我试图确定QuantLib中可赎回债券的OAS。然而,我的结果总是负面的
我想知道看涨期权计划中是否存在一些问题,因为根据赫尔-怀特模型对债券进行定价所获得的债券收益率似乎是合理的
考虑以下债券合同:
import QuantLib as ql
import numpy as np
import pandas as pd
bf = ql.BondFunctions
qd = ql.DateParser.parseFormatted
# Conventions
accrual_convention = ql.Unadjusted
Rule = ql.DateGeneration.Backward
endofMonth = False
firstDate = None
# OAS
compounding = ql.Compounded
frequency = ql.Annual
calendar = ql.UnitedStates()
a = 0.1
sigma = 0.1
grid_points = 100
face_amount = 100
mkt_price = 78
contract = {
'IssueDate': ql.Date(30,6,2016),
'MaturityDate': ql.Date(15,6,2023),
'SettlementDays': 2,
'FirstCouponDate': ql.Date(15,12,2016),
'NextToLastCouponDate': ql.Date(15,12,2022),
'RealValue': 0.0675,
'FirstCallDate': ql.Date(15,6,2019),
'OptionalityEndDate': ql.Date(15,6,2023),
'OperatingCountry': 'US',
'StrikeDate': [ql.Date(15,6,2019), ql.Date(15,6,2020), ql.Date(15,6,2021)],
'OptionalityType': ['Call', 'Call', 'Call'],
'NoticeDays': [30, 30, 30],
'StrikePrice': [103.375, 101.688, 100.0]}
# Here is the zero curve:
times= np.array(['0 MO', '1 MO', '2 MO', '3 MO', '6 MO', '1 YR', '2 YR', '3 YR',
'5 YR', '7 YR', '10 YR', '20 YR', '30 YR'], dtype=object)
dates = [ql.Date(9,2,2017), ql.Date(9,3,2017), ql. Date(9,4,2017),
ql.Date(9,5,2017),ql.Date(9,8,2017), ql.Date(9,2,2018),
ql.Date(9,2,2019),ql.Date(9,2,2020), ql.Date(9,2,2022),
ql.Date(9,2,2024), ql.Date(9,2,2027),ql.Date(9,2,2037),
ql.Date(9,2,2047)]
rates = np.array([0.51 , 0.51 , 0.525, 0.54 , 0.64 ,
0.8 , 1.2 , 1.46 , 1.88 , 2.2 ,
2.4 , 2.74 , 3.02 ])
day_count = ql.ActualActual()
calc_date = ql.Date(9,2,2017)
ql.Settings.instance().evaluationDate = calc_date
issue_date = contract["IssueDate"]
maturity_date = contract["MaturityDate"]
tenor = ql.Period(ql.Semiannual)
coupon = contract["RealValue"]
settlement_days = contract["SettlementDays"]
# Determine Schedule
schedule = ql.Schedule(issue_date,
maturity_date,
tenor,
calendar,
accrual_convention,
accrual_convention,
Rule,
endofMonth)
# Initiate Zero Curve
curve = ql.ZeroCurve(dates,
rates,
ql.ActualActual(),
calendar,
ql.Linear())
curve.enableExtrapolation()
ts_handle = ql.YieldTermStructureHandle(curve)
def get_call_schedule(df, period=ql.Period(ql.Annual)):
dates = df["StrikeDate"]
prices = df["StrikePrice"]
callability_schedule = ql.CallabilitySchedule()
null_calendar = ql.NullCalendar()
call_date = df["StrikeDate"][0]
for time in range(len(df["StrikeDate"])):
callability_price = ql.CallabilityPrice(prices[time],
ql.CallabilityPrice.Clean)
callability_schedule.append(ql.Callability(callability_price,
ql.Callability.Call,
dates[time]))
call_date = null_calendar.advance(call_date, period)
return callability_schedule
callability_schedule = get_call_schedule(contract)
bond = ql.CallableFixedRateBond(settlement_days,
face_amount,
schedule,
[coupon],
day_count,
ql.Following,
face_amount,
calc_date,
callability_schedule)
def value_bond(a, s, ts_handle, grid_points, bond):
model = ql.HullWhite(ts_handle, a, s)
engine = ql.TreeCallableFixedRateBondEngine(model, grid_points)
bond.setPricingEngine(engine)
return bond
bondprice = value_bond(a, sigma, ts_handle, grid_points, bond)
OAS = bondprice.OAS(mkt_price,
ts_handle,
day_count,
compounding,
frequency)
bond_yield = bondprice.bondYield(mkt_price,
day_count,
compounding,
frequency)
print(OAS)
print(bond_yield)
这将产生-6.69的OAS值和0.121或12.1%的债券收益率(YTM)。是否有很大的不同,如果一个要考虑欧洲选择在罢工日期与美式期权,其中罢工是应付在优惠券付款日期??p>
我会将预付罚款(电话罢工)设定得很高,这样打电话总是不经济的,然后观察/确认您的OAS为零。这至少会验证一些整体设置。如果它通过了测试,那么我会逐步使其中一个更经济,并尝试分别为欧洲期权定价(你可以在你的HW过程上使用Jamshidian引擎进行封闭形式,这是仿射的),然后看看债券dv01上期权的分解值是否足够接近你的OAS(假设后者为正). 虽然如果你有一个消极的美洲国家组织和一组美国的通话日期,它不太可能成为积极的欧洲通话时间表。但这些测试可能会提供一些见解
你们的价格差了100倍。2%的比率需要写为0.02,而不是2.0
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