Unifying Gaussian Dynamic Term Structure Models from a Heath-Jarrow-Morton Perspective

In this paper, we show that most existing Gaussian dynamic term structure models (GDTSMs) can be nested as special cases under a unified Heath-Jarrow-Morton (HJM)-based framework of GDTSM construction. Our study provides not only a systematic way to examine the commonality of many seemingly distinct GDTSMs, but also a novel and convenient approach to constructing GDTSMs that are otherwise unavailable or intractable under the traditional approach. In our empirical study using the Euro area forward rates, we conduct a specification analysis based on this novel approach. The analysis reveals that the traditional models impose restrictive constraints limiting their flexibility in capturing key features of the correlations and volatilities of the forward rates

Multifactorial Heath-Jarrow-Morton model using principal component analysis

In this study, we propose an implementation of the multifactor Heath-Jarrow-Morton (HJM) interest rate model using an approach that integrates principal component analysis (PCA) and Monte Carlo simulation (MCS) techniques. By integrating PCA and MCS with the multifactor HJM model, we successfully capture the principal factors driving the evolution of short-term interest rates in the US market. Additionally, we provide a framework for deriving spot interest rates through parameter calibration and forward rate estimation. For this, we use daily data from the US yield curve from June 2017 to December 2019. The integration of PCA, MCS with multifactor HJM model in this study represents a robust and precise approach to characterizing interest rate dynamics and compared to previous approaches, this method provided greater accuracy and improved understanding of the factors influencing US Treasury Yield interest rates

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Characteristic functions in the Cheyette Interest Rate Model

We investigate the characteristic functions of multi-factor Cheyette Models and the application to the valuation of interest rate derivatives. The model dynamic can be classiffied as an affine-diffusion process implying an exponential structure of the characteristic function. The characteristic function is determined by a model specific system of ODEs, that can be solved explicitly for arbitrary Cheyette Models. The necessary transform inversion turns out to be numerically stable as a singularity can be removed. Thus the pricing methodology is reliable and we use it for the calibration of multi-factor Cheyette Models to caps. --Cheyette Model,Characteristic Function,Fourier Transform,Calibration of Multi-Factor Models

Essays on Finance and Risk

Tato dizertace obsahuje tři kapitoly, ve kterých jsou empiricky zkoumány klasické otázky bankovní rizika a finanční ekonomie. V první kapitole zkoumám jestli bankovní likvidita, kapitál a riziko jsou společně určeny v bankovním sektoru eurozóny. Ve druhé kapitole, spolu s Adamom Geršlem, Petrem Jakubíkem, Stevnem Ongena a José- Luis Peydró, zkoumáme roli měnových podmínek pro bankovní rizika v sektoru v ČR. Používame komplexní úvěrověho registru České národní banky. Třetí kapitola se vztahuje na mod- eloveho rizika a analyzuje výkonnost vybraného modelu vynosove krivky při oceňování úrokové swapy na polském trhu. Cox-Ingersoll-Ross navrhuje ze volatilita souvisi z ve- likosti úrokových sazeb. Ex-post Nelson-Siegel model ukazuje, že prurez výnosove křivky je velmi informativni pro budoucnost.Dorota Kowalczyk: Essays on Finance and Risk Abstract This dissertation consists of three chapters that empirically investigate questions of increasing relevance in the banking risk and financial economics literature. The first chapter studies bank risk in the context of its joint determination with bank liquidity and capital in the Eurozone. The second chapter examines the banks' appetite for risk using the comprehensive credit register of the Czech National Bank. Finally, the last chapter refers to model risk and analyzes the ability of the selected term structure models to value the interest rate swaps in the Polish market. The first chapter analyzes the coordination of bank risk, liquidity and capital in the presence of securitization. Its outcome contributes to the debate on the effectiveness of the banking regulations. My findings with regard to the simultaneity of capital and risk decisions are consistent with previous empirical studies. Incorporation of bank liquidity permits me to establish the presence of the coordination of risk and liquidity decisions. At the same time, I find no evidence of the direct joint determination of capital and liquidity. Finally, the first chapter partially confirms the theoretical implications of Repullo (2005). The second chapter, coauthored with Adam Geršl, Petr...CERGEFaculty of Social SciencesFakulta sociálních vě

A Type of HJM Based Affine Model: Theory and Empirical Evidence

In this paper a type of Heath, Jarrow and Morton (1992) (HJM) based affine model is derived theoretically. This type of affine model is obtained by applying Linear Realization Theory to construct Finite Dimensional Realizations (FDRs) of the Gaussian HJM model. The algorithms of constructing Standard Observable Canonical Realization and Jordan Canonical Realization are introduced sequentially. And it is shown that the commonly adopted FDR is actually Jordan Canonical Realization. The empirical results show that a two-factor model of this type provides great fit to the term structure of interest rates data. The resulting state variables have clear economic interpretations. And it is found that the short end of the term structure can be precisely considered as a “medium-run factor” which uniformly shifts the yield curve. This finding has an important implication for bond portfolios management, and also helps us better understand the interactions between macro-economy and term structure dynamics

