Merge pull request #13 from GaetanoCodes/BGIG

Adding the BGIG model

Author: jkirkby3

.gitignore

@@ -5,6 +5,9 @@
 *.idea
 *.cache
 
+#temp develop
+temp_analyse/
+
 # Byte-compiled / optimized / DLL files
 __pycache__/
 *.py[cod]

fypy/model/levy/BGIG.py

@@ -0,0 +1,286 @@
+"""Implementation of the BGIG model for PROJ framework"""
+
+from typing import List, Tuple, Optional, Union
+
+import numpy as np
+import scipy
+
+from fypy.model.levy.LevyModel import LevyModel
+from fypy.model.FourierModel import Cumulants
+from fypy.termstructures.ForwardCurve import ForwardCurve
+from fypy.termstructures.DiscountCurve import DiscountCurve
+
+
+class BGIG(LevyModel):
+    """
+    Implementation of the BGIG model as introduced in:
+
+    The bilateral generalized inverse Gaussian process with applications
+    to financial modeling, G. AGAZZOTTI, JP. Aguilar
+    """
+
+    def __init__(
+        self,
+        forwardCurve: ForwardCurve,
+        discountCurve: DiscountCurve,
+        a_p: float = 500,
+        b_p: float = 0.05,
+        p_p: float = 2,
+        a_m: float = 300,
+        b_m: float = 0.03,
+        p_m: float = 2,
+    ):
+        """
+        BGIG model
+
+        Args:
+            forwardCurve (ForwardCurve): fwd
+            discountCurve (DiscountCurve): discount
+            a_p (float, optional): Defaults to 500.
+            b_p (float, optional): Defaults to 0.05.
+            p_p (float, optional): Defaults to 2.
+            a_m (float, optional): Defaults to 300.
+            b_m (float, optional): Defaults to 0.03.
+            p_m (float, optional): Defaults to 2.
+        """
+        super().__init__(
+            forwardCurve=forwardCurve,
+            discountCurve=discountCurve,
+            params=np.asarray([a_p, b_p, p_p, a_m, b_m, p_m]),
+        )
+
+    ####################################
+    ####### MODEL  PARAMETERS ##########
+    ####################################
+
+    @property
+    def a_p(self) -> float:
+        """Model Parameter"""
+        return self._params[0]
+
+    @property
+    def b_p(self) -> float:
+        """Model Parameter"""
+        return self._params[1]
+
+    @property
+    def p_p(self) -> float:
+        """Model Parameter"""
+        return self._params[2]
+
+    @property
+    def a_m(self) -> float:
+        """Model Parameter"""
+        return self._params[3]
+
+    @property
+    def b_m(self) -> float:
+        """Model Parameter"""
+        return self._params[4]
+
+    @property
+    def p_m(self) -> float:
+        """Model Parameter"""
+        return self._params[5]
+
+    ####################################
+    ####### CUMULANTS HELPERS ##########
+    ####################################
+
+    def ratio_bessel(self, omega: float, p: float) -> float:
+        """
+        ratio of bessel function
+
+        Args:
+            omega (float): omega
+            p (float): p params
+
+        Returns:
+            float: ratio of bessel
+        """
+        return scipy.special.kv(p + 1, omega) / scipy.special.kv(p, omega)
+
+    def c1(self, omega: float, eta: float, p: float) -> float:
+        """
+        cumulants of order 1 of a one sided BIG distribution
+
+        Args:
+            omega (float): omega
+            eta (float): eta
+            p (float): p
+
+        Returns:
+           float: c1
+        """
+        return self.ratio_bessel(omega, p) * eta
+
+    def c2(self, omega: float, eta: float, p: float) -> float:
+        """
+        cumulants of order 2 of a one sided BIG distribution
+
+        Args:
+            omega (float): omega
+            eta (float): eta
+            p (float): p
+
+        Returns:
+           float: c2
+        """
+        polynom = (
+            -(self.ratio_bessel(omega, p) ** 2)
+            + (2 * (p + 1) / omega) * self.ratio_bessel(omega, p)
+            + 1
+        )
+        return polynom * eta**2
+
+    def c3(self, omega: float, eta: float, p: float):
+        """
+        cumulants of order 3 of a one sided BIG distribution
+
+        Args:
+            omega (float): omega
+            eta (float): eta
+            p (float): p
+
+        Returns:
+           float: c3
+        """
+        polynom = (
+            2 * self.ratio_bessel(omega, p) ** 3
+            - (6 * (p + 1) / omega) * self.ratio_bessel(omega, p) ** 2
+            + ((4 * (p + 1) * (p + 2) / omega**2) - 2) * self.ratio_bessel(omega, p)
+            + 2 * (p + 1) / omega
+        )
