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Modelling the short term interest with stochastic differential equation in continuous time: linear versus non-linear modeThaba, Lethabo Jane 10 June 2014 (has links)
M.Com. (Financial Economics) / Recently, there has been a growth in the bond market. This growth has brought with it an ever-increasing volume and range of interest rate depended derivative products known as interest rate derivatives. Amongst the variables used in pricing these derivative products is the short-term interest rate. A numbers of short-term interest rate models that are used to fit the short-term interest rate exist. Therefore, understanding the features characterised by various short-term interest rate models, and determining the best fitting models is crucial as this variable is fundamental in pricing interest rate derivatives, which further determine the decision making of economic agents. This dissertation examines various short-term interest rate models in continuous time in order to determine which model best fits the South African short-term interest rates. Both the linear and nonlinear short-term interest rate models were estimated. The methodology adopted in estimating the models was parametric approach using Quasi Maximum Likelihood Estimation (QMLE). The findings indicate that nonlinear models seem to fit the South African short-term interest rate data better than the linear models
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Forecasting interest rates using pattern recognition techniquesPearson, John S. 01 January 1984 (has links)
Much depends on the future course of interest rates. The decisions of families to make major purchases, the willingness of businesses to expand and invest, the rise and fall of the economy and stock market, the ability of lesser developed countries to repay their debts, the tenure of presidents and prime ministers--all of these may turn on whether interest rates increase or decrease in the months ahead. Several decision functions developed in the dissertation permit the direction of change of interest rates on long-term U. S. government bonds to be forecast correctly about 60% of the time. When the different models are combined, effectiveness is increased, and when the forecasts are dollar-weighted, performance in excess of 70% is possible. The results are evaluated in comparison with a Bayesian forecasting model and a 10,000-event Monte Carlo simulation of a random decision rule. The forecasting ability of the models is statistically significant at the 99% level of confidence. The dissertation reports on one of the first application of powerful techniques recently developed in cybernetics and engineering to forecasting the direction of change in interest rates. Two forecasting algorithms, called linear decision functions or linear classifiers, are derived using the principles of pattern recognition. Because they are recursively updated, both algorithms operate dynamically and adapt their performance to changes in the economic environment. One classifier, a modification of the widely used least-mean-squared-error algorithm, is adapted to permit monthly revision and to allow larger movements of interest rates to have greater weight in future decisions. The second algorithm permits refinement of the parameter estimates generated by the first. These formal, mathematical constructs are then supplied with financial variables--leading indicators of inflation and investment activity--to permit unconditional, ex-ante forecasts of the direction of change of interest rates on long-term government bonds over a one-month time horizon throughout the period 1969-82. The results should be of interest to investment managers, speculators, corporate treasurers, policymakers, economists and forecasters.
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Building Interest Rate Curves and SABR Model CalibrationMbongo Nkounga, Jeffrey Ted Johnattan 03 1900 (has links)
Thesis (MSc)--Stellenbosch University / ENGLISH ABSTRACT : In this thesis, we first review the traditional pre-credit crunch approach that
considers a single curve to consistently price all instruments. We review the
theoretical pricing framework and introduce pricing formulas for plain vanilla
interest rate derivatives. We then review the curve construction methodologies
(bootstrapping and global methods) to build an interest rate curve using
the instruments described previously as inputs. Second, we extend this work
in the modern post-credit framework. Third, we review the calibration of the
SABR model. Finally we present applications that use interest rate curves and
SABR model: stripping implied volatilities, transforming the market observed
smile (given quotes for standard tenors) to non-standard tenors (or inversely)
and calibrating the market volatility smile coherently with the new market
evidences. / AFRIKAANSE OPSOMMING : Geen Afrikaanse opsomming geskikbaar nie
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Testing for the uncovered interest parity hypothesis in South AfricaMachobani, Dennis January 2016 (has links)
Research Report: BUSA7167 (MM Finance and Investment Management).
Submitted in Partial Fulfillment of the Requirements for the
(Master of Management in Finance and Investments).
