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GreekMixin#

Provides finite-difference calculations for Greeks.

This mixin is designed to be side-effect-free. It creates modified copies of the input objects for shifted calculations rather than mutating them in place. It also supports Common Random Numbers (CRN) for variance reduction in Monte Carlo-based calculations by checking for a self.rng attribute.

Source code in src/quantfin/techniques/base/greek_mixin.py 
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class GreekMixin:
    """
    Provides finite-difference calculations for Greeks.

    This mixin is designed to be side-effect-free. It creates modified copies
    of the input objects for shifted calculations rather than mutating them in place.
    It also supports Common Random Numbers (CRN) for variance reduction in
    Monte Carlo-based calculations by checking for a `self.rng` attribute.
    """

    def delta(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        h_frac: float = 1e-3,
        **kwargs: Any,
    ) -> float:
        """
        Calculates delta using a central difference formula.

        Parameters
        ----------
        option : Option
            The option contract to be priced.
        stock : Stock
            The underlying asset's properties.
        model : BaseModel
            The financial model to use for the calculation.
        rate : Rate
            The risk-free rate structure.
        h_frac : float, optional
            The fractional step size for shifting the spot price, by default 1e-3.

        Returns
        -------
        float
            The calculated delta.
        """
        h = stock.spot * h_frac
        stock_up = replace(stock, spot=stock.spot + h)
        stock_dn = replace(stock, spot=stock.spot - h)

        rng = getattr(self, "rng", None)
        if isinstance(rng, np.random.Generator):
            with crn(rng):
                p_up = self.price(option, stock_up, model, rate, **kwargs).price
            with crn(rng):
                p_dn = self.price(option, stock_dn, model, rate, **kwargs).price
        else:
            p_up = self.price(option, stock_up, model, rate, **kwargs).price
            p_dn = self.price(option, stock_dn, model, rate, **kwargs).price

        return (p_up - p_dn) / (2 * h)

    def gamma(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        h_frac: float = 1e-3,
        **kw: Any,
    ) -> float:
        """
        Calculates gamma using a central difference formula.

        Parameters
        ----------
        option : Option
            The option contract to be priced.
        stock : Stock
            The underlying asset's properties.
        model : BaseModel
            The financial model to use for the calculation.
        rate : Rate
            The risk-free rate structure.
        h_frac : float, optional
            The fractional step size for shifting the spot price, by default 1e-3.

        Returns
        -------
        float
            The calculated gamma.
        """
        h = stock.spot * h_frac
        stock_up = replace(stock, spot=stock.spot + h)
        stock_dn = replace(stock, spot=stock.spot - h)

        rng = getattr(self, "rng", None)
        if isinstance(rng, np.random.Generator):
            with crn(rng):
                p_up = self.price(option, stock_up, model, rate, **kw).price
            with crn(rng):
                p_0 = self.price(option, stock, model, rate, **kw).price
            with crn(rng):
                p_dn = self.price(option, stock_dn, model, rate, **kw).price
        else:
            p_up = self.price(option, stock_up, model, rate, **kw).price
            p_0 = self.price(option, stock, model, rate, **kw).price
            p_dn = self.price(option, stock_dn, model, rate, **kw).price

        return (p_up - 2 * p_0 + p_dn) / (h * h)

    def vega(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        h: float = 1e-4,
        **kw: Any,
    ) -> float:
        """
        Calculates vega using a central difference formula.

        Returns `np.nan` if the model does not have a 'sigma' parameter.

        Parameters
        ----------
        option : Option
            The option contract to be priced.
        stock : Stock
            The underlying asset's properties.
        model : BaseModel
            The financial model to use for the calculation.
        rate : Rate
            The risk-free rate structure.
        h : float, optional
            The absolute step size for shifting volatility, by default 1e-4.

