874b4a5a02
- Set ruff/black line length to 120 - Reformatted code with black - Fixed import ordering with ruff - Disabled lint for UI component files with long CSS strings - Updated pyproject.toml with proper tool configuration
213 lines
7.2 KiB
Python
213 lines
7.2 KiB
Python
from __future__ import annotations
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import math
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from dataclasses import dataclass
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from datetime import date, timedelta
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from typing import Any, Literal
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try: # pragma: no cover - optional dependency
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import QuantLib as ql
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except ImportError: # pragma: no cover - optional dependency
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ql = None
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OptionType = Literal["call", "put"]
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DEFAULT_GOLD_PRICE_PER_OUNCE: float = 4600.0
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DEFAULT_GLD_PRICE: float = 460.0
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DEFAULT_RISK_FREE_RATE: float = 0.045
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DEFAULT_VOLATILITY: float = 0.16
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DEFAULT_DIVIDEND_YIELD: float = 0.0
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@dataclass(frozen=True)
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class BlackScholesInputs:
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"""Inputs for European Black-Scholes pricing."""
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spot: float = DEFAULT_GLD_PRICE
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strike: float = DEFAULT_GLD_PRICE
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time_to_expiry: float = 0.25
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risk_free_rate: float = DEFAULT_RISK_FREE_RATE
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volatility: float = DEFAULT_VOLATILITY
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option_type: OptionType = "put"
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dividend_yield: float = DEFAULT_DIVIDEND_YIELD
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valuation_date: date | None = None
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@dataclass(frozen=True)
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class PricingResult:
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"""European option price and Greeks."""
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price: float
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delta: float
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gamma: float
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theta: float
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vega: float
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rho: float
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@dataclass(frozen=True)
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class HedgingCost:
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"""Annualized hedging cost summary."""
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premium_paid: float
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annual_cost_dollars: float
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annual_cost_pct: float
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def _validate_option_type(option_type: str) -> OptionType:
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option = option_type.lower()
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if option not in {"call", "put"}:
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raise ValueError("option_type must be either 'call' or 'put'")
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return option # type: ignore[return-value]
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def _to_quantlib_option_type(option_type: OptionType) -> Any:
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if ql is None:
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raise RuntimeError("QuantLib is not installed")
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return ql.Option.Call if option_type == "call" else ql.Option.Put
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def _build_dates(time_to_expiry: float, valuation_date: date | None) -> tuple[Any, Any]:
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if time_to_expiry <= 0.0:
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raise ValueError("time_to_expiry must be positive")
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if ql is None:
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return (None, None)
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valuation = valuation_date or date.today()
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maturity = valuation + timedelta(days=max(1, round(time_to_expiry * 365)))
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return (
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ql.Date(valuation.day, valuation.month, valuation.year),
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ql.Date(maturity.day, maturity.month, maturity.year),
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)
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def _norm_pdf(value: float) -> float:
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return math.exp(-(value**2) / 2.0) / math.sqrt(2.0 * math.pi)
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def _norm_cdf(value: float) -> float:
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return 0.5 * (1.0 + math.erf(value / math.sqrt(2.0)))
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def _analytic_black_scholes(params: BlackScholesInputs, option_type: OptionType) -> PricingResult:
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if params.spot <= 0 or params.strike <= 0 or params.time_to_expiry <= 0 or params.volatility <= 0:
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raise ValueError("spot, strike, time_to_expiry, and volatility must be positive")
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t = params.time_to_expiry
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sigma = params.volatility
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sqrt_t = math.sqrt(t)
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d1 = (
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math.log(params.spot / params.strike) + (params.risk_free_rate - params.dividend_yield + 0.5 * sigma**2) * t
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) / (sigma * sqrt_t)
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d2 = d1 - sigma * sqrt_t
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disc_r = math.exp(-params.risk_free_rate * t)
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disc_q = math.exp(-params.dividend_yield * t)
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pdf_d1 = _norm_pdf(d1)
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if option_type == "call":
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price = params.spot * disc_q * _norm_cdf(d1) - params.strike * disc_r * _norm_cdf(d2)
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delta = disc_q * _norm_cdf(d1)
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theta = (
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-(params.spot * disc_q * pdf_d1 * sigma) / (2 * sqrt_t)
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- params.risk_free_rate * params.strike * disc_r * _norm_cdf(d2)
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+ params.dividend_yield * params.spot * disc_q * _norm_cdf(d1)
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)
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rho = params.strike * t * disc_r * _norm_cdf(d2)
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else:
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price = params.strike * disc_r * _norm_cdf(-d2) - params.spot * disc_q * _norm_cdf(-d1)
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delta = disc_q * (_norm_cdf(d1) - 1.0)
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theta = (
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-(params.spot * disc_q * pdf_d1 * sigma) / (2 * sqrt_t)
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+ params.risk_free_rate * params.strike * disc_r * _norm_cdf(-d2)
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- params.dividend_yield * params.spot * disc_q * _norm_cdf(-d1)
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)
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rho = -params.strike * t * disc_r * _norm_cdf(-d2)
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gamma = (disc_q * pdf_d1) / (params.spot * sigma * sqrt_t)
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vega = params.spot * disc_q * pdf_d1 * sqrt_t
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return PricingResult(
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price=float(price),
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delta=float(delta),
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gamma=float(gamma),
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theta=float(theta),
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vega=float(vega),
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rho=float(rho),
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)
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def black_scholes_price_and_greeks(params: BlackScholesInputs) -> PricingResult:
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"""Price a European option with QuantLib when available, otherwise analytic BSM."""