Submitted on 06th June 2016 / The findings of the research have implications on the efficiency of the South African exchange rate market, and by extension, the efficiency of similar emerging foreign exchange markets. The study used Ordinary Least Square Approach and Johansen cointegration. Despite their theoretical appeal, and in line with a dozen of related past literature, the findings of the research generally favour the rejection UIP, PPP and IFE. The findings have implications on some regulatory measures that can be undertaken by the financial authority to improve the efficiency of the foreign exchange market. While there have been extensive studies on uncovered interest parity (UIP), purchasing power parity(PPP), and the international Fisher effect(IFE), research has scarcely tested these hypotheses in the context of emerging markets. This study attempts to bridge the existing gap by testing the three related parity condition for South Africa. / MT2016
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Long run fisher open hypothesis: an empirical study in Asian countries.January 1990 (has links)
by O'Yang Wiley. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 44-45. / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iv / ACKNOWLEDGEMENTS --- p.v / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- TIME SERIES AND UNIT ROOT --- p.5 / Definitions --- p.5 / Difference Between 1(0) and 1(1) Processes --- p.8 / Chapter III. --- FORMULATION OF LONG RUN FISHER OPEN HYPOTHESIS … --- p.10 / Chapter IV. --- UNIT ROOT TESTS --- p.14 / Dickey and Fuller Test --- p.14 / Augmented Dickey and Fuller Test --- p.16 / Phillips and Perron Test --- p.16 / Finite Sample Properties of Regression / Unit Root Tests --- p.18 / Chapter V. --- UNIT ROOT TEST RESULTS --- p.20 / Tentative ARIMA Model for the Interest Rate Series --- p.21 / Hong Kong --- p.21 / Singapore --- p.22 / Malaysia --- p.22 / Philippines and Japan --- p.23 / Tentative ARIMA Model for the Interest Rate Differentials --- p.23 / Hong Kong-Malaysia --- p.23 / Hong Kong-Singapore --- p.24 / Singapore-Malaysia --- p.24 / Others --- p.24 / Unit Root Test Results --- p.24 / Discussions and Findings --- p.36 / Chapter VI. --- CONCLUSIONS AND AREAS OF FURTHER RESEARCH --- p.40 / APPENDIX --- p.43 / BIBLIOGRAPHY --- p.44
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An empirical analysis of uncovered interest parity at short and long horizons.January 2001 (has links)
Zhang Haiyan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 48-50). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- An Introduction to the Uncovered Interest Parity (UIP) and previous works on UIP --- p.6 / Chapter 2.2 --- Previous empirical works applying Band Spectrum Regression(BSR) --- p.15 / Chapter 3 --- Basic Band Spectral Regression (BSR) Techniques --- p.20 / Chapter 3.1 --- BSR Based on the complex Fourier transform --- p.20 / Chapter 3.2 --- BSR based on the real-valued Fourier transform --- p.24 / Chapter 3.3 --- Testing for parameter stability in the frequency domain --- p.26 / Chapter 4 --- Data and Standard Time Series Analysis in the Time Domain --- p.29 / Chapter 5 --- Analyze the UIP relation in the frequency domain --- p.33 / Chapter 5.1 --- An overview of the UIP relation across frequency --- p.33 / Chapter 5.2 --- Testing parameter stability across different time horizons --- p.37 / Chapter 6 --- Test of UIP with the forward premium --- p.42 / Chapter 7 --- Conclusion --- p.45
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An analysis of the Libor and Swap market models for pricing interest-rate derivativesMutengwa, Tafadzwa Isaac January 2012 (has links)
This thesis focuses on the non-arbitrage (fair) pricing of interest rate derivatives, in particular caplets and swaptions using the LIBOR market model (LMM) developed by Brace, Gatarek, and Musiela (1997) and Swap market model (SMM) developed Jamshidan (1997), respectively. Today, in most financial markets, interest rate derivatives are priced using the renowned Black-Scholes formula developed by Black and Scholes (1973). We present new pricing models for caplets and swaptions, which can be implemented in the financial market other than the Black-Scholes model. We theoretically construct these "new market models" and then test their practical aspects. We show that the dynamics of the LMM imply a pricing formula for caplets that has the same structure as the Black-Scholes pricing formula for a caplet that is used by market practitioners. For the SMM we also theoretically construct an arbitrage-free interest rate model that implies a pricing formula for swaptions that has the same structure as the Black-Scholes pricing formula for swaptions. We empirically compare the pricing performance of the LMM against the Black-Scholes for pricing caplets using Monte Carlo methods.
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A no-arbitrage macro finance approach to the term structure of interest ratesThafeni, Phumza 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: This work analysis the main macro-finance models of the term structure of
interest rates that determines the joint dynamics of the term structure and the
macroeconomic fundamentals under no-arbitrage approach. There has been a
long search during the past decades of trying to study the relationship between
the term structure of interest rates and the economy, to the extent that much
of recent research has combined elements of finance, monetary economics, and
the macroeconomics to analyse the term structure.