        Returns
        -------
        float
            The calculated vega.
        """
        if "sigma" not in model.params:
            return np.nan

        sigma = model.params["sigma"]
        model_up = model.with_params(sigma=sigma + h)
        model_dn = model.with_params(sigma=sigma - h)

        rng = getattr(self, "rng", None)
        if isinstance(rng, np.random.Generator):
            with crn(rng):
                p_up = self.price(option, stock, model_up, rate, **kw).price
            with crn(rng):
                p_dn = self.price(option, stock, model_dn, rate, **kw).price
        else:
            p_up = self.price(option, stock, model_up, rate, **kw).price
            p_dn = self.price(option, stock, model_dn, rate, **kw).price

        return (p_up - p_dn) / (2 * h)

    def theta(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        h: float = 1e-5,
        **kw: Any,
    ) -> float:
        """
        Calculates theta using a central difference formula.

        Parameters
        ----------
        option : Option
            The option contract to be priced.
        stock : Stock
            The underlying asset's properties.
        model : BaseModel
            The financial model to use for the calculation.
        rate : Rate
            The risk-free rate structure.
        h : float, optional
            The absolute step size for shifting maturity, by default 1e-5.

        Returns
        -------
        float
            The calculated theta.
        """
        T0 = option.maturity
        opt_up = replace(option, maturity=T0 + h)
        opt_dn = replace(option, maturity=max(T0 - h, 1e-12))  # Avoid maturity of 0

        rng = getattr(self, "rng", None)
        if isinstance(rng, np.random.Generator):
            with crn(rng):
                p_up = self.price(opt_up, stock, model, rate, **kw).price
            with crn(rng):
                p_dn = self.price(opt_dn, stock, model, rate, **kw).price
        else:
            p_up = self.price(opt_up, stock, model, rate, **kw).price
            p_dn = self.price(opt_dn, stock, model, rate, **kw).price

        return (p_dn - p_up) / (2 * h)

    def rho(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        h: float = 1e-4,
        **kw: Any,
    ) -> float:
        """
        Calculates rho using a central difference formula.

        Parameters
        ----------
        option : Option
            The option contract to be priced.
        stock : Stock
            The underlying asset's properties.
        model : BaseModel
            The financial model to use for the calculation.
        rate : Rate
            The risk-free rate structure.
        h : float, optional
            The absolute step size for shifting the interest rate, by default 1e-4.

        Returns
        -------
        float
            The calculated rho.
        """
        r0 = rate.get_rate(option.maturity)
        rate_up = replace(rate, rate=r0 + h)
        rate_dn = replace(rate, rate=r0 - h)

        rng = getattr(self, "rng", None)
        if isinstance(rng, np.random.Generator):
            with crn(rng):
                p_up = self.price(option, stock, model, rate_up, **kw).price
            with crn(rng):
                p_dn = self.price(option, stock, model, rate_dn, **kw).price
        else:
            p_up = self.price(option, stock, model, rate_up, **kw).price
            p_dn = self.price(option, stock, model, rate_dn, **kw).price

        return (p_up - p_dn) / (2 * h)

delta(option: Option, stock: Stock, model: BaseModel, rate: Rate, h_frac: float = 0.001, **kwargs: Any) -> float #

Calculates delta using a central difference formula.

Parameters:

Name Type Description Default
option Option

The option contract to be priced.

 required
stock Stock

The underlying asset's properties.

 required
model BaseModel

The financial model to use for the calculation.

 required
rate Rate

The risk-free rate structure.

 required
h_frac float

The fractional step size for shifting the spot price, by default 1e-3.

 0.001

Returns:

Type Description
float

The calculated delta.
Source code in src/quantfin/techniques/base/greek_mixin.py 
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def delta(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    h_frac: float = 1e-3,
    **kwargs: Any,
) -> float:
    """
    Calculates delta using a central difference formula.

    Parameters
    ----------
    option : Option
        The option contract to be priced.
    stock : Stock
        The underlying asset's properties.
    model : BaseModel
        The financial model to use for the calculation.
    rate : Rate
        The risk-free rate structure.
    h_frac : float, optional
        The fractional step size for shifting the spot price, by default 1e-3.

