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Closed-Form Technique#

Bases: BaseTechnique, GreekMixin, IVMixin

A pricing technique for models that provide a closed-form solution.

This class acts as a generic wrapper. It calls the price_closed_form method on a given model. It also intelligently uses analytic Greeks if the model provides them, otherwise falling back to the finite-difference methods from GreekMixin.

Source code in src/quantfin/techniques/closed_form.py 
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class ClosedFormTechnique(BaseTechnique, GreekMixin, IVMixin):
    """
    A pricing technique for models that provide a closed-form solution.

    This class acts as a generic wrapper. It calls the `price_closed_form`
    method on a given model. It also intelligently uses analytic Greeks if the
    model provides them, otherwise falling back to the finite-difference methods
    from `GreekMixin`.
    """

    def __init__(
        self,
        *,
        use_analytic_greeks: bool = True,
    ):
        """
        Initializes the technique.

        Parameters
        ----------
        use_analytic_greeks : bool, optional
            If True, the technique will use the model's specific analytic Greek
            methods (e.g., `delta_analytic`) if they exist. If False or if the
            methods don't exist, it falls back to finite differences.
            Default is True.
        """
        self.use_analytic_greeks = use_analytic_greeks

    def price(
        self,
        option: Option | ZeroCouponBond,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        **kwargs: Any,
    ) -> PricingResult:
        """
        Prices the instrument using the model's closed-form solution.

        This method dynamically builds the required parameters based on the
        type of instrument being priced (e.g., Option or ZeroCouponBond) and
        calls the model's `price_closed_form` method.

        Parameters
        ----------
        option : Option | ZeroCouponBond
            The instrument to be priced.
        stock : Stock
            The underlying asset's properties. For rate models, `stock.spot` is
            re-interpreted as the initial short rate `r0`.
        model : BaseModel
            The financial model to use. Must have `has_closed_form=True`.
        rate : Rate
            The risk-free rate structure.

        Returns
        -------
        PricingResult
            An object containing the calculated price.

        Raises
        ------
        TypeError
            If the model does not have a closed-form solution or if the
            instrument type is not supported.
        """
        if not model.has_closed_form:
            raise TypeError(f"{model.name} has no closed-form solver.")

        base_params: dict[str, Any] = {}

        if isinstance(option, Option):
            base_params = {
                "spot": stock.spot,
                "strike": option.strike,
                "r": rate.get_rate(option.maturity),
                "q": stock.dividend,
                "t": option.maturity,
                "call": (option.option_type is OptionType.CALL),
            }
        elif isinstance(option, ZeroCouponBond):
            # For rate models, 'spot' is re-interpreted as the initial short rate r0.
            base_params = {
                "spot": stock.spot,
                "t": option.maturity,
                # passed to satisfy the model signature but are ignored.
                "strike": option.face_value,
                "r": rate.get_rate(option.maturity),
                "q": stock.dividend,
            }
        else:
            raise TypeError(
                f"Unsupported asset type for ClosedFormTechnique: {type(option)}"
            )

        # Add extra model-specific kwargs
        for key in getattr(model, "cf_kwargs", []):
            if key in base_params:
                continue
            if hasattr(stock, key):
                base_params[key] = getattr(stock, key)
            elif key in kwargs:
                base_params[key] = kwargs[key]
            else:
                if not (
                    isinstance(option, ZeroCouponBond)
                    and key in ["call_price", "put_price"]
                ):
                    raise ValueError(
                        f"{model.name} requires '{key}' for closed-form pricing."
                    )

        # For ImpliedRateModel, pass these explicitly
        if "call_price" in kwargs:
            base_params["call_price"] = kwargs["call_price"]
        if "put_price" in kwargs:
            base_params["put_price"] = kwargs["put_price"]

        price = model.price_closed_form(**base_params)
        return PricingResult(price=price)

    def delta(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        **kwargs: Any,
    ) -> float:
        """Overrides GreekMixin to use analytic delta if available.