The central interest of the thesis is based on two important notions. Firstly,
it is picking up from the important work of Ang and Piazzesi (2003) model
who suggested a joint macro- finance strategy in a discrete time affine setting,
by also imposing the classical Taylor (1993) rule to determine the association
between yields and macroeconomic variables through monetary policy. There
is a strong intuition from the Taylor rule literature that suggests that such
macroeconomic variables as in inflation and real activity should matter for the
interest rate, which is the monetary policy instrument. Since from this important
framework, no-arbitrage macro-finance approach to the term structure of
interest rates has become an active field of cross-disciplinary research between
financial economics and macroeconomics.
Secondly, the importance of forecasting the yield curve using the variations
on the Nelson and Siegel (1987) exponential components framework to capture
the dynamics of the entire yield curve into three dimensional parameters evolving
dynamically. Nelson-Siegel approach is a convenient and parsimonious
approximation method which has been trusted to work best for fitting and
forecasting the yield curve. The work that has caught quite much of interest
under this framework is the generalized arbitrage-free Nelson-Siegel macro-
nance term structure model with macroeconomic fundamentals, (Li et al.
(2012)), that characterises the joint dynamic interaction between yields and
the macroeconomy and the dynamic relationship between bond risk-premia
and the economy. According to Li et al. (2012), risk-premia is found to be
closely linked to macroeconomic activities and its variations can be analysed.
The approach improves the estimation and the challenges on identication of
risk parameters that has been faced in recent macro-finance literature. / AFRIKAANSE OPSOMMING: Hierdie werk ontleed die makro- nansiese modelle van die term struktuur van
rentekoers pryse wat die gesamentlike dinamika bepaal van die term struktuur
en die makroekonomiese fundamentele faktore in 'n geen arbitrage wêreld.
Daar was 'n lang gesoek in afgelope dekades gewees wat probeer om die
verhouding tussen die term struktuur van rentekoerse en die ekonomie te
bestudeer, tot die gevolg dat baie onlangse navorsing elemente van nansies,
monetêre ekonomie en die makroekonomie gekombineer het om die term struktuur
te analiseer.
Die sentrale belang van hierdie proefskrif is gebaseer op twee belangrike
begrippe. Eerstens, dit tel op by die belangrike werk van die Ang and Piazzesi
(2003) model wat 'n gesamentlike makro- nansiering strategie voorstel in 'n
diskrete tyd a ene ligging, deur ook die klassieke Taylor (1993) reël om assosiasie
te bepaal tussen opbrengste en makroekonomiese veranderlikes deur
middel van monetêre beleid te imposeer. Daar is 'n sterk aanvoeling van die
Taylor reël literatuur wat daarop dui dat sodanige makroekonomiese veranderlikes
soos in asie en die werklike aktiwiteit moet saak maak vir die rentekoers,
wat die monetêre beleid instrument is. Sedert hierdie belangrike raamwerk, het
geen-arbitrage makro- nansies benadering tot term struktuur van rentekoerse
'n aktiewe gebied van kruis-dissiplinêre navorsing tussen nansiële ekonomie
en makroekonomie geword.
Tweedens, die belangrikheid van voorspelling van opbrengskromme met
behulp van variasies op die Nelson and Siegel (1987) eksponensiële komponente
raamwerk om dinamika van die hele opbrengskromme te vang in drie
dimensionele parameters wat dinamies ontwikkel. Die Nelson-Siegel benadering
is 'n gerie ike en spaarsamige benaderingsmetode wat reeds vertrou word
om die beste pas te bewerkstellig en voorspelling van die opbrengskromme.
Die werk wat nogal baie belangstelling ontvang het onder hierdie raamwerk
is die algemene arbitrage-vrye Nelson-Siegel makro- nansiele term struktuur
model met makroekonomiese grondbeginsels, (Li et al. (2012)), wat kenmerkend
van die gesamentlike dinamiese interaksie tussen die opbrengs en die
makroekonomie en die dinamiese verhouding tussen band risiko-premies en
die ekonomie is. Volgens Li et al. (2012), word risiko-premies bevind om nou gekoppel te wees aan makroekonomiese aktiwiteite en wat se variasies ontleed
kan word. Die benadering verbeter die skatting en die uitdagings van identi-
sering van risiko parameters wat teegekom is in die afgelope makro- nansiese literatuur.
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Heath–Jarrow–Morton models with jumpsAlfeus, Mesias 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT : The standard-Heath–Jarrow–Morton (HJM) framework is well-known for its application to
pricing and hedging interest rate derivatives. This study implemented the extended HJM
framework introduced by Eberlein and Raible (1999), in which a Brownian motion (BM) is
replaced by a wide class of processes with jumps. In particular, the HJM driven by the generalised
hyperbolic processes was studied. This approach was motivated by empirical evidence
proving that models driven by a Brownian motion have several shortcomings, such as inability
to incorporate jumps and leptokurticity into the price dynamics. Non-homogeneous Lévy
processes and the change of measure techniques necessary for simplification and derivation of
pricing formulae were also investigated. For robustness in numerical valuation, several transform
methods were investigated and compared in terms of speed and accuracy. The models
were calibrated to liquid South African data (ATM) interest rate caps using two methods of
optimisation, namely the simulated annealing and secant-Levenberg–Marquardt methods.
