(expiry: Date, now: Date = new Date()): number {
  const ms = expiry.getTime() - now.getTime();
  return Math.max(0, ms / 86400000);
}

/**
 * Black-Scholes theoretical price at an arbitrary spot using a provided IV.
 * Used in scenario analysis: compute leg P&L at scenario spots with current market IV.
 */
export function calcTheoreticalPrice(
  spot: number, strike: number, dte: number, iv: number,
  type: 'CE' | 'PE', rfr = 0.065, dy = 0.012
): number {
  if (iv <= 0 || dte <= 0 || spot <= 0) {
    return type === 'CE' ? Math.max(spot - strike, 0) : Math.max(strike - spot, 0);
  }
  return bsPrice(spot, strike, dte / 365, rfr, dy, iv, type);
}