/
overnightindexedswap.cpp
524 lines (444 loc) · 21.3 KB
/
overnightindexedswap.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 Roland Lichters
Copyright (C) 2014 Peter Caspers
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include "overnightindexedswap.hpp"
#include "utilities.hpp"
#include <ql/termstructures/yield/oisratehelper.hpp>
#include <ql/instruments/makeois.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/termstructures/yield/piecewiseyieldcurve.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/daycounters/thirty360.hpp>
#include <ql/time/daycounters/actual365fixed.hpp>
#include <ql/time/daycounters/simpledaycounter.hpp>
#include <ql/time/schedule.hpp>
#include <ql/indexes/ibor/eonia.hpp>
#include <ql/indexes/ibor/euribor.hpp>
#include <ql/indexes/ibor/fedfunds.hpp>
#include <ql/cashflows/iborcoupon.hpp>
#include <ql/cashflows/cashflowvectors.hpp>
#include <ql/cashflows/cashflows.hpp>
#include <ql/cashflows/couponpricer.hpp>
#include <ql/currencies/europe.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <iostream>
#include <iomanip>
using namespace QuantLib;
using namespace boost::unit_test_framework;
using std::exp;
typedef PiecewiseYieldCurve<Discount,LogLinear> PiecewiseFlatForward;
namespace overnight_indexed_swap_test {
struct Datum {
Integer settlementDays;
Integer n;
TimeUnit unit;
Rate rate;
};
Datum depositData[] = {
{ 0, 1, Days, 1.10 },
{ 1, 1, Days, 1.10 },
{ 2, 1, Weeks, 1.40 },
{ 2, 2, Weeks, 1.50 },
{ 2, 1, Months, 1.70 },
{ 2, 2, Months, 1.90 },
{ 2, 3, Months, 2.05 },
{ 2, 4, Months, 2.08 },
{ 2, 5, Months, 2.11 },
{ 2, 6, Months, 2.13 }
};
Datum eoniaSwapData[] = {
{ 2, 1, Weeks, 1.245 },
{ 2, 2, Weeks, 1.269 },
{ 2, 3, Weeks, 1.277 },
{ 2, 1, Months, 1.281 },
{ 2, 2, Months, 1.18 },
{ 2, 3, Months, 1.143 },
{ 2, 4, Months, 1.125 },
{ 2, 5, Months, 1.116 },
{ 2, 6, Months, 1.111 },
{ 2, 7, Months, 1.109 },
{ 2, 8, Months, 1.111 },
{ 2, 9, Months, 1.117 },
{ 2, 10, Months, 1.129 },
{ 2, 11, Months, 1.141 },
{ 2, 12, Months, 1.153 },
{ 2, 15, Months, 1.218 },
{ 2, 18, Months, 1.308 },
{ 2, 21, Months, 1.407 },
{ 2, 2, Years, 1.510 },
{ 2, 3, Years, 1.916 },
{ 2, 4, Years, 2.254 },
{ 2, 5, Years, 2.523 },
{ 2, 6, Years, 2.746 },
{ 2, 7, Years, 2.934 },
{ 2, 8, Years, 3.092 },
{ 2, 9, Years, 3.231 },
{ 2, 10, Years, 3.380 },
{ 2, 11, Years, 3.457 },
{ 2, 12, Years, 3.544 },
{ 2, 15, Years, 3.702 },
{ 2, 20, Years, 3.703 },
{ 2, 25, Years, 3.541 },
{ 2, 30, Years, 3.369 }
};
struct CommonVars {
// global data
Date today, settlement;
Swap::Type type;
Real nominal;
Calendar calendar;
Natural settlementDays;
Period fixedEoniaPeriod, floatingEoniaPeriod;
DayCounter fixedEoniaDayCount;
BusinessDayConvention fixedEoniaConvention, floatingEoniaConvention;
ext::shared_ptr<Eonia> eoniaIndex;
RelinkableHandle<YieldTermStructure> eoniaTermStructure;
Frequency fixedSwapFrequency;
DayCounter fixedSwapDayCount;
BusinessDayConvention fixedSwapConvention;
ext::shared_ptr<IborIndex> swapIndex;
RelinkableHandle<YieldTermStructure> swapTermStructure;
// cleanup
SavedSettings backup;
// utilities
ext::shared_ptr<OvernightIndexedSwap>
makeSwap(Period length,
Rate fixedRate,
Spread spread,
bool telescopicValueDates,
Date effectiveDate = Null<Date>(),
