Question

在这个示例中，我们将指导用户如何使用平台的功能，完成从利率互换的市场报价完成收益率曲线的构造。

from CAL.PyCAL import *
SetEvaluationDate(Date(2015, 8, 6))

1. 构造收益率曲线

我们从一组市场标准化互换的市场报价中获取收益率曲线的信息：

• swap_rates：标准互换对应的固定端利率
• swap_tenor：标准互换对应的期限

swap_rates = [0.02, 0.03, 0.04 ,0.05, 0.055, 0.06, 0.065, 0.07]
swap_tenor = ['6M', '1Y', '2Y', '3Y', '4Y', '5Y',  '7Y', '10Y']
shiborIndex = Shibor('3M')

instruments = []
for rate, tenor in zip(swap_rates, swap_tenor):
    print('{0:3s} benchmark Shibor Swap fixed at: {1:.2f}%'.format(tenor, rate*100))
    rateHelper = ShiborSwapRateHelper(rate, Period(tenor), Frequency.Quarterly, shiborIndex)
    instruments.append(rateHelper)

6M  benchmark Shibor Swap fixed at: 2.00%
1Y  benchmark Shibor Swap fixed at: 3.00%
2Y  benchmark Shibor Swap fixed at: 4.00%
3Y  benchmark Shibor Swap fixed at: 5.00%
4Y  benchmark Shibor Swap fixed at: 5.50%
5Y  benchmark Shibor Swap fixed at: 6.00%
7Y  benchmark Shibor Swap fixed at: 6.50%
10Y benchmark Shibor Swap fixed at: 7.00%

通过标准互换校正（calibration）收益率曲线：

calibratedCurve = CalibratedYieldCurve(EvaluationDate(), instruments, 'Actual/365 (Fixed)')

收益率曲线的基本信息：

• discount：折现因子
• forward(%)：远期利率
• zero(%)：零息利率

calibratedCurve.curveProfile().head(10)

	date	discount	forward(%)	zero(%)
2015-08-06	2015-08-06	1.000000	1.994947	2.014979
2015-09-06	2015-09-06	0.998307	1.994947	2.014979
2015-10-06	2015-10-06	0.996672	1.994947	2.014979
2015-11-06	2015-11-06	0.994984	1.994947	2.014979
2015-12-06	2015-12-06	0.993354	1.994947	2.014979
2016-01-06	2016-01-06	0.991672	1.994947	2.014979
2016-02-06	2016-02-06	0.989994	1.994947	2.014979
2016-03-06	2016-03-06	0.986950	4.014304	2.276446
2016-04-06	2016-04-06	0.983591	4.014304	2.505840
2016-05-06	2016-05-06	0.980351	4.014304	2.678750

我们可以画图来看：

calibratedCurve.curveProfile()['zero(%)'].plot(figsize=(16,8))

<matplotlib.axes.AxesSubplot at 0x6bbabd0>

2. 测试

首先可以看这条收益率曲线是否真的可以完美定价基准互换（perfectly pricing）：

cal = Calendar('China.IB')
startDate = cal.advanceDate(Date(2015, 8, 6), '1B', BizDayConvention.Following)
shiborIndex = Shibor('3M', calibratedCurve)
nominal = 100000000.
pricingEngine = DiscountingSwapEngine(calibratedCurve)
for rate, tenor in zip(swap_rates, swap_tenor):
    benchmarkSwap = ShiborSwap(SwapLegType.Payer, nominal, startDate, Period(tenor), Period('3M'), rate, shiborIndex)
    benchmarkSwap.setPricingEngine(pricingEngine)
    print('{0:3s} benchmark Shibor Swap NPV: {1:>8.4f}'.format(tenor, benchmarkSwap.NPV()))

6M  benchmark Shibor Swap NPV:   0.0000
1Y  benchmark Shibor Swap NPV:  -0.0000
2Y  benchmark Shibor Swap NPV:   0.0000
3Y  benchmark Shibor Swap NPV:   0.0000
4Y  benchmark Shibor Swap NPV:  -0.0000
5Y  benchmark Shibor Swap NPV:   0.0000
7Y  benchmark Shibor Swap NPV:   0.0000
10Y benchmark Shibor Swap NPV:   0.0000

