Source code for LibPythonExample.intRates

"""
Interest rates module - proof of concept
"""

import math

def discFactorDeterministic(t, T, r):
    """
    This function implements :eq:`discSimple`
    """
    return math.exp(-r*T)



def discFactorLinearGaussian(t, T, r, x, a, v):
    r"""
    This function implements :eq:`discLinGauss`. 
    We calculate the integral in :eq:`discLinGaussA`,   

    .. math::
 
       A(t,T) =  \exp ( -r (T-t) )
         \exp \bigg( \frac{\sigma^2}{4 a^3} 
         \Big( - 4 e^{-a(T-t)} + 4 e^{-a T}  + e^{-2a(T-t)} - e^{- 2 a T}
               + 4             - 4 e^{-a t}  - 1            + e^{- 2 a t}
         \Big) \bigg)

    and implement this formula.
    """
    B = (1.0 - math.exp(-a*(T-t)))/a
    temp = -4*math.exp(-a*(T-t)) + 4*math.exp(-a*T) + math.exp(-2*a*(T-t)) - math.exp(-2*a*T)
    temp += 4.0                  - 4*math.exp(-a*t) - 1.0                  + math.exp(-2*a*t)
    A = math.exp(-r*(T-t)) * math.exp( 0.25*v*v*temp/(a*a*a) )
    return A*math.exp(-B*x)
    

def cpnBondPrice(t, Tlist, Clist, x, discFactFun):
    r""" 
    This function implements :eq:`cpnBond`. Tlist: - :math:`T_k`, Clist - :math:`C_k`, equal length.
    
    Usage: 
       discFactFun = lambda t, T, x: discFactorDeterministic(t, T, r)
    or
       discFactFun = lambda t, T, x: discFactorLinearGaussian(t, T, r, x, a, v)
    Then
       P = cpnBondPrice(t, Tlist, Clist, x, disFactFun)
    """
    if len(Clist) != len(Tlist):
        raise Exception("Tlist and Clist must have the same length!")
    P = 0.0
    for (C,T) in zip(Clist,Tlist):
        P += C*T*discFactFun(t,T,x)
    return P