Natural paymentLag = 0,
RateAveraging::Type averagingMethod = RateAveraging::Compound) {
return MakeOIS(length, eoniaIndex, fixedRate, 0 * Days)
.withEffectiveDate(effectiveDate == Null<Date>() ? settlement : effectiveDate)
.withOvernightLegSpread(spread)
.withNominal(nominal)
.withPaymentLag(paymentLag)
.withDiscountingTermStructure(eoniaTermStructure)
.withTelescopicValueDates(telescopicValueDates)
.withAveragingMethod(averagingMethod);
}
CommonVars() {
type = Swap::Payer;
settlementDays = 2;
nominal = 100.0;
fixedEoniaConvention = ModifiedFollowing;
floatingEoniaConvention = ModifiedFollowing;
fixedEoniaPeriod = 1*Years;
floatingEoniaPeriod = 1*Years;
fixedEoniaDayCount = Actual360();
eoniaIndex = ext::make_shared<Eonia>(eoniaTermStructure);
fixedSwapConvention = ModifiedFollowing;
fixedSwapFrequency = Annual;
fixedSwapDayCount = Thirty360(Thirty360::BondBasis);
swapIndex = ext::shared_ptr<IborIndex>(new Euribor3M(swapTermStructure));
calendar = eoniaIndex->fixingCalendar();
today = Date(5, February, 2009);
//today = calendar.adjust(Date::todaysDate());
Settings::instance().evaluationDate() = today;
settlement = calendar.advance(today,settlementDays*Days,Following);
eoniaTermStructure.linkTo(flatRate(today, 0.05,
Actual365Fixed()));
}
};
}
void OvernightIndexedSwapTest::testFairRate() {
BOOST_TEST_MESSAGE("Testing Eonia-swap calculation of fair fixed rate...");
using namespace overnight_indexed_swap_test;
CommonVars vars;
Period lengths[] = { 1*Years, 2*Years, 5*Years, 10*Years, 20*Years };
Spread spreads[] = { -0.001, -0.01, 0.0, 0.01, 0.001 };
for (auto& length : lengths) {
for (double spread : spreads) {
ext::shared_ptr<OvernightIndexedSwap> swap = vars.makeSwap(length, 0.0, spread, false);
ext::shared_ptr<OvernightIndexedSwap> swap2 = vars.makeSwap(length, 0.0, spread, true);
if(std::fabs(swap->fairRate()-swap2->fairRate()) > 1.0e-10) {
BOOST_ERROR("fair rates are different:\n"
<< std::setprecision(2) << " length: " << length << " \n"
<< " floating spread: " << io::rate(spread) << "\n"
<< std::setprecision(12)
<< " fair rate (non telescopic value dates): " << swap->fairRate()
<< "\n"
<< " fair rate (telescopic value dates) : " << swap2->fairRate());
}
swap = vars.makeSwap(length, swap->fairRate(), spread, false);
if (std::fabs(swap->NPV()) > 1.0e-10) {
BOOST_ERROR("recalculating with implied rate (non telescopic value dates):\n"
<< std::setprecision(2) << " length: " << length << " \n"
<< " floating spread: " << io::rate(spread) << "\n"
<< " swap value: " << swap->NPV());
}
swap = vars.makeSwap(length, swap->fairRate(), spread, true);
if (std::fabs(swap->NPV()) > 1.0e-10) {
BOOST_ERROR("recalculating with implied rate (telescopic value dates):\n"
<< std::setprecision(2) << " length: " << length << " \n"
<< " floating spread: " << io::rate(spread) << "\n"
<< " swap value: " << swap->NPV());
}
}
}
}
void OvernightIndexedSwapTest::testFairSpread() {
BOOST_TEST_MESSAGE("Testing Eonia-swap calculation of "
"fair floating spread...");
using namespace overnight_indexed_swap_test;
CommonVars vars;
Period lengths[] = { 1*Years, 2*Years, 5*Years, 10*Years, 20*Years };
Rate rates[] = { 0.04, 0.05, 0.06, 0.07 };
for (auto& length : lengths) {
for (double j : rates) {
