def test_FinDiscountCurve():
# Create a curve from times and discount factors
startDate = FinDate(1, 1, 2018)
years = np.linspace(0, 10, 6)
rate = 0.05 + 0.005 * years - 0.0003 * years * years
dfs = np.exp(-rate * years)
dates = startDate.addYears(years)
curve = FinDiscountCurve(startDate, dates, dfs,
FinInterpTypes.FLAT_FWD_RATES)
testCases.header("T", "DF", "ZERORATE", "CC_FWD", "MM_FWD", "SURVPROB")
plotYears = np.linspace(0, 12, 12 * 12 + 1)[1:]
plotDates = startDate.addYears(plotYears)
# Examine dependency of curve on compounding rate
zeroRates_A = curve.zeroRate(plotDates, FinFrequencyTypes.ANNUAL)
zeroRates_S = curve.zeroRate(plotDates, FinFrequencyTypes.SEMI_ANNUAL)
zeroRates_Q = curve.zeroRate(plotDates, FinFrequencyTypes.QUARTERLY)
zeroRates_M = curve.zeroRate(plotDates, FinFrequencyTypes.MONTHLY)
zeroRates_C = curve.zeroRate(plotDates, FinFrequencyTypes.CONTINUOUS)
if PLOT_GRAPHS:
plt.figure(figsize=(6, 4))
plt.plot(plotYears, scale(zeroRates_A, 100), label='A')
plt.plot(plotYears, scale(zeroRates_S, 100), label='S')
plt.plot(plotYears, scale(zeroRates_Q, 100), label='Q')
plt.plot(plotYears, scale(zeroRates_M, 100), label='M')
plt.plot(plotYears, scale(zeroRates_C, 100), label='C')
plt.ylim((5, 8))
plt.title('Discount Curves')
plt.xlabel('Time (years)')
plt.ylabel('Zero Rate (%)')
plt.legend(loc='lower right', frameon=False)
# Examine dependency of fwd curve on the interpolation scheme
for interp in FinInterpTypes:
curve = FinDiscountCurve(startDate, dates, dfs, interp)
fwdRates = curve.fwd(plotDates)
zeroRates = curve.zeroRate(plotDates, FinFrequencyTypes.ANNUAL)
parRates = curve.swapRate(startDate, plotDates,
FinFrequencyTypes.ANNUAL)
if PLOT_GRAPHS:
plt.figure(figsize=(6, 4))
plt.plot(plotYears, scale(fwdRates, 100), label='FWD RATES')
plt.plot(plotYears, scale(zeroRates, 100), label='ZERO RATES')
plt.plot(plotYears, scale(parRates, 100), label='PAR RATES')
plt.ylim((3.0, 8.5))
plt.title('Forward Curves using ' + str(interp))
plt.xlabel('Time (years)')
plt.ylabel('Fwd Rate (%)')
plt.legend(loc='lower right', frameon=False)
def test_FinNelsonSiegelSvenssonCurve():
tau1 = 2.0
tau2 = 0.5
times = np.linspace(0.0, 10.0, 5)
curve1 = FinNelsonSiegelSvenssonCurve(1., 0., 0., 0., tau1, tau2)
factor1loading = curve1.zero(times)
curve2 = FinNelsonSiegelSvenssonCurve(0., 1., 0., 0., tau1, tau2)
factor2loading = curve2.zero(times)
curve3 = FinNelsonSiegelSvenssonCurve(0., 0., 1., 0., tau1, tau2)
factor3loading = curve3.zero(times)
curve4 = FinNelsonSiegelSvenssonCurve(0., 0., 0., 1., tau1, tau2)
factor4loading = curve4.zero(times)
testCases.header("FACTOR LOADING ON ZERO RATES")
testCases.print(factor1loading)
testCases.print(factor2loading)
testCases.print(factor3loading)
testCases.print(factor4loading)
# plt.figure(figsize = (6,4))
# plt.plot(times,scaleVector(factor1loading,1),label='beta1');
# plt.plot(times,scaleVector(factor2loading,1),label='beta2');
# plt.plot(times,scaleVector(factor3loading,1),label='beta3');
# plt.ylim((0,1.05))
#
# plt.title('Factor Loadings in Nelson-Siegel Model');
# plt.xlabel('Time (years)');
# plt.ylabel('Loading');
# plt.legend(loc='best')
##########################################################################
testCases.header("BETA1", "BETA2", "BETA3", "BETA4", "ZEROS")
beta1 = 0.03
beta2 = -0.02
beta3 = -0.02
beta4 = 0.08
curve1 = FinNelsonSiegelSvenssonCurve(beta1, beta2, beta3, beta4, tau1,