然后我们取一个假设已经存在的互换（seasoned swap），通过这条收益率曲线估计它的现值：

startDate = Date(2015, 7, 15)
shiborIndex.addFixing(Date(2015, 7, 14), 0.045)
customizeSwap = ShiborSwap(SwapLegType.Receiver, nominal, startDate, Period('9Y'), Period('3M'), 0.06, shiborIndex)
customizeSwap.setPricingEngine(pricingEngine)
print('{0:3s} Shibor Swap fixed at {1:.2f}% NPV: {2:15.4f}'.format('9Y',6.00, customizeSwap.NPV()))

9Y  Shibor Swap fixed at 6.00% NPV:   -6308510.5573

customizeSwap.legAnalysis(0).head(10)

	AMOUNT	NOMINAL	ACCRUAL_START_DATE	ACCRUAL_END_DATE	ACCRUAL_DAYS	INDEX	FIXING_DAYS	FIXING_DATES	INDEX_FIXING	DAY_COUNTER	ACCRUAL_PERIOD	EFFECTIVE_RATE
PAYMENT_DATE
2015-10-15	1512329	1e+08	2015-07-15	2015-10-15	92	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2520548	0.06
2016-01-15	1512329	1e+08	2015-10-15	2016-01-15	92	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2520548	0.06
2016-04-15	1495890	1e+08	2016-01-15	2016-04-15	91	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2493151	0.06
2016-07-15	1495890	1e+08	2016-04-15	2016-07-15	91	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2493151	0.06
2016-10-17	1545205	1e+08	2016-07-15	2016-10-17	94	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2575342	0.06
2017-01-16	1495890	1e+08	2016-10-17	2017-01-16	91	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2493151	0.06
2017-04-17	1495890	1e+08	2017-01-16	2017-04-17	91	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2493151	0.06
2017-07-17	1495890	1e+08	2017-04-17	2017-07-17	91	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2493151	0.06
2017-10-16	1495890	1e+08	2017-07-17	2017-10-16	91	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2493151	0.06
2018-01-15	1495890	1e+08	2017-10-16	2018-01-15	91	#NA	#NA	#NA	#NA	Actual/365 (Fixed)	0.2493151	0.06

customizeSwap.legAnalysis(1).head(10)

	AMOUNT	NOMINAL	ACCRUAL_START_DATE	ACCRUAL_END_DATE	ACCRUAL_DAYS	INDEX	FIXING_DAYS	FIXING_DATES	INDEX_FIXING	DAY_COUNTER	ACCRUAL_PERIOD	EFFECTIVE_RATE
PAYMENT_DATE
2015-10-15	1150000	1e+08	2015-07-15	2015-10-15	92	Shibor3M Actual/360	1	2015-07-14	0.045	Actual/360	0.2555556	0.045
2016-01-15	504102.3	1e+08	2015-10-15	2016-01-15	92	Shibor3M Actual/360	1	2015-10-14	0.01972574	Actual/360	0.2555556	0.01972574
2016-04-15	871825.4	1e+08	2016-01-15	2016-04-15	91	Shibor3M Actual/360	1	2016-01-14	0.03448979	Actual/360	0.2527778	0.03448979
2016-07-15	1005852	1e+08	2016-04-15	2016-07-15	91	Shibor3M Actual/360	1	2016-04-14	0.03979193	Actual/360	0.2527778	0.03979193
2016-10-17	1234864	1e+08	2016-07-15	2016-10-17	94	Shibor3M Actual/360	1	2016-07-14	0.04729266	Actual/360	0.2611111	0.04729266
2017-01-16	1260227	1e+08	2016-10-17	2017-01-16	91	Shibor3M Actual/360	1	2016-10-14	0.04985512	Actual/360	0.2527778	0.04985512
2017-04-17	1260227	1e+08	2017-01-16	2017-04-17	91	Shibor3M Actual/360	1	2017-01-13	0.04985512	Actual/360	0.2527778	0.04985512
2017-07-17	1260227	1e+08	2017-04-17	2017-07-17	91	Shibor3M Actual/360	1	2017-04-14	0.04985512	Actual/360	0.2527778	0.04985512
2017-10-16	1668056	1e+08	2017-07-17	2017-10-16	91	Shibor3M Actual/360	1	2017-07-14	0.06598904	Actual/360	0.2527778	0.06598904
2018-01-15	1790725	1e+08	2017-10-16	2018-01-15	91	Shibor3M Actual/360	1	2017-10-13	0.07084187	Actual/360	0.2527778	0.07084187