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/american_pricing.py

@@ -0,0 +1,194 @@
+from __future__ import annotations
+
+from dataclasses import dataclass
+from datetime import date, timedelta
+from typing import Literal
+
+import QuantLib as ql
+
+OptionType = Literal["call", "put"]
+
+DEFAULT_RISK_FREE_RATE: float = 0.045
+DEFAULT_VOLATILITY: float = 0.16
+DEFAULT_DIVIDEND_YIELD: float = 0.0
+DEFAULT_GLD_PRICE: float = 460.0
+
+
+@dataclass(frozen=True)
+class AmericanOptionInputs:
+    """Inputs for American option pricing via a binomial tree.
+
+    This module is intended primarily for GLD protective puts, where early
+    exercise can matter in stressed scenarios.
+
+    Example:
+        >>> params = AmericanOptionInputs(
+        ...     spot=460.0,
+        ...     strike=420.0,
+        ...     time_to_expiry=0.5,
+        ...     option_type="put",
+        ... )
+        >>> params.steps
+        500
+    """
+
+    spot: float = DEFAULT_GLD_PRICE
+    strike: float = DEFAULT_GLD_PRICE
+    time_to_expiry: float = 0.5
+    risk_free_rate: float = DEFAULT_RISK_FREE_RATE
+    volatility: float = DEFAULT_VOLATILITY
+    option_type: OptionType = "put"
+    dividend_yield: float = DEFAULT_DIVIDEND_YIELD
+    steps: int = 500
+    valuation_date: date | None = None
+    tree: str = "crr"
+
+
+@dataclass(frozen=True)
+class AmericanPricingResult:
+    """American option price and finite-difference Greeks."""
+
+    price: float
+    delta: float
+    gamma: float
+    theta: float
+    vega: float
+    rho: 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) -> ql.Option.Type:
+    return ql.Option.Call if option_type == "call" else ql.Option.Put
+
+
+def _build_dates(time_to_expiry: float, valuation_date: date | None) -> tuple[ql.Date, ql.Date]:
+    if time_to_expiry <= 0.0:
+        raise ValueError("time_to_expiry must be positive")
+
+    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 _american_price(
+    params: AmericanOptionInputs,
+    *,
+    spot: float | None = None,
+    risk_free_rate: float | None = None,
+    volatility: float | None = None,
+    time_to_expiry: float | None = None,
+) -> float:
+    option_type = _validate_option_type(params.option_type)
+    used_spot = params.spot if spot is None else spot
+    used_rate = params.risk_free_rate if risk_free_rate is None else risk_free_rate
+    used_vol = params.volatility if volatility is None else volatility
+    used_time = params.time_to_expiry if time_to_expiry is None else time_to_expiry
+
+    if used_spot <= 0 or used_vol <= 0 or used_time <= 0:
+        raise ValueError("spot, volatility, and time_to_expiry must be positive")
+    if params.steps < 10:
+        raise ValueError("steps must be at least 10 for binomial pricing")
+
+    valuation_ql, maturity_ql = _build_dates(used_time, params.valuation_date)
+    ql.Settings.instance().evaluationDate = valuation_ql
+
+    day_count = ql.Actual365Fixed()
+    calendar = ql.NullCalendar()
+
+    spot_handle = ql.QuoteHandle(ql.SimpleQuote(used_spot))
+    dividend_curve = ql.YieldTermStructureHandle(
+        ql.FlatForward(valuation_ql, params.dividend_yield, day_count)
+    )
+    risk_free_curve = ql.YieldTermStructureHandle(
+        ql.FlatForward(valuation_ql, used_rate, day_count)
+    )
+    volatility_curve = ql.BlackVolTermStructureHandle(
+        ql.BlackConstantVol(valuation_ql, calendar, used_vol, day_count)
+    )
+
+    process = ql.BlackScholesMertonProcess(
+        spot_handle,
+        dividend_curve,
+        risk_free_curve,
+        volatility_curve,
+    )
+
+    payoff = ql.PlainVanillaPayoff(_to_quantlib_option_type(option_type), params.strike)
+    exercise = ql.AmericanExercise(valuation_ql, maturity_ql)
+    option = ql.VanillaOption(payoff, exercise)
+    option.setPricingEngine(ql.BinomialVanillaEngine(process, params.tree, params.steps))
+    return float(option.NPV())
+
+
+def american_option_price_and_greeks(params: AmericanOptionInputs) -> AmericanPricingResult:
+    """Price an American option and estimate Greeks with finite differences.
+
+    Notes:
+        - The price uses a QuantLib binomial tree engine.
+        - Greeks are finite-difference approximations because closed-form
+          American Greeks are not available in general.
+        - Theta is annualized and approximated by rolling one calendar day forward.
+
+    Args:
+        params: American option inputs.
+
+    Returns:
+        A price and finite-difference Greeks.
+
+    Example:
+        >>> params = AmericanOptionInputs(
+        ...     spot=460.0,
+        ...     strike=400.0,
+        ...     time_to_expiry=0.5,
+        ...     risk_free_rate=0.045,
+        ...     volatility=0.16,
+        ...     option_type="put",
+        ... )
+        >>> result = american_option_price_and_greeks(params)
+        >>> result.price > 0
+        True
+    """
+
+    base_price = _american_price(params)
+
+    spot_bump = max(0.01, params.spot * 0.01)
+    vol_bump = 0.01
+    rate_bump = 0.0001
+    dt = 1.0 / 365.0
+
+    price_up = _american_price(params, spot=params.spot + spot_bump)
+    price_down = _american_price(params, spot=max(1e-8, params.spot - spot_bump))
+    delta = (price_up - price_down) / (2.0 * spot_bump)
+    gamma = (price_up - 2.0 * base_price + price_down) / (spot_bump**2)
+
+    vega_up = _american_price(params, volatility=params.volatility + vol_bump)
+    vega_down = _american_price(params, volatility=max(1e-6, params.volatility - vol_bump))
+    vega = (vega_up - vega_down) / (2.0 * vol_bump)
+
+    rho_up = _american_price(params, risk_free_rate=params.risk_free_rate + rate_bump)
+    rho_down = _american_price(params, risk_free_rate=params.risk_free_rate - rate_bump)
+    rho = (rho_up - rho_down) / (2.0 * rate_bump)
+
+    if params.time_to_expiry <= dt:
+        theta = 0.0
+    else:
+        shorter_price = _american_price(params, time_to_expiry=params.time_to_expiry - dt)
+        theta = (shorter_price - base_price) / dt
+
+    return AmericanPricingResult(
+        price=base_price,
+        delta=delta,
+        gamma=gamma,
+        theta=theta,
+        vega=vega,
+        rho=rho,
+    )