使用 EONIA 贴现曲线和 6M EURIBOR 远期曲线定价计算 python 中 IR 互换的潜在未来风险敞口
Calculating the Potential Future Exposure for IR swaps in python using EONIA curve for discounting and 6M EURIBOR forward curve for pricing
我想使用 2 条曲线计算两个掉期投资组合的潜在未来风险敞口 (PFE) - EURIBOR 6M 对浮动部分定价，EONIA 曲线对掉期的固定部分进行贴现。我用 Quantlib Python Cookbook 构建了两条曲线，对于掉期定价和 PFE 计算器，我想使用这个例子：(https://ipythonquant.wordpress.com/2015/04/08/expected-exposure-and-pfe-simulation-with-quantlib-and-python/)。我的问题是，在这个例子中，他们使用一条曲线进行折扣和转发，根据一个费率计算（这不太现实）。我可以构建收益率曲线，但我无法将两个示例放在一个代码中以正常工作。 （请帮助我，我的论文工作的截止日期快到了！）我对可以解决此问题的任何其他代码或解决方案感兴趣。这是我的代码：
! pip install QuantLib-Python
# import the used libraries
%%capture
%pylab inline --no-import-all
import math
import utils
import datetime as dt
import pandas as pd
#utils.set_default_plot_size()
import QuantLib as ql
from QuantLib import *
today = Date(8, September, 2020)
Settings.instance().evaluationDate = today
eonia = Eonia()
helpers = [ OISRateHelper(2, Period(*tenor),
QuoteHandle(SimpleQuote(rate/100)), eonia)
for rate, tenor in [(-0.468, (1,Days)), (-0.470000013709068, (1,Weeks)),(-0.473499998450279, (2,Weeks)), (-0.476999998092651, (1,Months)), (-0.478000000119209, (2,Months)),(-0.480000004172325, (3,Months)), (-0.483400002121925, (4,Months)),(-0.486249998211861, (5,Months)), (-0.488499999046326, (6,Months)),(-0.493000000715256, (7,Months)), (-0.497000008821487, (8,Months)),(-0.500199988484383, (9,Months)), (-0.504599988460541, (10,Months)),(-0.50874999165535, (11,Months)), (-0.512099981307983, (12,Months)),(-0.531000018119812, (18,Months)), (-0.541999995708465, (2,Years)),(-0.546999990940093, (30,Months)), (-0.550999999046326, (3,Years)),(-0.544999986886978, (4,Years)), (-0.527999997138977, (5,Years)),(-0.49499998986721, (6,Years)), (-0.459999993443489, (7,Years)),(-0.417999997735023, (8,Years)), (-0.373999997973442, (9,Years)),(-0.326999992132187, (10,Years)), (-0.277999997138977, (11,Years)),(-0.236000001430512, (12,Years)), (-0.123999997973442, (15,Years)),(-0.0370000004768372, (20,Years)), (-0.0330000007525086, (25,Years)),(-0.0490000005811453, (30,Years)), (-0.0710000023245811,(35,Years)),(-0.0889999493956566, (40,Years)), (-0.128000002354383, (50,Years))] ]
eonia_curve_c = PiecewiseLogCubicDiscount(0, TARGET(),
helpers, Actual360())
eonia_curve_c.enableExtrapolation()
helpers = [ DepositRateHelper(QuoteHandle(SimpleQuote(-0.459/100)),Period(6,Months), 3,TARGET(), Following, False, Actual360()) ]
euribor6m = Euribor6M()
另外，这里有什么问题？？：
helpers += [ FraRateHelper(QuoteHandle(SimpleQuote(rate/100)),
start, euribor6m)
for rate, start in [(-0.43818798661232, 7), (-0.442768007516861, 8), (-0.440380990505219, 9),
(-0.437555998563766, 10), (-0.445408999919891, 11), (-0.452802002429962, 12),
(-0.453942000865936, 13), (-0.450417011976242, 14), (-0.466143995523453, 15),
(-0.450170010328293, 16), (-0.,452068001031876, 17), (-0.468688994646072, 18)] ]
（它说要解压的值太多）
discount_curve = RelinkableYieldTermStructureHandle()
discount_curve.linkTo(eonia_curve)
