He usado QuantLib Python para calcular las tasas forward de 1 mes a partir de tasas cero en la fecha 05 de diciembre de 2019.
Mi códigos se pueden encontrar a continuación:
import QuantLib as ql
calendar = ql.NullCalendar()
compounding = ql.Compounded
day_convention = ql.Actual360()
valuation_date = ql.Date(5, 12, 2019)
ql.Settings.instance().evaluationDate = valuation_date
dates = [calendar.advance(valuation_date, ql.Period(n, ql.Years)) for n in range(0, 4, 1)]
zero_rates = [0.01, 0.02, 0.03, 0.05]
zero_curve = ql.ZeroCurve(dates, zero_rates, day_convention)
forward_term_structure = ql.YieldTermStructureHandle(zero_curve)
forward_term_structure.enableExtrapolation()
forward_rates_quantlib = []
value_dates = []
maturity_dates = []
discount_factor_value_dates = []
discount_factor_maturity_dates = []
year_frac_value_maturity_dates = []
for date in dates:
value_date = date
value_dates.append(value_date)
maturity_date = date + ql.Period('1M')
maturity_dates.append(maturity_date)
forward_rate = forward_term_structure.forwardRate(value_date, maturity_date, day_convention, compounding).rate()
forward_rates_quantlib.append(forward_rate)
discount_factor_value_date = zero_curve.discount(value_date)
discount_factor_value_dates.append(discount_factor_value_date)
discount_factor_maturity_date = zero_curve.discount(maturity_date)
discount_factor_maturity_dates.append(discount_factor_maturity_date)
year_frac_value_maturity_date = day_convention.yearFraction(value_date, maturity_date)
year_frac_value_maturity_dates.append(year_frac_value_maturity_date)
import pandas as pd
manual_calculation = pd.DataFrame()
manual_calculation['Value_Date'] = value_dates
manual_calculation['Discount_Factor_Value_Date'] = discount_factor_value_dates
manual_calculation['Maturity_Date'] = maturity_dates
manual_calculation['Discount_Factor_Maturity_Date'] = discount_factor_maturity_dates
manual_calculation['Year_Frac_Value_Maturity'] = year_frac_value_maturity_dates
manual_calculation['Forward_Rate_QuantLib'] = forward_rates_quantlib
forward_rates_manual = []
for i in range(0, len(manual_calculation), 1):
df_value = manual_calculation.loc[i, 'Discount_Factor_Value_Date']
df_mat = manual_calculation.loc[i, 'Discount_Factor_Maturity_Date']
year_frac = manual_calculation.loc[i, 'Year_Frac_Value_Maturity']
forward_rates_manual.append(((df_value/df_mat) - 1) * (1/year_frac))
manual_calculation['Forward_Rate_Manual'] = forward_rates_manual
import matplotlib.pyplot as plt
plt.plot(zero_rates, 'o-', label = "Spot")
plt.plot(forward_rates, 'o-', label = "1M Forward (QuantLib)")
plt.plot(forward_rates_manual, 'o-', label = "1M Forward (Manual)")
plt.legend()Como se puede ver en la lista forward_rates_manual, he intentado volver a calcular manualmente las tasas forward de 1 mes utilizando la siguiente fórmula:
donde
significa factor de descuento desde la fecha de valoración hasta la fecha de valor
significa factor de descuento desde la fecha de vencimiento hasta la fecha de valoración, donde la fecha de vencimiento es la fecha de valor más 1 mes, y
significa la fracción de año entre la fecha de valor y la fecha de vencimiento.
Sin embargo, al comparar forward_rates_quantlib con forward_rates_manual, veo que surgen ligeras diferencias, y no puedo entender de dónde vienen.
Agradezco cualquier aclaración, gracias.