ext::shared_ptr<OvernightIndexedSwap> swap = vars.makeSwap(length, j, 0.0, false);
ext::shared_ptr<OvernightIndexedSwap> swap2 = vars.makeSwap(length, j, 0.0, true);
Spread fairSpread = swap->fairSpread();
Spread fairSpread2 = swap2->fairSpread();
if(std::fabs(fairSpread-fairSpread2) > 1.0e-10) {
BOOST_ERROR(
"fair spreads are different:\n"
<< std::setprecision(2) << "\n length: " << length
<< "\n fixed rate: " << io::rate(j)
<< "\nfair spread (non telescopic value dates): " << io::rate(fairSpread)
<< "\nfair spread (telescopic value dates) : " << io::rate(fairSpread2));
}
swap = vars.makeSwap(length, j, fairSpread, false);
if (std::fabs(swap->NPV()) > 1.0e-10) {
BOOST_ERROR("\nrecalculating with implied spread (non telescopic value dates):"
<< std::setprecision(2) << "\n length: " << length
<< "\n fixed rate: " << io::rate(j) << "\nfair spread: "
<< io::rate(fairSpread) << "\n swap value: " << swap->NPV());
}
swap = vars.makeSwap(length, j, fairSpread, true);
if (std::fabs(swap->NPV()) > 1.0e-10) {
BOOST_ERROR("\nrecalculating with implied spread (telescopic value dates):"
<< std::setprecision(2) << "\n length: " << length
<< "\n fixed rate: " << io::rate(j) << "\nfair spread: "
<< io::rate(fairSpread) << "\n swap value: " << swap->NPV());
}
}
}
}
void OvernightIndexedSwapTest::testCachedValue() {
BOOST_TEST_MESSAGE("Testing Eonia-swap calculation against cached value...");
using namespace overnight_indexed_swap_test;
CommonVars vars;
Settings::instance().evaluationDate() = vars.today;
vars.settlement =
vars.calendar.advance(vars.today,vars.settlementDays,Days);
Real flat = 0.05;
vars.eoniaTermStructure.linkTo(flatRate(vars.settlement,flat,Actual360()));
Real fixedRate = exp(flat) - 1;
ext::shared_ptr<OvernightIndexedSwap> swap = vars.makeSwap(1*Years, fixedRate, 0.0,false);
ext::shared_ptr<OvernightIndexedSwap> swap2 = vars.makeSwap(1*Years, fixedRate, 0.0,true);
Real cachedNPV = 0.001730450147;
Real tolerance = 1.0e-11;
if (std::fabs(swap->NPV()-cachedNPV) > tolerance)
BOOST_ERROR("\nfailed to reproduce cached swap value (non telescopic value dates):" <<
std::fixed << std::setprecision(12) <<
"\ncalculated: " << swap->NPV() <<
"\n expected: " << cachedNPV <<
"\n tolerance:" << tolerance);
if (std::fabs(swap2->NPV()-cachedNPV) > tolerance)
BOOST_ERROR("\nfailed to reproduce cached swap value (telescopic value dates):" <<
std::fixed << std::setprecision(12) <<
"\ncalculated: " << swap->NPV() <<
"\n expected: " << cachedNPV <<
"\n tolerance:" << tolerance);
}
namespace overnight_indexed_swap_test {
void testBootstrap(bool telescopicValueDates,
RateAveraging::Type averagingMethod,
Real tolerance = 1.0e-8) {
CommonVars vars;
Natural paymentLag = 2;
std::vector<ext::shared_ptr<RateHelper> > eoniaHelpers;
ext::shared_ptr<IborIndex> euribor3m(new Euribor3M);
ext::shared_ptr<Eonia> eonia(new Eonia);
for (auto& i : depositData) {
Real rate = 0.01 * i.rate;
ext::shared_ptr<SimpleQuote> simple = ext::make_shared<SimpleQuote>(rate);
ext::shared_ptr<Quote> quote (simple);
Period term = i.n * i.unit;
ext::shared_ptr<RateHelper> helper(new DepositRateHelper(
Handle<Quote>(quote), term, i.settlementDays, euribor3m->fixingCalendar(),
euribor3m->businessDayConvention(), euribor3m->endOfMonth(), euribor3m->dayCounter()));
