typing hints

Author: open-source-modelling

bisection_alpha/SWCalibrate.py

@@ -1,4 +1,6 @@
-def SWCalibrate(r, M, ufr, alpha):
+import numpy as np
+
+def SWCalibrate(r: np.ndarray, M: np.ndarray, ufr: float, alpha: float)-> np.ndarray:
  """
  Calculate the calibration vector using the Smith-Wilson algorithm.
 
@@ -16,7 +18,7 @@ def SWCalibrate(r, M, ufr, alpha):
  For more information, refer to the documentation at:
  https://www.eiopa.europa.eu/sites/default/files/risk_free_interest_rate/12092019-technical_documentation.pdf
  """
- import numpy as np
+
  from SWHeart import SWHeart as SWHeart
 
 

bisection_alpha/SWExtrapolate.py

@@ -1,30 +1,32 @@
-def SWExtrapolate(M_Target, M_Obs, b, ufr, alpha):
+import numpy as np 
+
+def SWExtrapolate(M_Target: np.ndarray, M_Obs: np.ndarray, b: np.ndarray, ufr: float, alpha:float)->np.ndarray:
  """
- Interpolate or extrapolate rates for targeted maturities using the Smith-Wilson algorithm.
+ Interpolate or extrapolate rates for targeted maturities using the Smith-Wilson algorithm.
+
+ Calculates the rates for maturities specified in `M_Target` using the calibration vector `b` obtained
+ from observed bond maturities in `M_Obs`.
 
- Calculates the rates for maturities specified in `M_Target` using the calibration vector `b` obtained
- from observed bond maturities in `M_Obs`.
+ Arguments:
+ M_Target: k x 1 ndarray representing each targeted bond maturity of interest. Example: M_Target = np.array([[1], [2], [3], [5]])
+ M_Obs: n x 1 ndarray representing the observed bond maturities used for calibrating the calibration vector `b`. Example: M_Obs = np.array([[1], [3]])
+ b: n x 1 ndarray representing the calibration vector calculated on observed bonds.
+ ufr: Floating number representing the ultimate forward rate. Example: ufr = 0.042
+ alpha: Floating number representing the convergence speed parameter alpha. Example: alpha = 0.05
 
- Arguments:
- M_Target: k x 1 ndarray representing each targeted bond maturity of interest. Example: M_Target = np.array([[1], [2], [3], [5]])
- M_Obs: n x 1 ndarray representing the observed bond maturities used for calibrating the calibration vector `b`. Example: M_Obs = np.array([[1], [3]])
- b: n x 1 ndarray representing the calibration vector calculated on observed bonds.
- ufr: Floating number representing the ultimate forward rate. Example: ufr = 0.042
- alpha: Floating number representing the convergence speed parameter alpha. Example: alpha = 0.05
+ Returns:
+ k x 1 ndarray representing the targeted rates for zero-coupon bonds. Each rate belongs to a targeted
+ zero-coupon bond with a maturity from `M_Target`. Example: r = np.array([0.0024, 0.0029, 0.0034, 0.0039])
+
+ For more information, refer to the documentation at:
+ https://www.eiopa.europa.eu/sites/default/files/risk_free_interest_rate/12092019-technical_documentation.pdf
+ """
 
- Returns:
- k x 1 ndarray representing the targeted rates for zero-coupon bonds. Each rate belongs to a targeted
- zero-coupon bond with a maturity from `M_Target`. Example: r = np.array([0.0024, 0.0029, 0.0034, 0.0039])
+ from SWHeart import SWHeart as SWHeart
 
- For more information, refer to the documentation at:
- https://www.eiopa.europa.eu/sites/default/files/risk_free_interest_rate/12092019-technical_documentation.pdf
- """
- 
- import numpy as np
- from SWHeart import SWHeart as SWHeart
- C = np.identity(M_Obs.size)
- d = np.exp(-np.log(1+ufr) * M_Obs) # Calculate vector d described in paragraph 138
- Q = np.diag(d) @ C # Matrix Q described in paragraph 139
- H = SWHeart(M_Target, M_Obs, alpha) # Heart of the Wilson function from paragraph 132
- p = np.exp(-np.log(1+ufr)* M_Target) + np.diag(np.exp(-np.log(1+ufr) * M_Target)) @ H @ Q @ b # Discount pricing function for targeted maturities from paragraph 147
- return p ** (-1/ M_Target) -1 # Convert obtained prices to rates and return prices
+ C = np.identity(M_Obs.size)
+ d = np.exp(-np.log(1+ufr) * M_Obs) # Calculate vector d described in paragraph 138
+ Q = np.diag(d) @ C # Matrix Q described in paragraph 139
+ H = SWHeart(M_Target, M_Obs, alpha) # Heart of the Wilson function from paragraph 132
+ p = np.exp(-np.log(1+ufr)* M_Target) + np.diag(np.exp(-np.log(1+ufr) * M_Target)) @ H @ Q @ b # Discount pricing function for targeted maturities from paragraph 147
+ return p ** (-1/ M_Target) -1 # Convert obtained prices to rates and return prices