    Returns
    -------
    float
        The calculated delta.
    """
    h = stock.spot * h_frac
    stock_up = replace(stock, spot=stock.spot + h)
    stock_dn = replace(stock, spot=stock.spot - h)

    rng = getattr(self, "rng", None)
    if isinstance(rng, np.random.Generator):
        with crn(rng):
            p_up = self.price(option, stock_up, model, rate, **kwargs).price
        with crn(rng):
            p_dn = self.price(option, stock_dn, model, rate, **kwargs).price
    else:
        p_up = self.price(option, stock_up, model, rate, **kwargs).price
        p_dn = self.price(option, stock_dn, model, rate, **kwargs).price

    return (p_up - p_dn) / (2 * h)

gamma(option: Option, stock: Stock, model: BaseModel, rate: Rate, h_frac: float = 0.001, **kw: Any) -> float #

Calculates gamma using a central difference formula.

Parameters:

Name Type Description Default
option Option

The option contract to be priced.

 required
stock Stock

The underlying asset's properties.

 required
model BaseModel

The financial model to use for the calculation.

 required
rate Rate

The risk-free rate structure.

 required
h_frac float

The fractional step size for shifting the spot price, by default 1e-3.

 0.001

Returns:

Type Description
float

The calculated gamma.
Source code in src/quantfin/techniques/base/greek_mixin.py 
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def gamma(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    h_frac: float = 1e-3,
    **kw: Any,
) -> float:
    """
    Calculates gamma using a central difference formula.

    Parameters
    ----------
    option : Option
        The option contract to be priced.
    stock : Stock
        The underlying asset's properties.
    model : BaseModel
        The financial model to use for the calculation.
    rate : Rate
        The risk-free rate structure.
    h_frac : float, optional
        The fractional step size for shifting the spot price, by default 1e-3.

    Returns
    -------
    float
        The calculated gamma.
    """
    h = stock.spot * h_frac
    stock_up = replace(stock, spot=stock.spot + h)
    stock_dn = replace(stock, spot=stock.spot - h)

    rng = getattr(self, "rng", None)
    if isinstance(rng, np.random.Generator):
        with crn(rng):
            p_up = self.price(option, stock_up, model, rate, **kw).price
        with crn(rng):
            p_0 = self.price(option, stock, model, rate, **kw).price
        with crn(rng):
            p_dn = self.price(option, stock_dn, model, rate, **kw).price
    else:
        p_up = self.price(option, stock_up, model, rate, **kw).price
        p_0 = self.price(option, stock, model, rate, **kw).price
        p_dn = self.price(option, stock_dn, model, rate, **kw).price

    return (p_up - 2 * p_0 + p_dn) / (h * h)

rho(option: Option, stock: Stock, model: BaseModel, rate: Rate, h: float = 0.0001, **kw: Any) -> float #

Calculates rho using a central difference formula.

Parameters:

Name Type Description Default
option Option

The option contract to be priced.

 required
stock Stock

The underlying asset's properties.

 required
model BaseModel

The financial model to use for the calculation.

 required
rate Rate

The risk-free rate structure.

 required
h float

The absolute step size for shifting the interest rate, by default 1e-4.

 0.0001

Returns:

Type Description
float

The calculated rho.
Source code in src/quantfin/techniques/base/greek_mixin.py 
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def rho(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    h: float = 1e-4,
    **kw: Any,
) -> float:
    """
    Calculates rho using a central difference formula.

    Parameters
    ----------
    option : Option
        The option contract to be priced.
    stock : Stock
        The underlying asset's properties.
    model : BaseModel
        The financial model to use for the calculation.
    rate : Rate
        The risk-free rate structure.
    h : float, optional
        The absolute step size for shifting the interest rate, by default 1e-4.

