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
124 lines
4.1 KiB
Python
124 lines
4.1 KiB
Python
from __future__ import annotations
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from datetime import date, timedelta
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from typing import Literal
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import QuantLib as ql
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OptionType = Literal["call", "put"]
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DEFAULT_RISK_FREE_RATE: float = 0.045
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DEFAULT_VOLATILITY_GUESS: float = 0.16
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DEFAULT_DIVIDEND_YIELD: float = 0.0
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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) -> ql.Option.Type:
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return ql.Option.Call if option_type == "call" else ql.Option.Put
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def implied_volatility(
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option_price: float,
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spot: float,
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strike: float,
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time_to_expiry: float,
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risk_free_rate: float = DEFAULT_RISK_FREE_RATE,
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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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initial_guess: float = DEFAULT_VOLATILITY_GUESS,
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min_vol: float = 1e-4,
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max_vol: float = 4.0,
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accuracy: float = 1e-8,
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max_evaluations: int = 500,
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) -> float:
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"""Invert the Black-Scholes-Merton model to solve for implied volatility.
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Assumptions:
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- European option exercise
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- Flat rate, dividend, and volatility term structures
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- GLD dividend yield defaults to zero
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Args:
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option_price: Observed market premium.
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spot: Current underlying price.
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strike: Option strike price.
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time_to_expiry: Time to maturity in years.
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risk_free_rate: Annual risk-free rate.
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option_type: ``"call"`` or ``"put"``.
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dividend_yield: Continuous dividend yield.
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valuation_date: Pricing date, defaults to today.
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initial_guess: Starting volatility guess used in the pricing process.
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min_vol: Lower volatility search bound.
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max_vol: Upper volatility search bound.
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accuracy: Root-finding tolerance.
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max_evaluations: Maximum solver iterations.
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Returns:
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The annualized implied volatility as a decimal.
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Example:
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>>> vol = implied_volatility(
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... option_price=12.0,
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... spot=460.0,
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... strike=430.0,
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... time_to_expiry=0.5,
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... risk_free_rate=0.045,
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... option_type="put",
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... )
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>>> vol > 0
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True
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"""
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if option_price <= 0 or spot <= 0 or strike <= 0 or time_to_expiry <= 0:
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raise ValueError("option_price, spot, strike, and time_to_expiry must be positive")
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if initial_guess <= 0 or min_vol <= 0 or max_vol <= min_vol:
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raise ValueError("invalid volatility bounds or initial_guess")
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option_type = _validate_option_type(option_type)
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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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valuation_ql = ql.Date(valuation.day, valuation.month, valuation.year)
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maturity_ql = ql.Date(maturity.day, maturity.month, maturity.year)
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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(spot))
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dividend_curve = ql.YieldTermStructureHandle(ql.FlatForward(valuation_ql, dividend_yield, day_count))
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risk_free_curve = ql.YieldTermStructureHandle(ql.FlatForward(valuation_ql, risk_free_rate, day_count))
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volatility_curve = ql.BlackVolTermStructureHandle(
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ql.BlackConstantVol(valuation_ql, calendar, initial_guess, day_count)
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)
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process = ql.BlackScholesMertonProcess(
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spot_handle,
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dividend_curve,
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risk_free_curve,
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volatility_curve,
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)
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payoff = ql.PlainVanillaPayoff(_to_quantlib_option_type(option_type), 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 float(
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option.impliedVolatility(
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option_price,
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process,
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accuracy,
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max_evaluations,
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min_vol,
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max_vol,
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)
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)
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