         Parameters
        ----------
        option : Option | ZeroCouponBond
            The instrument to be priced.
        stock : Stock
            The underlying asset's properties. For rate models, `stock.spot` is
            re-interpreted as the initial short rate `r0`.
        model : BaseModel
            The financial model to use. Must have `has_closed_form=True`.
        rate : Rate
            The risk-free rate structure.
        """
        if self.use_analytic_greeks and hasattr(model, "delta_analytic"):
            return model.delta_analytic(
                spot=stock.spot,
                strike=option.strike,
                r=rate.get_rate(option.maturity),
                q=stock.dividend,
                t=option.maturity,
                call=(option.option_type is OptionType.CALL),
            )
        return super().delta(option, stock, model, rate, **kwargs)

    def gamma(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        **kwargs: Any,
    ) -> float:
        """Overrides GreekMixin to use analytic gamma if available.

        Parameters
        ----------
        option : Option | ZeroCouponBond
            The instrument to be priced.
        stock : Stock
            The underlying asset's properties. For rate models, `stock.spot` is
            re-interpreted as the initial short rate `r0`.
        model : BaseModel
            The financial model to use. Must have `has_closed_form=True`.
        rate : Rate
            The risk-free rate structure.
        """
        if self.use_analytic_greeks and hasattr(model, "gamma_analytic"):
            return model.gamma_analytic(
                spot=stock.spot,
                strike=option.strike,
                r=rate.get_rate(option.maturity),
                q=stock.dividend,
                t=option.maturity,
            )
        return super().gamma(option, stock, model, rate, **kwargs)

    def vega(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        **kwargs: Any,
    ) -> float:
        """Overrides GreekMixin to use analytic vega if available.

        Parameters
        ----------
        option : Option | ZeroCouponBond
            The instrument to be priced.
        stock : Stock
            The underlying asset's properties. For rate models, `stock.spot` is
            re-interpreted as the initial short rate `r0`.
        model : BaseModel
            The financial model to use. Must have `has_closed_form=True`.
        rate : Rate
            The risk-free rate structure.
        """
        if self.use_analytic_greeks and hasattr(model, "vega_analytic"):
            return model.vega_analytic(
                spot=stock.spot,
                strike=option.strike,
                r=rate.get_rate(option.maturity),
                q=stock.dividend,
                t=option.maturity,
            )
        return super().vega(option, stock, model, rate, **kwargs)

    def theta(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        **kwargs: Any,
    ) -> float:
        """Overrides GreekMixin to use analytic theta if available.

        Parameters
        ----------
        option : Option | ZeroCouponBond
            The instrument to be priced.
        stock : Stock
            The underlying asset's properties. For rate models, `stock.spot` is
            re-interpreted as the initial short rate `r0`.
        model : BaseModel
            The financial model to use. Must have `has_closed_form=True`.
        rate : Rate
            The risk-free rate structure.
        """
        if self.use_analytic_greeks and hasattr(model, "theta_analytic"):
            return model.theta_analytic(
                spot=stock.spot,
                strike=option.strike,
                r=rate.get_rate(option.maturity),
                q=stock.dividend,
                t=option.maturity,
                call=(option.option_type is OptionType.CALL),
            )
        return super().theta(option, stock, model, rate, **kwargs)

    def rho(
        self,
        option: Option,
        stock: Stock,
        model: BaseModel,
        rate: Rate,
        **kwargs: Any,
    ) -> float:
        """Overrides GreekMixin to use analytic rho if available.