tau2)
zeroRates1 = curve1.zero(times)
testCases.print(beta1, beta2, beta3, beta4, zeroRates1)
beta1 = 0.04
beta2 = -0.02
beta3 = -0.02
beta4 = 0.08
curve2 = FinNelsonSiegelSvenssonCurve(beta1, beta2, beta3, beta4, tau1,
tau2)
zeroRates2 = curve2.zero(times)
testCases.print(beta1, beta2, beta3, beta4, zeroRates2)
beta1 = 0.05
beta2 = -0.02
beta3 = -0.02
beta4 = 0.08
curve3 = FinNelsonSiegelSvenssonCurve(beta1, beta2, beta3, beta4, tau1,
tau2)
zeroRates3 = curve3.zero(times)
testCases.print(beta1, beta2, beta3, beta4, zeroRates3)
beta1 = 0.06
beta2 = -0.02
beta3 = -0.02
beta4 = 0.08
curve4 = FinNelsonSiegelSvenssonCurve(beta1, beta2, beta3, beta4, tau1,
tau2)
zeroRates4 = curve4.zero(times)
testCases.print(beta1, beta2, beta3, beta4, zeroRates4)
beta1 = 0.07
beta2 = -0.02
beta3 = -0.02
beta4 = 0.08
curve5 = FinNelsonSiegelSvenssonCurve(beta1, beta2, beta3, beta4, tau1,
tau2)
zeroRates5 = curve5.zero(times)
testCases.print(beta1, beta2, beta3, beta4, zeroRates5)
if 1 == 0:
plt.figure(figsize=(6, 4))
plt.plot(times, scale(zeroRates1, 100), label='beta1=3%')
plt.plot(times, scale(zeroRates2, 100), label='beta1=4%')
plt.plot(times, scale(zeroRates3, 100), label='beta1=5%')
plt.plot(times, scale(zeroRates4, 100), label='beta1=6%')
plt.plot(times, scale(zeroRates5, 100), label='beta1=7%')
plt.ylim((0, 7.5))
plt.title('Nelson-Siegel Zero Rate Curves')
plt.xlabel('Time (years)')
plt.ylabel('Zero Rate (%)')
plt.legend(loc='lower right', frameon=False)
def test_FinNelsonSiegelCurve():
tau = 2.0
times = np.linspace(0.0, 10.0, 5)
curveDate = FinDate(2019, 6, 6)
dates = curveDate.addYears(times)
curve1 = FinDiscountCurveNS(curveDate, 1, 0, 0, tau)
factor1loading = curve1.zeroRate(dates)
curve2 = FinDiscountCurveNS(curveDate, 0, 1, 0, tau)
factor2loading = curve2.zeroRate(dates)
curve3 = FinDiscountCurveNS(curveDate, 0, 0, 1, tau)
factor3loading = curve3.zeroRate(dates)
testCases.header("FACTOR LOADING ON ZERO RATES")
testCases.print(factor1loading)
testCases.print(factor2loading)
testCases.print(factor3loading)
if PLOT_GRAPHS:
plt.figure(figsize=(6, 4))
plt.plot(times, scale(factor1loading, 1), label='beta1')
plt.plot(times, scale(factor2loading, 1), label='beta2')
plt.plot(times, scale(factor3loading, 1), label='beta3')
plt.ylim((0, 1.05))
plt.title('Factor Loadings in Nelson-Siegel Model')
plt.xlabel('Time (years)')
plt.ylabel('Loading')
plt.legend(loc='best')
###########################################################################
testCases.header("BETA1", "BETA2", "BETA3", "ZEROS")
beta1 = 0.03
beta2 = -0.02
beta3 = 0.02
curve1 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates1 = curve1.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates1)
beta1 = 0.04
beta2 = -0.02
beta3 = 0.02
curve2 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates2 = curve2.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates2)
beta1 = 0.05
beta2 = -0.02
beta3 = 0.02
curve3 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates3 = curve3.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates3)
beta1 = 0.06
beta2 = -0.02
beta3 = 0.02
curve4 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates4 = curve4.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates4)
beta1 = 0.07
beta2 = -0.02
beta3 = 0.02
curve5 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates5 = curve5.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates5)
