lognormal mixture model

financepy.models.lognormal_mixture_model

Created on Mon Sep 7 17:59:06 2026 @author: Dominic

Class

LognormalMixtureModel

LognormalMixtureModel(
    F,
    T,
    r = 0.0,
)

Two-component lognormal mixture model for a single maturity. Parameters ---------- F : float Market forward price. T : float Time to maturity. r : float Continuously compounded risk-free rate. Model parameters ---------------- p : float Weight of first component. displacement : float Determines F1 through F1 = F * exp(displacement). sigma1 : float Volatility of first component. sigma2 : float Volatility of second component. The second component forward F2 is determined by p F1 + (1-p) F2 = F so that the mixture satisfies the risk-neutral forward condition.

Methods

black_call


black_call(
    F,
    K,
    T,
    r,
    sigma,
)

Black call price in forward form: C = exp(-rT) [F N(d1) - K N(d2)]

black_implied_vol


black_implied_vol(
    price,
    F,
    K,
    T,
    r,
)

Recover Black implied volatility from a European call price.

price


price(
    self,
    K,
    p = None,
    displacement = None,
    sigma1 = None,
    sigma2 = None,
)

Price European calls under the two-component mixture.

implied_vol


implied_vol(
    self,
    K,
)

Return model implied volatility for one or several strikes.

density


density(
    self,
    ST,
)

Evaluate the calibrated terminal risk-neutral density.

calibrate


calibrate(
    self,
    strikes,
    market_vols,
    weights = None,
    initial_guess = None,
)

Calibrate the model to market implied volatilities. Parameters ---------- strikes : array-like Market strikes. market_vols : array-like Market implied volatilities in decimal form. weights : array-like, optional Calibration weights. initial_guess : array-like, optional Initial guess in raw optimisation coordinates. Returns ------- dict Calibrated parameters.

parameters

Return calibrated model parameters.

forward_check

Verify the risk-neutral forward condition.

calibration_errors


calibration_errors(
    self,
    strikes,
    market_vols,
)

Return model IVs and calibration errors.

Generated automatically from the FinancePy source code. Do not edit this file manually.