        Parameters
        ----------
        option : Option | ZeroCouponBond
            The instrument to be priced.
        stock : Stock
            The underlying asset's properties. For rate models, `stock.spot` is
            re-interpreted as the initial short rate `r0`.
        model : BaseModel
            The financial model to use. Must have `has_closed_form=True`.
        rate : Rate
            The risk-free rate structure.
        """
        if self.use_analytic_greeks and hasattr(model, "rho_analytic"):
            return model.rho_analytic(
                spot=stock.spot,
                strike=option.strike,
                r=rate.get_rate(option.maturity),
                q=stock.dividend,
                t=option.maturity,
                call=(option.option_type is OptionType.CALL),
            )
        return super().rho(option, stock, model, rate, **kwargs)

__init__(*, use_analytic_greeks: bool = True) #

Initializes the technique.

Parameters:

Name Type Description Default
use_analytic_greeks bool

If True, the technique will use the model's specific analytic Greek methods (e.g., delta_analytic) if they exist. If False or if the methods don't exist, it falls back to finite differences. Default is True.

 True
Source code in src/quantfin/techniques/closed_form.py 
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def __init__(
    self,
    *,
    use_analytic_greeks: bool = True,
):
    """
    Initializes the technique.

    Parameters
    ----------
    use_analytic_greeks : bool, optional
        If True, the technique will use the model's specific analytic Greek
        methods (e.g., `delta_analytic`) if they exist. If False or if the
        methods don't exist, it falls back to finite differences.
        Default is True.
    """
    self.use_analytic_greeks = use_analytic_greeks

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

Overrides GreekMixin to use analytic delta if available.

Parameters

option : Option | ZeroCouponBond The instrument to be priced. stock : Stock The underlying asset's properties. For rate models, stock.spot is re-interpreted as the initial short rate r0. model : BaseModel The financial model to use. Must have has_closed_form=True. rate : Rate The risk-free rate structure.

Source code in src/quantfin/techniques/closed_form.py 
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def delta(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    **kwargs: Any,
) -> float:
    """Overrides GreekMixin to use analytic delta if available.

     Parameters
    ----------
    option : Option | ZeroCouponBond
        The instrument to be priced.
    stock : Stock
        The underlying asset's properties. For rate models, `stock.spot` is
        re-interpreted as the initial short rate `r0`.
    model : BaseModel
        The financial model to use. Must have `has_closed_form=True`.
    rate : Rate
        The risk-free rate structure.
    """
    if self.use_analytic_greeks and hasattr(model, "delta_analytic"):
        return model.delta_analytic(
            spot=stock.spot,
            strike=option.strike,
            r=rate.get_rate(option.maturity),
            q=stock.dividend,
            t=option.maturity,
            call=(option.option_type is OptionType.CALL),
        )
    return super().delta(option, stock, model, rate, **kwargs)

gamma(option: Option, stock: Stock, model: BaseModel, rate: Rate, **kwargs: Any) -> float #

Overrides GreekMixin to use analytic gamma if available.

Parameters:

Name Type Description Default
option Option | ZeroCouponBond

The instrument to be priced.

 required
stock Stock

The underlying asset's properties. For rate models, stock.spot is re-interpreted as the initial short rate r0.

 required
model BaseModel

The financial model to use. Must have has_closed_form=True.

 required
rate Rate

The risk-free rate structure.

 required
Source code in src/quantfin/techniques/closed_form.py 
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def gamma(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    **kwargs: Any,
) -> float:
    """Overrides GreekMixin to use analytic gamma if available.

    Parameters
    ----------
    option : Option | ZeroCouponBond
        The instrument to be priced.
    stock : Stock
        The underlying asset's properties. For rate models, `stock.spot` is
        re-interpreted as the initial short rate `r0`.
    model : BaseModel
        The financial model to use. Must have `has_closed_form=True`.
    rate : Rate
        The risk-free rate structure.
    """
    if self.use_analytic_greeks and hasattr(model, "gamma_analytic"):
        return model.gamma_analytic(
            spot=stock.spot,
            strike=option.strike,
            r=rate.get_rate(option.maturity),
            q=stock.dividend,
            t=option.maturity,
        )
    return super().gamma(option, stock, model, rate, **kwargs)

price(option: Option | ZeroCouponBond, stock: Stock, model: BaseModel, rate: Rate, **kwargs: Any) -> PricingResult #

Prices the instrument using the model's closed-form solution.