if (term <= 2*Days)
eoniaHelpers.push_back(helper);
}
for (auto& i : eoniaSwapData) {
Real rate = 0.01 * i.rate;
ext::shared_ptr<SimpleQuote> simple = ext::make_shared<SimpleQuote>(rate);
ext::shared_ptr<Quote> quote (simple);
Period term = i.n * i.unit;
ext::shared_ptr<RateHelper> helper(new
OISRateHelper(i.settlementDays,
term,
Handle<Quote>(quote),
eonia,
Handle<YieldTermStructure>(),
telescopicValueDates,
paymentLag,
Following,
Annual,
Calendar(),
0 * Days,
0.0,
Pillar::LastRelevantDate,
Date(),
averagingMethod));
eoniaHelpers.push_back(helper);
}
ext::shared_ptr<PiecewiseFlatForward> eoniaTS(
new PiecewiseFlatForward (vars.today, eoniaHelpers, Actual365Fixed()));
vars.eoniaTermStructure.linkTo(eoniaTS);
// test curve consistency
for (auto& i : eoniaSwapData) {
Rate expected = i.rate / 100;
Period term = i.n * i.unit;
// test telescopic value dates (in bootstrap) against non telescopic value dates (swap here)
ext::shared_ptr<OvernightIndexedSwap> swap =
vars.makeSwap(term, 0.0, 0.0, false, Null<Date>(), paymentLag, averagingMethod);
Rate calculated = swap->fairRate();
Rate error = std::fabs(expected-calculated);
if (error>tolerance)
BOOST_FAIL("curve inconsistency:" << std::setprecision(10) <<
"\n swap length: " << term <<
"\n quoted rate: " << expected <<
"\n calculated rate: " << calculated <<
"\n error: " << error <<
"\n tolerance: " << tolerance);
}
} // testBootstrap(telescopicValueDates)
} // anonymous namespace
void OvernightIndexedSwapTest::testBootstrap() {
BOOST_TEST_MESSAGE("Testing Eonia-swap curve building with daily compounded ON rates...");
overnight_indexed_swap_test::testBootstrap(false, RateAveraging::Compound);
}
void OvernightIndexedSwapTest::testBootstrapWithArithmeticAverage() {
BOOST_TEST_MESSAGE("Testing Eonia-swap curve building with arithmetic average ON rates...");
overnight_indexed_swap_test::testBootstrap(false, RateAveraging::Simple);
}
void OvernightIndexedSwapTest::testBootstrapWithTelescopicDates() {
BOOST_TEST_MESSAGE(
"Testing Eonia-swap curve building with telescopic value dates and DCON rates...");
overnight_indexed_swap_test::testBootstrap(true, RateAveraging::Compound);
}
void OvernightIndexedSwapTest::testBootstrapWithTelescopicDatesAndArithmeticAverage() {
BOOST_TEST_MESSAGE(
"Testing Eonia-swap curve building with telescopic value dates and AAON rates...");
// Given that we are using an approximation that omits
// the required convexity correction, a lower tolerance
// is needed.
overnight_indexed_swap_test::testBootstrap(true, RateAveraging::Simple, 1.0e-5);
}
void OvernightIndexedSwapTest::testSeasonedSwaps() {
BOOST_TEST_MESSAGE("Testing seasoned Eonia-swap calculation...");
using namespace overnight_indexed_swap_test;
CommonVars vars;
Period lengths[] = { 1*Years, 2*Years, 5*Years, 10*Years, 20*Years };
Spread spreads[] = { -0.001, -0.01, 0.0, 0.01, 0.001 };
Date effectiveDate = Date(2, February, 2009);
vars.eoniaIndex->addFixing(Date(2,February,2009), 0.0010); // fake fixing values
vars.eoniaIndex->addFixing(Date(3,February,2009), 0.0011);
vars.eoniaIndex->addFixing(Date(4,February,2009), 0.0012);
vars.eoniaIndex->addFixing(Date(5,February,2009), 0.0013);
for (auto& length : lengths) {
for (double spread : spreads) {
