Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The interest rates market has changed dramatically since the 2007 credit
crunch with the explosion of basis spreads between rates of different tenors
and currencies. Consequently, the classical replication of FRA rates with spot
LIBOR rates is no longer valid. Moreover, the 2007 credit crunch yields a separation
between the curve used for discounting and the forward or projection
curves that estimate all future cash-fl ows. Another impact of the credit crunch
in risk management is that market participants have started to give more importance
to the difference between collateralized and uncollateralized trades.
Nowadays, the wide spread use of collateral, especially in swap contracts, has
made the overnight index swap (OIS) rate the appropriate benchmark for
discounting collateralized trades. Inspired by the seminal works of Mercurio
(2010a,b), Kijima et al. (2008), Fujii et al. (2011), Bianchetti (2010b), with
the contributions of other authors, and motivated by the evolution of the interest
rates market and models, this thesis examines a new framework that uses
multiple-curves to value interest rate derivatives which is compatible with the
current market practice.
Firstly, we discuss the roots of the 2007 credit crunch and its serious consequences
for pricing interest rate derivatives. We underscore the necessity of a
multiple-curve pricing framework for interest rate derivatives. This is followed
by a discussion on the importance of collateralization and OIS discounting in
pricing Over-The-Counter (OTC) derivatives. The central part of the thesis
discusses the modern theoretical framework and the practical implementation of the multiple curve pricing method. We present a bootstrapping algorithm
used to construct and fit the multiple-yield curves to market prices of plainvanilla
contracts.
Secondly, starting with the single-currency economy, the extended version
of the LIBOR Market Model, developed by Mercurio (2010a,b), which proposes
a joint model of FRA rates, implied forward rates and their corresponding
spread is investigated. Analogously, the extended version of short-rate model
in a multiple-curve setup and in the presence of basis spread, proposed by
Kijima et al. (2008), is presented and discussed. This work provides a detailed
analysis of these extensions and the corresponding closed formulae for liquid
products such as caps and swaptions. Finally, in the multiple-currencies case,
the HJM model with stochastic basis spreads, introduced by Fujii et al. (2011),
consistent with the foreign exchange and cross-currency swaps markets that
includes the effect of collateralization is examined thoroughly. / AFRIKAANSE OPSOMMING: Die rentekoers mark het dramaties verander sedert die 2007 krediet krisis met
'n ontplo ng van basisverspreidings tussen koerse van verskillende looptye
("tenor") en geldeenhede. As gevolg, is die klassieke replikasie van FRA koerse
met LIBOR sigkoerse nie langer geldig nie. Verder het die 2007 kredietkrisis
'n skeiding veroorsaak tussen die kromme wat gebruik word vir diskontering
en die voorwaardse of vooruitskattings krommes wat toekomstige kontantvloei
voorspel. 'n Verdere impak van die kredietkrisis in risikobestuur is dat mark
deelnemers begin het om meer klem te lê op verskille tussen aangevulde en
onaangevulde handel. Deesdae, met die algemene gebruik van kollaterale sekuriteit, veral in ruiltransaksiekontrakte,
is die oornagse indeks ruiltransaksie (overnight index swap, OIS) koers die geskikte maatstaf om aangevulde handel te diskonteer. Geïnspireer
deur die gedagteryke werk van Mercurio (2010a,b), Kijima et al. (2008),
Fujii et al. (2011), Bianchetti (2010b), met bydrae van menige outeurs, en
gemotiveer deur die evolusie van die rentekoers markte en modelle, ondersoek
hierdie tesis 'n nuwe raamwerk wat multikrommes gebruik om rentekoers
afgeleide effekte te waardeer wat versoenbaar is met die lopende mark praktyk.
Eerstens, bespreek ons die oorsake van die 2007 kredietkrisis en die ernstige
nagevolge vir die waardering van rentekoers afgeleide effekte. Ons beklemtoon
die noodsaaklikheid van 'n multikromme waarderings raamwerk vir rentekoers
afgeleide effekte. Dit word gevolg deur 'n bespreking oor die belangrikheid
van aanvulling en OIS diskontering in die waardering van oor-die-toonbank (over-the-counter, OTC) effekte. Die teoretiese raamwerk en die praktiese
implimentering van die multikromme waarderings metode word bespreek. Ons
stel ook ten toon 'n skoenlus ("bootstrapping") algoritme wat gebruik kan word
om meervoudige opbrengs krommes saam te stel en die dan te pas op mark
pryse van vanielje kontrakte.
Tweedens, met 'n enkel geldeenheid ekonomie as beginpunt, word die uitgebreide
weergawe van die LIBOR Mark Model (ontwikkel deur Mercurio
(2010a,b), wat 'n gesamentlike model van FRA koerse voorstel), geïmpliseerde
termyn koerse en hul ooreenstemmende verspreiding bestudeer. Ooreenkomstig
word die uitgebreide weergawe van die kort koers model in 'n multikromme
opset en in die aanwesigheid van basisspreiding (voorgestel deur Kijima
et al. (2008)) uiteengesit en bespreek. Hierdie werk verskaf 'n uitvoerige
analise van hierdie uitbreidings en die ooreenstemmende geslote formules
vir vloeibare produkte soos perke en ruiltransaksie opsies. Ten slotte, in die
multi-geldeenheid geval, word die HJM model met stogastiese basisverspreiding
(voorgestel deur Fujii et al. (2011)), nie-strydig met buitelandse valuta en
kruisvaluta ruiltransaksie markte wat die effekte van aanvulling insluit word
deuglik bestudeer.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/20413 |
| Date | 03 1900 |
| Creators | Rahantamialisoa, Tahirivonizaka Fanirisoa Zazaravaka |
| Contributors | Ghomrasni, Raouf, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Rights | Stellenbosch University |
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