Sankt Gallen, Univ., Diss., 2003.

Modelos bastante utilizados atualmente no apreçamento de derivativos de taxas de juros realizam, muitas vezes, premissas excessivamente restritivas com relação à volatilidade da série do ativo objeto. O método de Black and Scholes e o de Vasicek, por exemplo, consideram a variância da série como constante no tempo e entre as diferentes maturidades, suposição que pode não ser a mais adequada para todos os casos. Assim, entre as técnicas alternativas de modelagem da volatilidade que vêm sendo estudadas, destacam-se as regressões por kernel. Discutimos neste trabalho a modelagem não paramétrica por meio da referida técnica e posterior apreçamento das opções em um modelo HJM Gaussiano. Analisamos diferentes especificações possíveis para a estimação não paramétrica da função de volatilidade através de simulações de Monte Carlo para o apreçamento de opções sobre títulos zero cupom, e realizamos um estudo empírico utilizando a metodologia proposta para o apreçamento de opções sobre IDI no mercado brasileiro. Um dos principais resultados encontrados é o bom ajuste da metodologia proposta no apreçamento de opções sobre títulos zero cupom. / Many models which have been recently used for derivatives pricing make restrictive assumptions about the volatility of the underlying object. Black-Scholes and Vasicek models, for instance, consider the volatility of the series as constant throughout time and maturity, an assumption that might not be the most appropriate for all cases. In this context, kernel regressions are important technics which have been researched recently. We discuss in this framework nonparametric modeling using the aforementioned technic and posterior option pricing using a Gaussian HJM model. We analyze different specifications for the nonparametric estimation of the volatility function using Monte Carlo simulations for the pricing of options on zero coupon bonds and conduct an empirical study using the proposed methodology for the pricing of options on the Interbank Deposit Index (IDI) in the Brazilian market. One of our main results is the good adjustment of the proposed methodology on the pricing of options on zero coupon bonds.

Modelos bastante utilizados atualmente no apreçamento de derivativos de taxas de juros realizam, muitas vezes, premissas excessivamente restritivas com relação à volatilidade da série do ativo objeto. O método de Black and Scholes e o de Vasicek, por exemplo, consideram a variância da série como constante no tempo e entre as diferentes maturidades, suposição que pode não ser a mais adequada para todos os casos. Assim, entre as técnicas alternativas de modelagem da volatilidade que vêm sendo estudadas, destacam-se as regressões por kernel. Discutimos neste trabalho a modelagem não paramétrica por meio da referida técnica e posterior apreçamento das opções em um modelo HJM Gaussiano. Analisamos diferentes especificações possíveis para a estimação não paramétrica da função de volatilidade através de simulações de Monte Carlo para o apreçamento de opções sobre títulos zero cupom, e realizamos um estudo empírico utilizando a metodologia proposta para o apreçamento de opções sobre IDI no mercado brasileiro. Um dos principais resultados encontrados é o bom ajuste da metodologia proposta no apreçamento de opções sobre títulos zero cupom. / Many models which have been recently used for derivatives pricing make restrictive assumptions about the volatility of the underlying object. Black-Scholes and Vasicek models, for instance, consider the volatility of the series as constant throughout time and maturity, an assumption that might not be the most appropriate for all cases. In this context, kernel regressions are important technics which have been researched recently. We discuss in this framework nonparametric modeling using the aforementioned technic and posterior option pricing using a Gaussian HJM model. We analyze different specifications for the nonparametric estimation of the volatility function using Monte Carlo simulations for the pricing of options on zero coupon bonds and conduct an empirical study using the proposed methodology for the pricing of options on the Interbank Deposit Index (IDI) in the Brazilian market. One of our main results is the good adjustment of the proposed methodology on the pricing of options on zero coupon bonds.

我們使用一個新方法來評價美式或歐式的或有求償權，其受到本地利率和權益價值的影響。我們使用標的資產的遠期價格的樹狀圖，進而對或有求償權作定價。其中我們評價了美式與歐式的股票選擇權，以及利率期貨和利率期貨選擇權。 / We introduce a methodology for pricing American or European style contingent claims, influenced by domestic interest rates, and equity prices. Instead of using trees of short-term interest rate, bond price or forward interest rate, this tree method will use the forward prices of underlying assets to derive implied binomial spot-price tree and in turn price long term American or European options, and interest rate futures and interest rate futures options.

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

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.

Protection against inflation is an essential part of the today&#039 / 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.

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.

Inflation indexed instruments are designed to help protect investors against the changes in the general level of prices. So, they are frequently preferred by investors and they have become increasingly developing part of the market. In this study, firstly, the HJM model and foreign currency analogy used to price of inflation indexed instruments are investigated. Then, the HJM model is extended with finite number of Poisson process. Finally, under the extended HJM model, a pricing derivation of inflation indexed swaps, which are the most liquid ones among inflation indexed instruments in the market, is given.

In this thesis we use techniques from white noise analysis to study solutions of semilinear stochastic differential equations in a Hilbert space H: {dX[subscript]t = (AX[subscript]t + F(t,X[subscript]t)) dt + ơ(t,X[subscript]t) δB[subscript]t, t∈ (0,T], X[subscript]0 = ξ, where A is a generator of either a C[subscript]0-semigroup or an n-times integrated semigroup, and B is a cylindrical Wiener process. We then consider applications to forward interest rate models, such as in the Heath-Jarrow-Morton framework. We also reformulate a phenomenological model of the forward rate. / Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Science, 2009