+        return polynom * eta**3
+
+    def c4(self, omega: float, eta: float, p: float):
+        """
+        cumulants of order 4 of a one sided BIG distribution
+
+        Args:
+            omega (float): omega
+            eta (float): eta
+            p (float): p
+
+        Returns:
+           float: c4
+        """
+        polynom = (
+            2 * self.ratio_bessel(omega, p) ** 3
+            - (6 * (p + 1) / omega) * self.ratio_bessel(omega, p) ** 2
+            + ((4 * (p + 1) * (p + 2) / omega**2) - 2) * self.ratio_bessel(omega, p)
+            + 2 * (p + 1) / omega
+        )
+        return polynom * eta**4
+
+    def cumulants_gen(
+        self,
+        order: int,
+    ) -> float:
+        """
+        compute cumulants of order "order"
+
+        Args:
+            order (int): order of the cumulant
+
+        Raises:
+            NotImplementedError: if order > 4
+
+        Returns:
+            cumulant (float)
+        """
+        a_p, b_p, p_p = self.a_p, self.b_p, self.p_p
+        a_m, b_m, p_m = self.a_m, self.b_m, self.p_m
+
+        omega_p = (a_p * b_p) ** 0.5
+        omega_m = (a_m * b_m) ** 0.5
+        eta_p = (a_p / b_p) ** (-0.5)
+        eta_m = (a_m / b_m) ** (-0.5)
+
+        match order:
+            case 1:
+                return self.c1(omega_p, eta_p, p_p) - self.c1(omega_m, eta_m, p_m)
+            case 2:
+                return self.c2(omega_p, eta_p, p_p) + self.c2(omega_m, eta_m, p_m)
+            case 3:
+                return self.c3(omega_p, eta_p, p_p) - self.c3(omega_m, eta_m, p_m)
+            case 4:
+                return self.c4(omega_p, eta_p, p_p) + self.c4(omega_m, eta_m, p_m)
+            case _:
+                raise NotImplementedError
+
+    def cumulants(self, T: float) -> Cumulants:
+        """
+        Evaluate the cumulants of the model at a given time.
+        This is useful e.g. to figure out integration bounds etc
+        during pricing
+        :param T: float, time to maturity (time at which cumulants are evaluated)
+        :return: Cumulants object
+        """
+        rn_drift = self.risk_neutral_log_drift()
+
+        return Cumulants(
+            T=T,
+            rn_drift=rn_drift,
+            c1=T * (rn_drift + self.cumulants_gen(1)),
+            c2=T * self.cumulants_gen(2),
+            c4=T * self.cumulants_gen(4),
+        )
+
+    def symbol(self, xi: Union[float, np.ndarray]):
+        """
+        Levy symbol, uniquely defines Characteristic Function via:
+        chf(T,xi) = exp(T*symbol(xi)),  for all T>=0
+        :param xi: np.ndarray or float, points in frequency domain
+        :return: np.ndarray or float, symbol evaluated at input points in frequency domain
+        """
+        a_p, b_p, p_p = self.a_p, self.b_p, self.p_p
+        a_m, b_m, p_m = self.a_m, self.b_m, self.p_m
+        rn_drift = self.risk_neutral_log_drift()
+
+        return 1j * xi * rn_drift + np.log(
+            (a_p / (a_p - 2j * xi)) ** (p_p / 2)
+            * scipy.special.kv(p_p, (b_p * (a_p - 2j * xi)))
+            / scipy.special.kv(p_p, (b_p * a_p))
+            * (a_m / (a_m + 2j * xi)) ** (p_m / 2)
+            * scipy.special.kv(p_m, (b_m * (a_m - 2j * xi)))
+            / scipy.special.kv(p_m, (b_m * a_m))
+        )
+
+    def convexity_correction(self) -> float:
+        """
+        Computes the convexity correction for the Levy model,
+        added to log process drift to ensure
+        risk neutrality
+        """
+        a_p, b_p, p_p = self.a_p, self.b_p, self.p_p
+        a_m, b_m, p_m = self.a_m, self.b_m, self.p_m
+
+        return -np.log(
+            (a_p / (a_p - 2)) ** (p_p / 2)
+            * scipy.special.kv(p_p, (b_p * (a_p - 2)))
+            / scipy.special.kv(p_p, (b_p * a_p))
+            * (a_m / (a_m + 2)) ** (p_m / 2)
+            * scipy.special.kv(p_m, (b_m * (a_m + 2)))
+            / scipy.special.kv(p_m, (b_m * a_m))
+        )
+
+    #############################################
+    ### Calibration Interface Implementation  ###
+    #############################################
+
+    def num_params(self) -> int:
+        return 6
+
+    def param_bounds(self) -> Optional[List[Tuple]]:
+        return [
+            (2, np.inf),
+            (0, np.inf),
+            (-np.inf, np.inf),
+            (0, np.inf),
+            (0, np.inf),
+            (-np.inf, np.inf),
+        ]
+
+    def default_params(self) -> Optional[np.ndarray]:
+        return np.asarray([500, 0.05, 2, 300, 0.03, 2])