helpers += [ SwapRateHelper(QuoteHandle(SimpleQuote(rate/100)),Period(tenor, Years), TARGET(),Annual, Unadjusted,Thirty360(Thirty360.BondBasis),euribor6m, QuoteHandle(), Period(0, Days),discount_curve)for rate, tenor in [(-0.471998006105423, 2), (-0.4668410122394563, 3), (-0.448518991470337, 4),(-0.419505000114441, 5),(-0.386981993913651, 6), (-0.345064997673035, 7), (-0.301272988319397, 8),(-0.259175002574921, 9), (-0.206983998417854, 10), (-0.164517998695374, 11),(-0.123749002814293, 12),(-0.0165138002485037, 15), (0.0642198026180267, 20),(0.0658923983573914, 25), (0.0394961982965469, 30),(-0.0109016001224518, 40),(-0.0604206994175911, 50)] ]
euribor6m_curve = PiecewiseLogCubicDiscount(2, TARGET(), helpers,Actual365Fixed())
euribor6m_curve.enableExtrapolation()
然后，我想将这条曲线添加到这段代码中：https://ipythonquant.wordpress.com/2015/04/08/expected-exposure-and-pfe-simulation-with-quantlib-and-python/
要替换它：
# Setup Marketdata
rate = ql.SimpleQuote(0.0536)
rate_handle = ql.QuoteHandle(rate)
dc = ql.Actual365Fixed()
yts = ql.FlatForward(today, rate_handle, dc)
yts.enableExtrapolation()
hyts = ql.RelinkableYieldTermStructureHandle(yts)
t0_curve = ql.YieldTermStructureHandle(yts)
euribor6m = ql.Euribor6M(hyts)
然后用这些曲线给掉期定价。
如果您知道解决此问题的方法，请与我分享！或者任何建议，我如何用两条自举曲线为掉期定价。谢谢
你其实有两个问题：
1。 PFE 示例
首先，您无法提取 FraRateHelper 数据的原因是其中一个元素中有一个额外的逗号。注意这里的类型使那个特定的元组有 3 个元素而不是 2 个：
(-0.,452068001031876, 17)
之后，替换这段代码（创建平坦曲线的地方）：
rate = ql.SimpleQuote(0.0536)
rate_handle = ql.QuoteHandle(rate)
dc = ql.Actual365Fixed()
yts = ql.FlatForward(today, rate_handle, dc)
yts.enableExtrapolation()
与...
yts = euribor6m_curve
你应该很好地使用你提到的例子。
2。定价掉期
现在用两条曲线进行掉期定价，想法是使用指数的远期曲线：
euribor6m = ql.Euribor6M(hyts)
然后是引擎的折扣曲线：
engine = ql.DiscountingSwapEngine(discount_curve)
swap.setPricingEngine(engine)
print( swap.NPV() )
print( swap.fairRate() )
我想使用 2 条曲线计算两个掉期投资组合的潜在未来风险敞口 (PFE) - EURIBOR 6M 对浮动部分定价，EONIA 曲线对掉期的固定部分进行贴现。我用 Quantlib Python Cookbook 构建了两条曲线，对于掉期定价和 PFE 计算器，我想使用这个例子：(https://ipythonquant.wordpress.com/2015/04/08/expected-exposure-and-pfe-simulation-with-quantlib-and-python/)。我的问题是，在这个例子中，他们使用一条曲线进行折扣和转发，根据一个费率计算（这不太现实）。我可以构建收益率曲线，但我无法将两个示例放在一个代码中以正常工作。 （请帮助我，我的论文工作的截止日期快到了！）我对可以解决此问题的任何其他代码或解决方案感兴趣。这是我的代码：
! pip install QuantLib-Python
# import the used libraries
%%capture
%pylab inline --no-import-all
import math
import utils
import datetime as dt
import pandas as pd
#utils.set_default_plot_size()
import QuantLib as ql
from QuantLib import *
today = Date(8, September, 2020)
Settings.instance().evaluationDate = today
eonia = Eonia()
helpers = [ OISRateHelper(2, Period(*tenor),
QuoteHandle(SimpleQuote(rate/100)), eonia)
for rate, tenor in [(-0.468, (1,Days)), (-0.470000013709068, (1,Weeks)),(-0.473499998450279, (2,Weeks)), (-0.476999998092651, (1,Months)), (-0.478000000119209, (2,Months)),(-0.480000004172325, (3,Months)), (-0.483400002121925, (4,Months)),(-0.486249998211861, (5,Months)), (-0.488499999046326, (6,Months)),(-0.493000000715256, (7,Months)), (-0.497000008821487, (8,Months)),(-0.500199988484383, (9,Months)), (-0.504599988460541, (10,Months)),(-0.50874999165535, (11,Months)), (-0.512099981307983, (12,Months)),(-0.531000018119812, (18,Months)), (-0.541999995708465, (2,Years)),(-0.546999990940093, (30,Months)), (-0.550999999046326, (3,Years)),(-0.544999986886978