This method dynamically builds the required parameters based on the type of instrument being priced (e.g., Option or ZeroCouponBond) and calls the model's price_closed_form method.

Parameters:

Name Type Description Default
option Option | ZeroCouponBond

The instrument to be priced.

 required
stock Stock

The underlying asset's properties. For rate models, stock.spot is re-interpreted as the initial short rate r0.

 required
model BaseModel

The financial model to use. Must have has_closed_form=True.

 required
rate Rate

The risk-free rate structure.

 required

Returns:

Type Description
PricingResult

An object containing the calculated price.

Raises:

Type Description
TypeError

If the model does not have a closed-form solution or if the instrument type is not supported.
Source code in src/quantfin/techniques/closed_form.py 
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def price(
    self,
    option: Option | ZeroCouponBond,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    **kwargs: Any,
) -> PricingResult:
    """
    Prices the instrument using the model's closed-form solution.

    This method dynamically builds the required parameters based on the
    type of instrument being priced (e.g., Option or ZeroCouponBond) and
    calls the model's `price_closed_form` method.

    Parameters
    ----------
    option : Option | ZeroCouponBond
        The instrument to be priced.
    stock : Stock
        The underlying asset's properties. For rate models, `stock.spot` is
        re-interpreted as the initial short rate `r0`.
    model : BaseModel
        The financial model to use. Must have `has_closed_form=True`.
    rate : Rate
        The risk-free rate structure.

    Returns
    -------
    PricingResult
        An object containing the calculated price.

    Raises
    ------
    TypeError
        If the model does not have a closed-form solution or if the
        instrument type is not supported.
    """
    if not model.has_closed_form:
        raise TypeError(f"{model.name} has no closed-form solver.")

    base_params: dict[str, Any] = {}

    if isinstance(option, Option):
        base_params = {
            "spot": stock.spot,
            "strike": option.strike,
            "r": rate.get_rate(option.maturity),
            "q": stock.dividend,
            "t": option.maturity,
            "call": (option.option_type is OptionType.CALL),
        }
    elif isinstance(option, ZeroCouponBond):
        # For rate models, 'spot' is re-interpreted as the initial short rate r0.
        base_params = {
            "spot": stock.spot,
            "t": option.maturity,
            # passed to satisfy the model signature but are ignored.
            "strike": option.face_value,
            "r": rate.get_rate(option.maturity),
            "q": stock.dividend,
        }
    else:
        raise TypeError(
            f"Unsupported asset type for ClosedFormTechnique: {type(option)}"
        )

    # Add extra model-specific kwargs
    for key in getattr(model, "cf_kwargs", []):
        if key in base_params:
            continue
        if hasattr(stock, key):
            base_params[key] = getattr(stock, key)
        elif key in kwargs:
            base_params[key] = kwargs[key]
        else:
            if not (
                isinstance(option, ZeroCouponBond)
                and key in ["call_price", "put_price"]
            ):
                raise ValueError(
                    f"{model.name} requires '{key}' for closed-form pricing."
                )

    # For ImpliedRateModel, pass these explicitly
    if "call_price" in kwargs:
        base_params["call_price"] = kwargs["call_price"]
    if "put_price" in kwargs:
        base_params["put_price"] = kwargs["put_price"]

    price = model.price_closed_form(**base_params)
    return PricingResult(price=price)

rho(option: Option, stock: Stock, model: BaseModel, rate: Rate, **kwargs: Any) -> float #

Overrides GreekMixin to use analytic rho if available.

Parameters:

Name Type Description Default
option Option | ZeroCouponBond

The instrument to be priced.

 required
stock Stock

The underlying asset's properties. For rate models, stock.spot is re-interpreted as the initial short rate r0.

 required
model BaseModel

The financial model to use. Must have has_closed_form=True.

 required
rate Rate

The risk-free rate structure.

 required
Source code in src/quantfin/techniques/closed_form.py 
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def rho(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    **kwargs: Any,
) -> float:
    """Overrides GreekMixin to use analytic rho if available.

