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On Forward Interest Rate Models: Via Random Fields And Markov Jump ProcessesAltay, Suhan 01 May 2007 (has links) (PDF)
The essence of the interest rate modeling by using Heath-Jarrow-Morton framework is to find the drift condition of the instantaneous forward rate dynamics so that the entire term structure is arbitrage free. In this study, instantaneous forward interest rates are modeled using random fields and Markov Jump processes and the drift conditions of the forward rate dynamics are given. Moreover, the methodology presented in this study is extended to certain financial settings and instruments such as multi-country interest rate models, term structure of defaultable bond prices and forward measures. Also a general framework for bond prices via nuclear space valued semi-martingales is introduced.
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A Market Model For Pricing Inflation Indexed Bonds With Jumps IncorporationGuney, Ibrahim Ethem 01 August 2008 (has links) (PDF)
Protection against inflation is an essential part of the today' / s financial markets, particularly in high-inflation economies. Hence, nowadays inflation indexed instruments are being increasingly popular in the world financial markets. In this
thesis, we focus on pricing of the inflation-indexed bonds which are the unique inflation-indexed instruments traded in the Turkish bond market. Firstly, we review the Jarrow-Yildirim model which deals with pricing of the inflation-indexed instruments within the HJM framework. Then, we propose a pricing model that is an extension of the Jarrow-Yildirim model. The model allows instantaneous forward rates, inflation index and bond prices to be driven by both a standard
Brownian motion and a finite number of Poisson processes. A closed-form pricing formula for an European call option on the inflation index is also derived.
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Pricing Inflation-indexed Swaps And Swaptions Using An Hjm ModelTemiz, Zeynep Canan 01 December 2009 (has links) (PDF)
Inflation-indexed instruments provide a real return and protect investors from the erosion of
the purchasing power of money. Hence, inflation-indexed markets grow very fast day by day.
In this thesis, we focus on pricing of the inflation-indexed swaps and swaptions which are the
most liquid derivative products traded in the inflation-indexed markets. Firstly, we review the
Hull-White extended Vasicek model in the HJM framework. Then, we use this model to price
inflation-indexed swaps. Also, pricing of inflation-indexed swaptions is given using Black&rsquo / s
market model.
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Implied volatility with HJM–type Stochastic Volatility modelCap, Thi Diu January 2021 (has links)
In this thesis, we propose a new and simple approach of extending the single-factor Heston stochastic volatility model to a more flexible one in solving option pricing problems. In this approach, the volatility process for the underlying asset dynamics depends on the time to maturity of the option. As this idea is inspired by the Heath-Jarrow-Morton framework which models the evolution of the full dynamics of forward rate curves for various maturities, we name this approach as the HJM-type stochastic volatility (HJM-SV) model. We conduct an empirical analysis by calibrating this model to real-market option data for underlying assets including an equity (ABB stock) and a market index (EURO STOXX 50), for two separated time spans from Jan 2017 to Dec 2017 (before the COVID-19 pandemic) and from Nov 2019 to Nov 2020 (after the start of COVID-19 pandemic). We investigate the optimal way of dividing the set of option maturities into three classes, namely, the short-maturity, middle-maturity, and long-maturity classes. We calibrate our HJM-SV model to the data in the following way, for each class a single-factor Heston stochastic volatility model is calibrated to the corresponding market data. We address the question that how well the new HJM-SV model captures the feature of implied volatility surface given by the market data.
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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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Pokročilé metody kalibrace modelů úrokových sazeb / Advanced methods of interest rate models calibrationHolotňáková, Dominika January 2013 (has links)
This thesis is focused on the study of advanced methods of interest rate mo- dels calibration. The theoretical part provides introduction to basic terminology of financial mathematics, financial, concretely interest rate derivatives. It presents interest rate models, it is mainly aimed at HJM approach and describes in detail the Libor market model, then introduces the use of Bayesian principle in calcula- ting the probability of MCMC methods. At the end of this section the methods of calibration of volatility to market data are described. The last chapter consists of the practical application of different methods of calibration Libor market model and consequently pricing od interest rate swaption. The introduction describes procedure of arrangement of input data and process of pricing of interest rate derivatives. It is consequently used for the valuation of derivative contract accor- ding to mentioned methods. 1
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