Two numerical valuation approaches had been implemented in this study, the COS method
and the fractional fast Fourier transform (FrFT), and were compared to the existing methods
in the context. Our numerical results showed that these two methods are quite efficient and
very competitive. We have chose the COS method for calibration due to its rapidly speed and
we have suggested a suitable approach for truncating the integration range to address the
problems it has with short-maturity options. Our calibration results provided a nearly perfect
fit, such that it was difficult to decide which model has a better fit to the current market state.
Finally, all the implementations were done in MATLAB and the codes included in appendices. / AFRIKAANSE OPSOMMING : Die standaard-Heath–Jarrow–Morton-raamwerk (kortom die HJM-raamwerk) is daarvoor bekend
dat dit op die prysbepaling en verskansing van afgeleide finansiële instrumente vir rentekoerse
toegepas kan word. Hierdie studie het die uitgebreide HJM-raamwerk geïmplementeer
wat deur Eberlein en Raible (1999) bekendgestel is en waarin ’n Brown-beweging deur ’n
breë klas prosesse met spronge vervang word. In die besonder is die HJM wat deur veralgemeende
hiperboliese prosesse gedryf word ondersoek. Hierdie benadering is gemotiveer
deur empiriese bewyse dat modelle wat deur ’n Brown-beweging gedryf word verskeie tekortkominge
het, soos die onvermoë om spronge en leptokurtose in prysdinamika te inkorporeer.
Nie-homogene Lévy-prosesse en die maatveranderingstegnieke wat vir die vereenvoudiging en
afleiding van prysbepalingsformules nodig is, is ook ondersoek. Vir robuustheid in numeriese
waardasie is verskeie transformmetodes ondersoek en ten opsigte van spoed en akkuraatheid
vergelyk. Die modelle is vir likiede Suid-Afrikaanse data vir boperke van rentekoerse sonder
intrinsieke waarde gekalibreer deur twee optimiseringsmetodes te gebruik, naamlik die gesimuleerde
uitgloeimetode en die sekans-Levenberg–Marquardt-metode.
Twee benaderings tot numeriese waardasie is in hierdie studie gebruik, naamlik die kosinusmetode
en die fraksionele vinnige Fourier-transform, en met bestaande metodes in die konteks
vergelyk. Die numeriese resultate het getoon dat hierdie twee metodes redelik doeltreffend
en uiters mededingend is. Ons het op grond van die motiveringspoed van die kosinus-metode
daardie metode vir kalibrering gekies en ’n geskikte benadering tot die trunkering van die
integrasiereeks voorgestel ten einde die probleem ten opsigte van opsies met kort uitkeringstermyne
op te los. Die kalibreringsresultate het ’n byna perfekte passing gelewer, sodat dit
moeilik was om te besluit watter model die huidige marksituasie die beste pas. Ten slotte is
alle implementerings in MATLAB gedoen en die kodes in bylaes ingesluit.
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Assessing the ability of the interest rates term structure to forecast recessions in South Africa: a comparison of three binary-type models07 October 2014 (has links)
M.Com. (Financial Economics) / The use of the yield curve spread in forecasting future recessions has become popular as it is a simple tool to use, due to the positive relationship between the yield curve spread and economic activity. The inversion or flattening of the yield curve spread usually signals a future recession. This has been the subject of several studies both internationally and in South Africa. This research provides an analysis of the yield curve spread’s ability to accurately forecast future recessions in South Africa through the use of three probit models. Furthermore, the yield curve spread’s ability to estimate is compared to that of share prices, using the JSE All Share Index. This research extends on studies by Khomo and Aziakpono (2006) and Clay and Keeton (2011), who used the static and dynamic probit models to forecast recessions in South Africa. In addition to these models, this research also makes use of the business cycle conditionally independent probit model for estimation. The findings suggest that share prices improve the yield curve spread’s ability to forecast recessions when estimating using the static probit model; however when comparing the results between the financial variables, the yield curve spread continues to produce the best forecast of recessions in South Africa. These results support those of Khomo and Aziakpono (2006) and Clay and Keeton (2011). Of the three probit models, the dynamic probit model estimate using the yield curve spread produced the most accurate forecast of recessions one quarter ahead. Therefore, the yield curve spread continues to provide the most accurate forecast of recessions in South Africa.
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