Initial commit: Vault Dashboard for options hedging

- FastAPI + NiceGUI web application
- QuantLib-based Black-Scholes pricing with Greeks
- Protective put, laddered, and LEAPS strategies
- Real-time WebSocket updates
- TradingView-style charts via Lightweight-Charts
- Docker containerization
- GitLab CI/CD pipeline for VPS deployment
- VPN-only access configuration

app/core/pricing/black_scholes.py

@@ -0,0 +1,210 @@
+from __future__ import annotations
+
+from dataclasses import dataclass
+from datetime import date, timedelta
+import math
+from typing import Any, Literal
+
+try:  # pragma: no cover - optional dependency
+    import QuantLib as ql
+except ImportError:  # pragma: no cover - optional dependency
+    ql = None
+
+OptionType = Literal["call", "put"]
+
+DEFAULT_GOLD_PRICE_PER_OUNCE: float = 4600.0
+DEFAULT_GLD_PRICE: float = 460.0
+DEFAULT_RISK_FREE_RATE: float = 0.045
+DEFAULT_VOLATILITY: float = 0.16
+DEFAULT_DIVIDEND_YIELD: float = 0.0
+
+
+@dataclass(frozen=True)
+class BlackScholesInputs:
+    """Inputs for European Black-Scholes pricing."""
+
+    spot: float = DEFAULT_GLD_PRICE
+    strike: float = DEFAULT_GLD_PRICE
+    time_to_expiry: float = 0.25
+    risk_free_rate: float = DEFAULT_RISK_FREE_RATE
+    volatility: float = DEFAULT_VOLATILITY
+    option_type: OptionType = "put"
+    dividend_yield: float = DEFAULT_DIVIDEND_YIELD
+    valuation_date: date | None = None
+
+
+@dataclass(frozen=True)
+class PricingResult:
+    """European option price and Greeks."""
+
+    price: float
+    delta: float
+    gamma: float
+    theta: float
+    vega: float
+    rho: float
+
+
+@dataclass(frozen=True)
+class HedgingCost:
+    """Annualized hedging cost summary."""
+
+    premium_paid: float
+    annual_cost_dollars: float
+    annual_cost_pct: float
+
+
+def _validate_option_type(option_type: str) -> OptionType:
+    option = option_type.lower()
+    if option not in {"call", "put"}:
+        raise ValueError("option_type must be either 'call' or 'put'")
+    return option  # type: ignore[return-value]
+
+
+def _to_quantlib_option_type(option_type: OptionType) -> Any:
+    if ql is None:
+        raise RuntimeError("QuantLib is not installed")
+    return ql.Option.Call if option_type == "call" else ql.Option.Put
+
+
+def _build_dates(time_to_expiry: float, valuation_date: date | None) -> tuple[Any, Any]:
+    if time_to_expiry <= 0.0:
+        raise ValueError("time_to_expiry must be positive")
+    if ql is None:
+        return (None, None)
+
+    valuation = valuation_date or date.today()
+    maturity = valuation + timedelta(days=max(1, round(time_to_expiry * 365)))
+    return (
+        ql.Date(valuation.day, valuation.month, valuation.year),
+        ql.Date(maturity.day, maturity.month, maturity.year),
+    )
+
+
+def _norm_pdf(value: float) -> float:
+    return math.exp(-(value**2) / 2.0) / math.sqrt(2.0 * math.pi)
+
+
+def _norm_cdf(value: float) -> float:
+    return 0.5 * (1.0 + math.erf(value / math.sqrt(2.0)))
+
+
+def _analytic_black_scholes(params: BlackScholesInputs, option_type: OptionType) -> PricingResult:
+    if params.spot <= 0 or params.strike <= 0 or params.time_to_expiry <= 0 or params.volatility <= 0:
+        raise ValueError("spot, strike, time_to_expiry, and volatility must be positive")
+
+    t = params.time_to_expiry
+    sigma = params.volatility
+    sqrt_t = math.sqrt(t)
+    d1 = (
+        math.log(params.spot / params.strike)
+        + (params.risk_free_rate - params.dividend_yield + 0.5 * sigma**2) * t
+    ) / (sigma * sqrt_t)
+    d2 = d1 - sigma * sqrt_t
+    disc_r = math.exp(-params.risk_free_rate * t)
+    disc_q = math.exp(-params.dividend_yield * t)
+    pdf_d1 = _norm_pdf(d1)
+
+    if option_type == "call":
+        price = params.spot * disc_q * _norm_cdf(d1) - params.strike * disc_r * _norm_cdf(d2)
+        delta = disc_q * _norm_cdf(d1)
+        theta = (
+            -(params.spot * disc_q * pdf_d1 * sigma) / (2 * sqrt_t)
+            - params.risk_free_rate * params.strike * disc_r * _norm_cdf(d2)
