merton jump diffusion

financepy.models.merton_jump_diffusion

Classes

MertonCalibrationResult

MertonCalibrationResult(
    model,
    sigma,
    jump_intensity,
    jump_mean,
    jump_volatility,
    fitted_vols,
    market_vols,
    vol_errors,
    rmse,
    mae,
    max_abs_error,
    optimizer_result,
)

Container for a Merton volatility-surface calibration.

Methods

success

No description available.

jump_compensator

No description available.

expected_jump_size

Expected proportional jump E[J-1].

MertonJumpDiffusion

MertonJumpDiffusion(
    sigma,
    jump_intensity,
    jump_mean,
    jump_volatility,
    poisson_tolerance = 1e-12,
    max_jumps = 200,
)

Merton jump-diffusion model for European equity options. The risk-neutral stock-price process is dS/S_- = (r - q - lambda * kappa_j) dt + sigma dW + (J - 1) dN where log(J) ~ Normal(mu_j, delta_j^2) and kappa_j = E[J - 1] = exp(mu_j + 0.5 * delta_j^2) - 1. Parameters ---------- sigma : float Diffusive volatility. jump_intensity : float Poisson jump intensity lambda, in jumps per year. jump_mean : float Mean log jump size mu_j. jump_volatility : float Standard deviation delta_j of log jump sizes. poisson_tolerance : float Remaining Poisson probability below which the pricing summation is terminated. max_jumps : int Maximum number of jump terms in the pricing summation.

Methods

jump_compensator

Expected proportional jump: E[J - 1] = exp(mu_j + 0.5 delta_j^2) - 1.

expected_jump_multiplier

Return E[J].

value


value(
    self,
    stock_price,
    time_to_expiry,
    strike_price,
    risk_free_rate,
    dividend_yield,
    option_type = <OptionTypes.EUROPEAN_CALL: 1>,
)

Value a European option using Merton's Poisson-mixture solution. Conditional on N_T=n jumps, log(S_T) is Gaussian. Therefore the option value is a Poisson-weighted sum of Black-Scholes values.

implied_volatility


implied_volatility(
    self,
    stock_price,
    time_to_expiry,
    strike_price,
    risk_free_rate,
    dividend_yield,
    option_type = <OptionTypes.EUROPEAN_CALL: 1>,
)

Return Black-Scholes implied volatility of the Merton price.

volatility_smile


volatility_smile(
    self,
    stock_price,
    time_to_expiry,
    strikes,
    risk_free_rate,
    dividend_yield,
    option_type = <OptionTypes.EUROPEAN_CALL: 1>,
)

Generate the Merton Black-Scholes implied-volatility smile.

volatility_surface


volatility_surface(
    self,
    stock_price,
    strikes,
    expiries,
    risk_free_rates,
    dividend_yields,
    option_type = <OptionTypes.EUROPEAN_CALL: 1>,
)

Generate a matrix of Black-Scholes implied volatilities. Returns ------- vols : ndarray Shape = (number of expiries, number of strikes).

calibrate


calibrate(
    cls,
    stock_price,
    strikes,
    expiries,
    market_vols,
    risk_free_rates,
    dividend_yields,
    option_type = <OptionTypes.EUROPEAN_CALL: 1>,
    initial_guess = None,
    lower_bounds = None,
    upper_bounds = None,
    weights = None,
    calibration_type = 'VOL',
    max_nfev = 3000,
)

Calibrate one global Merton parameter set to an entire implied-volatility surface. The calibrated parameters are sigma jump_intensity lambda jump_mean mu_j jump_volatility delta_j Parameters ---------- market_vols : ndarray Matrix of Black-Scholes implied volatilities with shape (len(expiries), len(strikes)) calibration_type : str "VOL" Minimise errors directly in Black-Scholes implied volatility. "VEGA" Minimise Black-Scholes vega-scaled price errors. weights : ndarray or None Optional calibration weights with the same dimensions as market_vols. Returns ------- MertonCalibrationResult

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