def calc_ytm(self):
tvm = TVM(self.ttm() * self.freq, 0, -self.mid(),
self.couponRate / self.freq, 1) #semiannual payment
try:
return tvm.calc_r() * self.freq
except Exception:
return None
def calc_duration(self): price = (self.bid+self.ask)/2 tvm = TVM(n=ttm*self.freq, pv=-price, pmt=self.couponRate/self.freq, fv=1) ytm = tvm.calc_r() * self.freq ytmDelta = .001 tvm.r = (ytm-ytmDelta)/b.freq priceHigh = -tvm.calc_pv() tvm.r = (ytm+ytmDelta)/b.freq priceLow = -tvm.calc_pv() duration = ((priceHigh-priceLow)*2 / (priceHigh+priceLow)) / (ytmDelta*2) return duration
def calc_duration(self):
price = (self.bid + self.ask) / 2
tvm = TVM(n=ttm * self.freq,
pv=-price,
pmt=self.couponRate / self.freq,
fv=1)
ytm = tvm.calc_r() * self.freq
ytmDelta = .001
tvm.r = (ytm - ytmDelta) / b.freq
priceHigh = -tvm.calc_pv()
tvm.r = (ytm + ytmDelta) / b.freq
priceLow = -tvm.calc_pv()
duration = ((priceHigh - priceLow) * 2 /
(priceHigh + priceLow)) / (ytmDelta * 2)
return duration
import io
#local time
localtime = datetime(2012,9,19)
#load bonds
bonds = readfromfile('data/gilts_2012_09_19.csv')
#calculate yield curve
# Calculated YTMs doesn't necessarily correspond to those quoted in data file (source: Bondscape.net), due to accrued interest
# and a fact that coupon payment are bound to some specific calendar date, not necessarily, one semiannually
tr, yr = [], []
for b in bonds:
ttm = (b.maturity - localtime).days / 360
price = (b.bid+b.ask)/2
ytm = TVM(n=ttm*b.freq, pv=-price, pmt=b.couponRate/b.freq, fv=1).calc_r() * b.freq
tr.append(ttm)
yr.append(ytm)
print('Raw yield curve')
for i in range(0, len(tr)):
print("%.2f\t%.2f%%" % (tr[i], 100*yr[i]))
# interpolation
t = list(i for i in range(1,41))
y = []
interp = scipy.interpolate.interp1d(tr, yr, bounds_error=False, fill_value=scipy.nan)
for i in t:
value = float(interp(i))
if not scipy.isnan(value):
y.append(value)
def calc_ytm(self): tvm = TVM(self.ttm()*self.freq, 0, -self.mid(), self.couponRate/self.freq, 1) #semiannual payment try: return tvm.calc_r() * self.freq except Exception: return None
if (self.mode==TVM.bgn): pva += self.pmt
z = (-pva-self.pv) / (self.fv-pva)
return -log(z) / log(1+self.r)
def calc_r(self):
def function_fv(r, self):
z = pow(1+r, -self.n)
pva = self.pmt / r
if (self.mode==TVM.bgn): pva += self.pmt
return -(self.pv + (1-z) * pva)/z
return newton(f=function_fv, fArg=self, x0=.05,
y=self.fv, maxIter=1000, minError=0.0001)
## example #1 Mortgage payments
from quant.tvm import TVM
pmt = TVM(n=25*12, r=.04/12, pv=500000, fv=0).calc_pmt()
print("Payment = %f" % pmt)
## Example #2 Yield to Maturity
r = 2*TVM(n=10*2, pmt=6/2, pv=-80, fv=100).calc_r()
print("Interest Rate = %f" % r)
### Example 3: Arbitrage-free Bond Pricing
pv = TVM(r=.06, n=8, pmt=5, fv=100).calc_pv()
print("Present Value = %f" % pv)
## Example of boostrapping
'''
epic, description, coupon, maturity, bid, ask
TR13, Uk Gilt Treasury Stk, 4.5, 07-Mar-13, 101.92, 102.07
T813, Uk Gilt Treasury Stk, 8, 27-Sep-13, 107.86, 107.98
# Copyright (c) 2012 Quantitative & Financial, All rights reserved
# www.quantandfinancial.com
from quant.tvm import TVM
pmt = TVM(n=25 * 12, r=.04 / 12, pv=500000, fv=0).calc_pmt()
print("Payment = %f" % pmt)
i = TVM(n=10 * 2, pmt=6 / 2, pv=-80, fv=100).calc_r()
print("r = %f" % i)