THREE ESSAYS ON MORTGAGE BACKED SECURITIES: HEDGING INTEREST RATE AND CREDIT RISKS

This dissertation includes three essays on hedging the interest rate and credit risks of Mortgage-Backed Securities (MBS). Essay one addresses the problem of how to efficiently estimate interest rate sensitivity parameters of MBS. To do this in Monte Carlo simulation, we derive perturbation analysis (PA) gradient estimators in a general setting. Then we apply the Hull-White interest rate model and a common prepayment model to derive the corresponding specific PA estimators, assuming the shock of interest rate term structure takes the form of a trigonometric polynomial series. Numerical experiments comparing finite difference (FD) estimators with our PA estimators indicate that the PA estimators can provide better accuracy than FD estimators, while using much lower computational cost. Using the estimators, we analyze the impact of term structure shifts on various mortgage products. Based these analysis, we propose a new product to mitigate interest rate risk. Essay two addresses the problem of how to measure interest rate yield curve shift more realistically, and how to use these risk measures to hedge the interest rate risk of MBS. We use a Principal Components Analysis (PCA) approach to analyze historical interest rate data, and acquire the volatility factors we need in Heath-Jarrow-Morton interest rate model simulation. Then we propose a hedging algorithm to hedge MBS, based on PA gradient estimators derived upon these PCA factors. Our results show that the new hedging method can achieve much better hedging efficiency than traditional duration and convexity hedging. Essay three addresses the application a new regression method on credit spread data. Previous research has shown that variables in traditional structural model have limited explanatory power in credit spread regression. We argue that this is partially due to the non-constancy of the credit spread gradients to state variables. We use a Random Coefficient Regression (RCR) model to accommodate this problem. The explanatory power increases dramatically with the new RCR model, without adding new independent variables. This is the first work to address the dependence between credit spread sensitivities and state variables of structural in a systematic way. Also our estimates are consistent with prediction from Merton’s structural model

Connecting Silos : On linking macroeconomics and finance, and the role of econometrics therein

The crises of this century have stressed how intertwined macroeconomics and finance are in practice. This intertwinement was absent in most economic models. This led to calls for economists to step out of their specialized silos. Since then, the literature of macro-finance, which studies the relationship between asset prices and economic fluctuations, has been developed. In this inaugural address, I argue for a prominent role of econometrics to study the macro-finance interaction. Key elements such as mixed frequencies and the selection of factors can be incorporated using recent econometric advances. I discuss some of the results, such as estimation of continuous-time equilibrium models for macroeconomic and financial series, as well as characteristics of trading on financial markets after macroeconomic news releases. Finally, I discuss the outstanding challenges, which include developing a yield curve model based on macroeconomic foundations, modeling how financial markets anticipate news releases, and developing a macro-finance model for European bond markets taking into account the large heterogeneity across the continent

Inflation derivatives pricing with a forward CPI model

The Zero-Coupon Inflation Indexed Swap (ZCIIS) is a derivative contract through which inflation expectations on the Consumer Price Index (CPI) are actively traded in the US. In this thesis we consider different ways to use the information from the ZCIIS market for modeling forward inflation in a risk-neutral framework. We choose to implement a model using a Monte Carlo methodology that simulates the evolution of the forward CPI ratio. We prefer this approach for its flexibility, ease of implementation, instant calibration to the ZCIIS market and intrinsic convexity adjustment on the inflation-linked payoff. Subsequently, we present a series of results we obtain when modeling a chain of consecutive CPI ratios for simulating the evolution of spot inflation. Furthermore, we use this for pricing inflation caplets and floorlets. Finally, we use the intuition gained from this exercise to analyse our results for pricing inflation caps

Stochastic analysis of longevity and investment risk in the context of life annuities

This thesis aims to investigate the effect oflongevity risk in the context of life annuities. It develops different tools and frameworks to measure this risk as a step to facilitate the risk management oflongevity risk. Particular attention is directed to stochastic modelling which allows the uncertainty of future projections to be incorporated. Hence, simulation methods are used to consider the distribution of the annuity cost, as well as the more often quoted point estimates. A theoretical extension of the use of the entropy measure applied in population biology by Demetrius (1976) has been developed to measure the effect of a proportionate change in the force of mortality on the cost of life annuity. The properties of the corresponding entropy measure have been then investigated using the Gompertz and the Sithole et al (2000) mortality projection models. Numerical results suggest that, at very high or low levels of mortality, the effect of mortality changes on the value of life annuity is of reduced importance. A full Bayesian model has been developed which incorporates the estimation of the parameters of both the Sithole et al (2000) and the Lee - Carter (1992) mortality projection models within the simulation of the annuity cost. This has been extended to an environment in which the future rates of interest are stochastic. The effect of parameter uncertainty of the Sithole et al (2000) mortality projection model has been considered and shown to be less important than the associated model uncertainty