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option_type = _validate_option_type(params.option_type)
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if ql is None:
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return _analytic_black_scholes(params, option_type)
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valuation_ql, maturity_ql = _build_dates(params.time_to_expiry, params.valuation_date)
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ql.Settings.instance().evaluationDate = valuation_ql
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day_count = ql.Actual365Fixed()
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calendar = ql.NullCalendar()
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spot_handle = ql.QuoteHandle(ql.SimpleQuote(params.spot))
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dividend_curve = ql.YieldTermStructureHandle(ql.FlatForward(valuation_ql, params.dividend_yield, day_count))
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risk_free_curve = ql.YieldTermStructureHandle(ql.FlatForward(valuation_ql, params.risk_free_rate, day_count))
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volatility = ql.BlackVolTermStructureHandle(
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ql.BlackConstantVol(valuation_ql, calendar, params.volatility, day_count)
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)
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process = ql.BlackScholesMertonProcess(spot_handle, dividend_curve, risk_free_curve, volatility)
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payoff = ql.PlainVanillaPayoff(_to_quantlib_option_type(option_type), params.strike)
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exercise = ql.EuropeanExercise(maturity_ql)
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option = ql.VanillaOption(payoff, exercise)
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option.setPricingEngine(ql.AnalyticEuropeanEngine(process))
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return PricingResult(
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price=float(option.NPV()),
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delta=float(option.delta()),
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gamma=float(option.gamma()),
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theta=float(option.theta()),
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vega=float(option.vega()),
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rho=float(option.rho()),
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)
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def margin_call_threshold_price(
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portfolio_value: float,
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loan_amount: float,
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current_price: float = DEFAULT_GLD_PRICE,
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margin_call_ltv: float = 0.75,
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) -> float:
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"""Calculate the underlying price where a margin call is triggered."""
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if portfolio_value <= 0 or loan_amount <= 0 or current_price <= 0:
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raise ValueError("portfolio_value, loan_amount, and current_price must be positive")
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if not 0 < margin_call_ltv < 1:
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raise ValueError("margin_call_ltv must be between 0 and 1")
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units = portfolio_value / current_price
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return loan_amount / (margin_call_ltv * units)
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def annual_hedging_cost(
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premium_per_share: float,
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shares_hedged: float,
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portfolio_value: float,
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hedge_term_years: float,
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) -> HedgingCost:
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"""Annualize the premium cost of a hedging program."""
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if premium_per_share < 0 or shares_hedged <= 0 or portfolio_value <= 0 or hedge_term_years <= 0:
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raise ValueError(
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"premium_per_share must be non-negative and shares_hedged, portfolio_value, "
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"and hedge_term_years must be positive"
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)
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premium_paid = premium_per_share * shares_hedged
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annual_cost_dollars = premium_paid / hedge_term_years
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annual_cost_pct = annual_cost_dollars / portfolio_value
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return HedgingCost(
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premium_paid=premium_paid,
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annual_cost_dollars=annual_cost_dollars,
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annual_cost_pct=annual_cost_pct,
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)
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