    Returns
    -------
    float
        The calculated rho.
    """
    r0 = rate.get_rate(option.maturity)
    rate_up = replace(rate, rate=r0 + h)
    rate_dn = replace(rate, rate=r0 - h)

    rng = getattr(self, "rng", None)
    if isinstance(rng, np.random.Generator):
        with crn(rng):
            p_up = self.price(option, stock, model, rate_up, **kw).price
        with crn(rng):
            p_dn = self.price(option, stock, model, rate_dn, **kw).price
    else:
        p_up = self.price(option, stock, model, rate_up, **kw).price
        p_dn = self.price(option, stock, model, rate_dn, **kw).price

    return (p_up - p_dn) / (2 * h)

theta(option: Option, stock: Stock, model: BaseModel, rate: Rate, h: float = 1e-05, **kw: Any) -> float #

Calculates theta using a central difference formula.

Parameters:

Name Type Description Default
option Option

The option contract to be priced.

 required
stock Stock

The underlying asset's properties.

 required
model BaseModel

The financial model to use for the calculation.

 required
rate Rate

The risk-free rate structure.

 required
h float

The absolute step size for shifting maturity, by default 1e-5.

 1e-05

Returns:

Type Description
float

The calculated theta.
Source code in src/quantfin/techniques/base/greek_mixin.py 
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def theta(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    h: float = 1e-5,
    **kw: Any,
) -> float:
    """
    Calculates theta using a central difference formula.

    Parameters
    ----------
    option : Option
        The option contract to be priced.
    stock : Stock
        The underlying asset's properties.
    model : BaseModel
        The financial model to use for the calculation.
    rate : Rate
        The risk-free rate structure.
    h : float, optional
        The absolute step size for shifting maturity, by default 1e-5.

    Returns
    -------
    float
        The calculated theta.
    """
    T0 = option.maturity
    opt_up = replace(option, maturity=T0 + h)
    opt_dn = replace(option, maturity=max(T0 - h, 1e-12))  # Avoid maturity of 0

    rng = getattr(self, "rng", None)
    if isinstance(rng, np.random.Generator):
        with crn(rng):
            p_up = self.price(opt_up, stock, model, rate, **kw).price
        with crn(rng):
            p_dn = self.price(opt_dn, stock, model, rate, **kw).price
    else:
        p_up = self.price(opt_up, stock, model, rate, **kw).price
        p_dn = self.price(opt_dn, stock, model, rate, **kw).price

    return (p_dn - p_up) / (2 * h)

vega(option: Option, stock: Stock, model: BaseModel, rate: Rate, h: float = 0.0001, **kw: Any) -> float #

Calculates vega using a central difference formula.

Returns np.nan if the model does not have a 'sigma' parameter.

Parameters:

Name Type Description Default
option Option

The option contract to be priced.

 required
stock Stock

The underlying asset's properties.

 required
model BaseModel

The financial model to use for the calculation.

 required
rate Rate

The risk-free rate structure.

 required
h float

The absolute step size for shifting volatility, by default 1e-4.

 0.0001

Returns:

Type Description
float

The calculated vega.
Source code in src/quantfin/techniques/base/greek_mixin.py 
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def vega(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    h: float = 1e-4,
    **kw: Any,
) -> float:
    """
    Calculates vega using a central difference formula.

    Returns `np.nan` if the model does not have a 'sigma' parameter.

    Parameters
    ----------
    option : Option
        The option contract to be priced.
    stock : Stock
        The underlying asset's properties.
    model : BaseModel
        The financial model to use for the calculation.
    rate : Rate
        The risk-free rate structure.
    h : float, optional
        The absolute step size for shifting volatility, by default 1e-4.

    Returns
    -------
    float
        The calculated vega.
    """
    if "sigma" not in model.params:
        return np.nan

    sigma = model.params["sigma"]
    model_up = model.with_params(sigma=sigma + h)
    model_dn = model.with_params(sigma=sigma - h)

    rng = getattr(self, "rng", None)
    if isinstance(rng, np.random.Generator):
        with crn(rng):
            p_up = self.price(option, stock, model_up, rate, **kw).price
        with crn(rng):
            p_dn = self.price(option, stock, model_dn, rate, **kw).price
    else:
        p_up = self.price(option, stock, model_up, rate, **kw).price
        p_dn = self.price(option, stock, model_dn, rate, **kw).price

    return (p_up - p_dn) / (2 * h)