bisection_alpha/SWHeart.py

@@ -1,24 +1,25 @@
-def SWHeart(u, v, alpha):
+import numpy as np
+
+def SWHeart(u: np.ndarray, v: np.ndarray, alpha: float)->np.ndarray:
  """
-  Calculate the heart of the Wilson function.
+ Calculate the heart of the Wilson function.
 
-  Calculates the matrix H (Heart of the Wilson function) for maturities specified by vectors u and v.
-  The formula is taken from the EIOPA technical specifications paragraph 132.
+ Calculates the matrix H (Heart of the Wilson function) for maturities specified by vectors u and v.
+ The formula is taken from the EIOPA technical specifications paragraph 132.
 
-  Arguments:
-  u: n_1 x 1 vector of maturities. Example: u = [1, 3]
-  v: n_2 x 1 vector of maturities. Example: v = [1, 2, 3, 5]
-  alpha: 1 x 1 floating number representing the convergence speed parameter alpha. Example: alpha = 0.05
+ Arguments:
+ u: n_1 x 1 vector of maturities. Example: u = [1, 3]
+ v: n_2 x 1 vector of maturities. Example: v = [1, 2, 3, 5]
+ alpha: 1 x 1 floating number representing the convergence speed parameter alpha. Example: alpha = 0.05
 
-  Returns:
-  n_1 x n_2 matrix representing the Heart of the Wilson function for selected maturities and parameter alpha.
-  H is calculated as described in paragraph 132 of the EIOPA documentation.
+ Returns:
+ n_1 x n_2 matrix representing the Heart of the Wilson function for selected maturities and parameter alpha.
+ H is calculated as described in paragraph 132 of the EIOPA documentation.
 
- For more information, see:
- https://www.eiopa.europa.eu/sites/default/files/risk_free_interest_rate/12092019-technical_documentation.pdf
- """
- import numpy as np
- 
+ For more information, see:
+ https://www.eiopa.europa.eu/sites/default/files/risk_free_interest_rate/12092019-technical_documentation.pdf
+ """
+ 
  u_Mat = np.tile(u, [v.size, 1]).transpose()
  v_Mat = np.tile(v, [u.size, 1])
  return 0.5 * (alpha * (u_Mat + v_Mat) + np.exp(-alpha * (u_Mat + v_Mat)) - alpha * np.absolute(u_Mat-v_Mat) - np.exp(-alpha * np.absolute(u_Mat-v_Mat))); # Heart of the Wilson function from paragraph 132

bisection_alpha/bisection_alpha.py

@@ -2,7 +2,7 @@
 from SWCalibrate import SWCalibrate as SWCalibrate
 from SWExtrapolate import SWExtrapolate as SWExtrapolate
 
-def Galfa(M_Obs: np.ndarray, r_Obs: np.ndarray, ufr, alpha, Tau):
+def Galfa(M_Obs: np.ndarray, r_Obs: np.ndarray, ufr: float, alpha: float, Tau: float)->float:
  """
  Calculates the gap at the convergence point between the allowable tolerance Tau and the curve extrapolated using the Smith-Wilson algorithm.
  interpolation and extrapolation of rates.
@@ -44,7 +44,7 @@ def Galfa(M_Obs: np.ndarray, r_Obs: np.ndarray, ufr, alpha, Tau):
  K = (1+alpha * M_Obs @ Q@ b) / (np.sinh(alpha * M_Obs.transpose())@ Q@ b) # Calculate kappa as defined in the paragraph 155
  return( alpha/np.abs(1 - K*np.exp(alpha*T))-Tau) # Size of the gap at the convergence point between the allowable tolerance Tau and the actual curve. Defined in paragraph 158
 
-def BisectionAlpha(xStart, xEnd, M_Obs, r_Obs, ufr, Tau, Precision, maxIter):
+def BisectionAlpha(xStart: float, xEnd: float, M_Obs: np.ndarray, r_Obs: np.ndarray, ufr: float, Tau: float, Precision: float, maxIter: int)->float:
  """
  Bisection root finding algorithm for finding the root of a function. The function here is the allowed difference between the ultimate forward rate and the extrapolated curve using Smith & Wilson.