ext::shared_ptr<OvernightIndexedSwap> swap =
vars.makeSwap(length, 0.0, spread, false, effectiveDate);
ext::shared_ptr<OvernightIndexedSwap> swap2 =
vars.makeSwap(length, 0.0, spread, true, effectiveDate);
if (std::fabs(swap->NPV() - swap2->NPV()) > 1.0e-10) {
BOOST_ERROR("swap npv is different:\n"
<< std::setprecision(2) << " length: " << length << " \n"
<< " floating spread: " << io::rate(spread) << "\n"
<< " swap value (non telescopic value dates): " << swap->NPV()
<< "\n swap value (telescopic value dates ): " << swap2->NPV());
}
}
}
}
void OvernightIndexedSwapTest::testBootstrapRegression() {
BOOST_TEST_MESSAGE("Testing 1.16 regression with OIS bootstrap...");
using namespace overnight_indexed_swap_test;
SavedSettings backup;
Datum data[] = {
{ 0, 1, Days, 0.0066 },
{ 2, 1, Weeks, 0.006445 },
{ 2, 2, Weeks, 0.006455 },
{ 2, 3, Weeks, 0.00645 },
{ 2, 1, Months, 0.00675 },
{ 2, 2, Months, 0.007 },
{ 2, 3, Months, 0.00724 },
{ 2, 4, Months, 0.007533 },
{ 2, 5, Months, 0.00785 },
{ 2, 6, Months, 0.00814 },
{ 2, 9, Months, 0.00889 },
{ 2, 1, Years, 0.00967 },
{ 2, 2, Years, 0.01221 },
{ 2, 3, Years, 0.01413 },
{ 2, 4, Years, 0.01555 },
{ 2, 5, Years, 0.01672 },
{ 2, 10, Years, 0.02005 },
{ 2, 12, Years, 0.0208 },
{ 2, 15, Years, 0.02152 },
{ 2, 20, Years, 0.02215 },
{ 2, 25, Years, 0.02233 },
{ 2, 30, Years, 0.02234 },
{ 2, 40, Years, 0.02233 }
};
Settings::instance().evaluationDate() = Date(21, February, 2017);
std::vector<ext::shared_ptr<RateHelper> > helpers;
ext::shared_ptr<FedFunds> index(new FedFunds);
helpers.push_back(
ext::make_shared<DepositRateHelper>(data[0].rate,
Period(data[0].n, data[0].unit),
index->fixingDays(),
index->fixingCalendar(),
index->businessDayConvention(),
index->endOfMonth(),
index->dayCounter()));
for (Size i=1; i<LENGTH(data); ++i) {
helpers.push_back(
ext::shared_ptr<RateHelper>(
new OISRateHelper(data[i].settlementDays,
Period(data[i].n, data[i].unit),
Handle<Quote>(ext::make_shared<SimpleQuote>(data[i].rate)),
index,
Handle<YieldTermStructure>(),
false, 2,
Following, Annual, Calendar(), 0*Days, 0.0,
// this bootstrap fails with the default LastRelevantDate choice
Pillar::MaturityDate)));
}
PiecewiseYieldCurve<Discount,LogCubic> curve(0, UnitedStates(UnitedStates::GovernmentBond),
helpers, Actual365Fixed(), MonotonicLogCubic());
BOOST_CHECK_NO_THROW(curve.discount(1.0));
}
test_suite* OvernightIndexedSwapTest::suite() {
auto* suite = BOOST_TEST_SUITE("Overnight-indexed swap tests");
suite->add(QUANTLIB_TEST_CASE(&OvernightIndexedSwapTest::testFairRate));
suite->add(QUANTLIB_TEST_CASE(&OvernightIndexedSwapTest::testFairSpread));
suite->add(QUANTLIB_TEST_CASE(&OvernightIndexedSwapTest::testCachedValue));
suite->add(QUANTLIB_TEST_CASE(&OvernightIndexedSwapTest::testBootstrap));
suite->add(QUANTLIB_TEST_CASE(&OvernightIndexedSwapTest::testBootstrapWithArithmeticAverage));
suite->add(QUANTLIB_TEST_CASE(
&OvernightIndexedSwapTest::testBootstrapWithTelescopicDates));
suite->add(QUANTLIB_TEST_CASE(
&OvernightIndexedSwapTest::testBootstrapWithTelescopicDatesAndArithmeticAverage));
suite->add(QUANTLIB_TEST_CASE(&OvernightIndexedSwapTest::testSeasonedSwaps));
suite->add(QUANTLIB_TEST_CASE(&OvernightIndexedSwapTest::testBootstrapRegression));
return suite;
}