    Parameters
    ----------
    option : Option | ZeroCouponBond
        The instrument to be priced.
    stock : Stock
        The underlying asset's properties. For rate models, `stock.spot` is
        re-interpreted as the initial short rate `r0`.
    model : BaseModel
        The financial model to use. Must have `has_closed_form=True`.
    rate : Rate
        The risk-free rate structure.
    """
    if self.use_analytic_greeks and hasattr(model, "rho_analytic"):
        return model.rho_analytic(
            spot=stock.spot,
            strike=option.strike,
            r=rate.get_rate(option.maturity),
            q=stock.dividend,
            t=option.maturity,
            call=(option.option_type is OptionType.CALL),
        )
    return super().rho(option, stock, model, rate, **kwargs)

theta(option: Option, stock: Stock, model: BaseModel, rate: Rate, **kwargs: Any) -> float #

Overrides GreekMixin to use analytic theta if available.

Parameters:

Name Type Description Default
option Option | ZeroCouponBond

The instrument to be priced.

 required
stock Stock

The underlying asset's properties. For rate models, stock.spot is re-interpreted as the initial short rate r0.

 required
model BaseModel

The financial model to use. Must have has_closed_form=True.

 required
rate Rate

The risk-free rate structure.

 required
Source code in src/quantfin/techniques/closed_form.py 
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def theta(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    **kwargs: Any,
) -> float:
    """Overrides GreekMixin to use analytic theta if available.

    Parameters
    ----------
    option : Option | ZeroCouponBond
        The instrument to be priced.
    stock : Stock
        The underlying asset's properties. For rate models, `stock.spot` is
        re-interpreted as the initial short rate `r0`.
    model : BaseModel
        The financial model to use. Must have `has_closed_form=True`.
    rate : Rate
        The risk-free rate structure.
    """
    if self.use_analytic_greeks and hasattr(model, "theta_analytic"):
        return model.theta_analytic(
            spot=stock.spot,
            strike=option.strike,
            r=rate.get_rate(option.maturity),
            q=stock.dividend,
            t=option.maturity,
            call=(option.option_type is OptionType.CALL),
        )
    return super().theta(option, stock, model, rate, **kwargs)

vega(option: Option, stock: Stock, model: BaseModel, rate: Rate, **kwargs: Any) -> float #

Overrides GreekMixin to use analytic vega if available.

Parameters:

Name Type Description Default
option Option | ZeroCouponBond

The instrument to be priced.

 required
stock Stock

The underlying asset's properties. For rate models, stock.spot is re-interpreted as the initial short rate r0.

 required
model BaseModel

The financial model to use. Must have has_closed_form=True.

 required
rate Rate

The risk-free rate structure.

 required
Source code in src/quantfin/techniques/closed_form.py 
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def vega(
    self,
    option: Option,
    stock: Stock,
    model: BaseModel,
    rate: Rate,
    **kwargs: Any,
) -> float:
    """Overrides GreekMixin to use analytic vega if available.

    Parameters
    ----------
    option : Option | ZeroCouponBond
        The instrument to be priced.
    stock : Stock
        The underlying asset's properties. For rate models, `stock.spot` is
        re-interpreted as the initial short rate `r0`.
    model : BaseModel
        The financial model to use. Must have `has_closed_form=True`.
    rate : Rate
        The risk-free rate structure.
    """
    if self.use_analytic_greeks and hasattr(model, "vega_analytic"):
        return model.vega_analytic(
            spot=stock.spot,
            strike=option.strike,
            r=rate.get_rate(option.maturity),
            q=stock.dividend,
            t=option.maturity,
        )
    return super().vega(option, stock, model, rate, **kwargs)