Bond pricing HW 2 | Python Fiddle

""" AUTHOR JONATHAN LAU"""

import math

"""
def f(x):

return 0.05+ 0.005* math.sqrt(1+x)
    return math.exp((-x**2.0)/2.0) ==> e^(-x^2/2), which is the integral in the cumulative distributive function
    
"""

def f(x):
    return math.exp((-x**2.0)/2.0)

def mid_rule (a, b, n):

h = (b-a)/float(n)
	total = 0.0

for i in range (1, n+1):
		z = (a + (i -0.5)*h )
		
    
		total = total + f((a + (i- 0.5)*h))
       
	return total * h

def simp_rule(a, b, n):
    h = (b-a)/float(n)
    total = f(a) / 6.0 + f(b) / 6.0
    
    for i in range (1, n):
        total = total + f(a + i*h) / 3.0
        
    for i in range (1, n+1):
        total = total + 2 * f(a + (i-0.5) * h) / 3.0
        
    return total * h

def cum_distrib(x, n):
    total = 0.5
    return total + 1/(math.sqrt(2.0 * math.pi)) * simp_rule(0.0, x, n)

""" x refers to N(x); for example, N(0) should be equal to 1/2"""

def cum_distrib_tol(tol, x):
    tolerance = float(tol)
    n = 4
    old_int = cum_distrib(x,n)
    n = 2 * n
    new_int = cum_distrib(x,n)
    
    while abs(new_int - old_int) > tolerance:
        old_int = new_int
        n = 2* n
        new_int = cum_distrib(x,n)
    
    return (n, new_int, abs(new_int - old_int) )

"""The previous definitions are tied to one another, it is to solve N(x), which is the cumulative distribution of the standard normal. I have repeated 
f(x) and simp approx below for other problems"""

def f_all(x):
    return 0.05 / (1 + 2 * math.exp(-(1+x)**2.0) )

def simp_rule_all(a, b, n):
    h = (b-a)/float(n)
    total = f_all(a) / 6.0 + f_all(b) / 6.0
    
    for i in range (1, n):
        total = total + f_all(a + i*h) / 3.0
        
    for i in range (1, n+1):
        total = total + 2 * f_all(a + (i-0.5) * h) / 3.0
        
    return total * h

def disc_simp_rule_all (a, b, n):
    return math.exp(- simp_rule_all(a, b, n) )

def disc_simp_rule_all_tol (a, b, tol):
    tolerance = float(tol)
    n = 4
    old_int = disc_simp_rule_all(a, b, n)
    n = 2 * n
    new_int = disc_simp_rule_all(a, b, n)
    
    while abs(new_int - old_int) > tolerance:
        old_int = new_int
        n = 2* n
        new_int = disc_simp_rule_all(a, b, n)
    
    return (n, new_int, abs(new_int - old_int) )

"""Bond Calculator, bond price function given defined rate function"""

def zero_rate (period):
    return 0.02 + period / (200.0 - period)

def disc_factor(period):
    return math.exp( - period * zero_rate(period))

""" n = number of cash flows
	t = vector of cash flow dates (of size n) - think of this as your time part of the discount factor
    v = cash flows (of size n) """

def BondPrice_ZeroRate (n, t_cashflow, v_cashflow):
    B = 0.0
    disc = range(0,n)
    for i in range(0, n):
        disc[i] = math.exp(- t_cashflow[i] * zero_rate(t_cashflow[i]) )
        print disc[i]
        B = B + v_cashflow[i] * disc[i]
                
    return B

""" number 8 on HW 2"""

def Bond_BDC (n, t_cashflow, v_cashflow, y):
    B = 0.0
    D = 0.0
    C = 0.0
    disc = range(0,n)
    for i in range (0,n):
        disc[i] = math.exp(- t_cashflow[i] * y)
        print disc[i]
        B = B + v_cashflow[i] * disc[i] 
        D = D + t_cashflow[i] * v_cashflow[i] * disc[i]
        C = C + (t_cashflow[i] ** 2.0) * v_cashflow[i] * disc[i]
    return [B, D/B, C/B]

def BondPrice_no9 (n, t_cashflow, v_cashflow):
    B = 0.0
    disc = range(0,n)
    for i in range(0, n):
        disc[i] = disc_simp_rule_all(0, t_cashflow[i], 64)
        print disc[i]
        B = B + v_cashflow[i] * disc[i]
    
    return B
    
def PVcouponCF(couponrate, numbcomp, period):
    return 100.0 * couponrate / numbcomp * discountfactor(period)

"""
print f(1.0)
print discountfactor(1.0)
print PVcouponCF(0.07, 2, 1.0)
print mid_rule(0, 2, 8)
print simp_rule(0, 2, 4)
"""

"""
print cum_distrib(1.0,128)	
print cum_distrib_tol(10**-12, 1.0)
print disc_factor(3/12.0)
print BondPrice_ZeroRate(5, [3/12.0, 7/12.0, 11/12.0, 15/12.0, 19/12.0], [1, 1, 1, 1, 101] )
print Bond_BDC(4, [1/12.0, 7/12.0, 13/12.0, 19/12.0], [2, 2, 2, 102], 0.025 )"""
print disc_simp_rule_all(0, 1.5, 32)
print simp_rule_all(0, 1.5, 1000)
print disc_simp_rule_all_tol (0, 2.0, 10**-8)
print BondPrice_no9 (4, [0.5, 1.0, 1.5, 2.0], [2.5, 2.5, 2.5, 102.5])

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