, (4,Years)), (-0.527999997138977, (5,Years)),(-0.49499998986721, (6,Years)), (-0.459999993443489, (7,Years)),(-0.417999997735023, (8,Years)), (-0.373999997973442, (9,Years)),(-0.326999992132187, (10,Years)), (-0.277999997138977, (11,Years)),(-0.236000001430512, (12,Years)), (-0.123999997973442, (15,Years)),(-0.0370000004768372, (20,Years)), (-0.0330000007525086, (25,Years)),(-0.0490000005811453, (30,Years)), (-0.0710000023245811,(35,Years)),(-0.0889999493956566, (40,Years)), (-0.128000002354383, (50,Years))] ]
eonia_curve_c = PiecewiseLogCubicDiscount(0, TARGET(),
helpers, Actual360())
eonia_curve_c.enableExtrapolation()
helpers = [ DepositRateHelper(QuoteHandle(SimpleQuote(-0.459/100)),Period(6,Months), 3,TARGET(), Following, False, Actual360()) ]
euribor6m = Euribor6M()
另外，这里有什么问题？？：
helpers += [ FraRateHelper(QuoteHandle(SimpleQuote(rate/100)),
start, euribor6m)
for rate, start in [(-0.43818798661232, 7), (-0.442768007516861, 8), (-0.440380990505219, 9),
(-0.437555998563766, 10), (-0.445408999919891, 11), (-0.452802002429962, 12),
(-0.453942000865936, 13), (-0.450417011976242, 14), (-0.466143995523453, 15),
(-0.450170010328293, 16), (-0.,452068001031876, 17), (-0.468688994646072, 18)] ]
（它说要解压的值太多）
discount_curve = RelinkableYieldTermStructureHandle()
discount_curve.linkTo(eonia_curve)
helpers += [ SwapRateHelper(QuoteHandle(SimpleQuote(rate/100)),Period(tenor, Years), TARGET(),Annual, Unadjusted,Thirty360(Thirty360.BondBasis),euribor6m, QuoteHandle(), Period(0, Days),discount_curve)for rate, tenor in [(-0.471998006105423, 2), (-0.4668410122394563, 3), (-0.448518991470337, 4),(-0.419505000114441, 5),(-0.386981993913651, 6), (-0.345064997673035, 7), (-0.301272988319397, 8),(-0.259175002574921, 9), (-0.206983998417854, 10), (-0.164517998695374, 11),(-0.123749002814293, 12),(-0.0165138002485037, 15), (0.0642198026180267, 20),(0.0658923983573914, 25), (0.0394961982965469, 30),(-0.0109016001224518, 40),(-0.0604206994175911, 50)] ]
euribor6m_curve = PiecewiseLogCubicDiscount(2, TARGET(), helpers,Actual365Fixed())
euribor6m_curve.enableExtrapolation()
然后，我想将这条曲线添加到这段代码中：https://ipythonquant.wordpress.com/2015/04/08/expected-exposure-and-pfe-simulation-with-quantlib-and-python/ 要替换它：
# Setup Marketdata
rate = ql.SimpleQuote(0.0536)
rate_handle = ql.QuoteHandle(rate)
dc = ql.Actual365Fixed()
yts = ql.FlatForward(today, rate_handle, dc)
yts.enableExtrapolation()
hyts = ql.RelinkableYieldTermStructureHandle(yts)
t0_curve = ql.YieldTermStructureHandle(yts)
euribor6m = ql.Euribor6M(hyts)
然后用这些曲线给掉期定价。 如果您知道解决此问题的方法，请与我分享！或者任何建议，我如何用两条自举曲线为掉期定价。谢谢
你其实有两个问题：
1。 PFE 示例
首先，您无法提取 FraRateHelper 数据的原因是其中一个元素中有一个额外的逗号。注意这里的类型使那个特定的元组有 3 个元素而不是 2 个：
(-0.,452068001031876, 17)
之后，替换这段代码（创建平坦曲线的地方）：
rate = ql.SimpleQuote(0.0536)
rate_handle = ql.QuoteHandle(rate)
dc = ql.Actual365Fixed()
yts = ql.FlatForward(today, rate_handle, dc)
yts.enableExtrapolation()
与...
yts = euribor6m_curve
你应该很好地使用你提到的例子。
2。定价掉期
现在用两条曲线进行掉期定价，想法是使用指数的远期曲线：
euribor6m = ql.Euribor6M(hyts)
然后是引擎的折扣曲线：
engine = ql.DiscountingSwapEngine(discount_curve)
swap.setPricingEngine(engine)
print( swap.NPV() )
print( swap.fairRate() )