+            + params.dividend_yield * params.spot * disc_q * _norm_cdf(d1)
+        )
+        rho = params.strike * t * disc_r * _norm_cdf(d2)
+    else:
+        price = params.strike * disc_r * _norm_cdf(-d2) - params.spot * disc_q * _norm_cdf(-d1)
+        delta = disc_q * (_norm_cdf(d1) - 1.0)
+        theta = (
+            -(params.spot * disc_q * pdf_d1 * sigma) / (2 * sqrt_t)
+            + params.risk_free_rate * params.strike * disc_r * _norm_cdf(-d2)
+            - params.dividend_yield * params.spot * disc_q * _norm_cdf(-d1)
+        )
+        rho = -params.strike * t * disc_r * _norm_cdf(-d2)
+
+    gamma = (disc_q * pdf_d1) / (params.spot * sigma * sqrt_t)
+    vega = params.spot * disc_q * pdf_d1 * sqrt_t
+    return PricingResult(price=float(price), delta=float(delta), gamma=float(gamma), theta=float(theta), vega=float(vega), rho=float(rho))
+
+
+def black_scholes_price_and_greeks(params: BlackScholesInputs) -> PricingResult:
+    """Price a European option with QuantLib when available, otherwise analytic BSM."""
+
+    option_type = _validate_option_type(params.option_type)
+    if ql is None:
+        return _analytic_black_scholes(params, option_type)
+
+    valuation_ql, maturity_ql = _build_dates(params.time_to_expiry, params.valuation_date)
+    ql.Settings.instance().evaluationDate = valuation_ql
+
+    day_count = ql.Actual365Fixed()
+    calendar = ql.NullCalendar()
+
+    spot_handle = ql.QuoteHandle(ql.SimpleQuote(params.spot))
+    dividend_curve = ql.YieldTermStructureHandle(
+        ql.FlatForward(valuation_ql, params.dividend_yield, day_count)
+    )
+    risk_free_curve = ql.YieldTermStructureHandle(
+        ql.FlatForward(valuation_ql, params.risk_free_rate, day_count)
+    )
+    volatility = ql.BlackVolTermStructureHandle(
+        ql.BlackConstantVol(valuation_ql, calendar, params.volatility, day_count)
+    )
+
+    process = ql.BlackScholesMertonProcess(spot_handle, dividend_curve, risk_free_curve, volatility)
+    payoff = ql.PlainVanillaPayoff(_to_quantlib_option_type(option_type), params.strike)
+    exercise = ql.EuropeanExercise(maturity_ql)
+    option = ql.VanillaOption(payoff, exercise)
+    option.setPricingEngine(ql.AnalyticEuropeanEngine(process))
+
+    return PricingResult(
+        price=float(option.NPV()),
+        delta=float(option.delta()),
+        gamma=float(option.gamma()),
+        theta=float(option.theta()),
+        vega=float(option.vega()),
+        rho=float(option.rho()),
+    )
+
+
+def margin_call_threshold_price(
+    portfolio_value: float,
+    loan_amount: float,
+    current_price: float = DEFAULT_GLD_PRICE,
+    margin_call_ltv: float = 0.75,
+) -> float:
+    """Calculate the underlying price where a margin call is triggered."""
+
+    if portfolio_value <= 0 or loan_amount <= 0 or current_price <= 0:
+        raise ValueError("portfolio_value, loan_amount, and current_price must be positive")
+    if not 0 < margin_call_ltv < 1:
+        raise ValueError("margin_call_ltv must be between 0 and 1")
+
+    units = portfolio_value / current_price
+    return loan_amount / (margin_call_ltv * units)
+
+
+def annual_hedging_cost(
+    premium_per_share: float,
+    shares_hedged: float,
+    portfolio_value: float,
+    hedge_term_years: float,
+) -> HedgingCost:
+    """Annualize the premium cost of a hedging program."""
+
+    if premium_per_share < 0 or shares_hedged <= 0 or portfolio_value <= 0 or hedge_term_years <= 0:
+        raise ValueError(
+            "premium_per_share must be non-negative and shares_hedged, portfolio_value, "
+            "and hedge_term_years must be positive"
+        )
+
+    premium_paid = premium_per_share * shares_hedged
+    annual_cost_dollars = premium_paid / hedge_term_years
+    annual_cost_pct = annual_cost_dollars / portfolio_value
+    return HedgingCost(
+        premium_paid=premium_paid,
+        annual_cost_dollars=annual_cost_dollars,
+        annual_cost_pct=annual_cost_pct,
+    )