if PLOT_GRAPHS:
plt.figure(figsize=(6, 4))
plt.plot(times, scale(zeroRates1, 100), label='beta1=3%')
plt.plot(times, scale(zeroRates2, 100), label='beta1=4%')
plt.plot(times, scale(zeroRates3, 100), label='beta1=5%')
plt.plot(times, scale(zeroRates4, 100), label='beta1=6%')
plt.plot(times, scale(zeroRates5, 100), label='beta1=7%')
plt.ylim((0, 7.5))
plt.title('Nelson-Siegel Zero Rate Curves')
plt.xlabel('Time (years)')
plt.ylabel('Zero Rate (%)')
plt.legend(loc='lower right', frameon=False)
###########################################################################
beta1 = 0.06
beta2 = -0.04
beta3 = 0.02
curve1 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates1 = curve1.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates1)
beta1 = 0.06
beta2 = -0.02
beta3 = 0.02
curve2 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates2 = curve2.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates2)
beta1 = 0.06
beta2 = 0.00
beta3 = 0.02
curve3 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates3 = curve3.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates3)
beta1 = 0.06
beta2 = 0.02
beta3 = 0.02
curve4 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates4 = curve4.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates4)
beta1 = 0.06
beta2 = 0.04
beta3 = 0.02
curve5 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates5 = curve5.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates5)
if PLOT_GRAPHS:
plt.figure(figsize=(6, 4))
plt.plot(times, scale(zeroRates1, 100), label='beta2=-4%')
plt.plot(times, scale(zeroRates2, 100), label='beta2=-2%')
plt.plot(times, scale(zeroRates3, 100), label='beta2=0%')
plt.plot(times, scale(zeroRates4, 100), label='beta2=2%')
plt.plot(times, scale(zeroRates5, 100), label='beta2=4%')
plt.ylim((0, 10))
plt.title('Nelson-Siegel Zero Rate Curves: Varying beta2')
plt.xlabel('Time (years)')
plt.ylabel('Zero Rate (%)')
plt.legend(loc='lower right', frameon=False)
beta1 = 0.06
beta2 = -0.02
beta3 = -0.02
curve1 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates1 = curve1.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates1)
beta1 = 0.06
beta2 = -0.02
beta3 = 0.00
curve2 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates2 = curve2.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates2)
beta1 = 0.06
beta2 = -0.02
beta3 = 0.02
curve3 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates3 = curve3.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates3)
beta1 = 0.06
beta2 = -0.02
beta3 = 0.04
curve4 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates4 = curve4.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates4)
beta1 = 0.06
beta2 = -0.02
beta3 = 0.06
curve5 = FinDiscountCurveNS(curveDate, beta1, beta2, beta3, tau)
zeroRates5 = curve5.zeroRate(dates)
testCases.print(beta1, beta2, beta3, zeroRates5)
if PLOT_GRAPHS:
plt.figure(figsize=(6, 4))
plt.plot(times, scale(zeroRates1, 100), label='beta3=-2%')
plt.plot(times, scale(zeroRates2, 100), label='beta3=0%')
plt.plot(times, scale(zeroRates3, 100), label='beta3=2%')
plt.plot(times, scale(zeroRates4, 100), label='beta3=4%')
plt.plot(times, scale(zeroRates5, 100), label='beta3=6%')
plt.ylim((3.5, 7.5))
plt.title('Nelson-Siegel Zero Rate Curves: Varying beta3')
plt.xlabel('Time (years)')
plt.ylabel('Zero Rate (%)')
plt.legend(loc='lower right', frameon=False)