Essays in credit and inflation linked derivatives

Das Ziel dieser Studie ist zweifach. Einer von ihnen ist das Pricing und Hedg- ing von Collateralized Debt Obligations (CDOs) und die andere ist die Modellierung von Inflation Linked-Derivaten. Im ersten Teil untersuchen wir die Modellierung Setup in Filipović et al. (2009) für die Pricing und Hedging von CDOs. In einem ersten Schritt auf dem Weg der Untersuchung des Marktes Unvollständigkeit, untersuchen wir die Einzigartigkeit des Martingalmass in der gegebenen (T,x)-bond Markt und zeigen, dass die entsprechenden äquivalenten lokalen Martingalmass (ELMM) einzigartig ist. Dann schlagen wir eine affine Zwei-Faktor-stochastische Drift-Modell für die Pricing und Hedg- ing von synthetischen Single-Tranche CDOs. Wir schätzen die affine Faktor- Modell auf den iTraxx Europe-Daten. Die Neuheit dieses Teils liegt in der Tatsache, dass die Daten Periode eine Periode, die unterschiedlichen Mark- tbedingungen wie die Kreditkrise erlebt abdeckt. Für die Abschätzung der affine Faktor-Modell verwenden wir quasi Maximum- Likelihood- Schätzung basierend auf dem Kalman-Filter. Schätzergebnisse zeigen, dass die Zwei- Faktor- stochastische Drift-Modell erfolgreich in Bezug auf die fit der Mark- tdaten auch für Super- Senior- Tranchen ist. Abgesehen von der Schätzung des Modells analysieren wir die reale Welt Performance von zwei Hedge- Strategien, nämlich die Varianz minimizing und Regression based Hedging. Wir führen auch eine Simulation Analyse, wo normale und Extremschaden- szenarien via Methode importance sampling generiert werden. Schliesslich bewerten wir die Hedging-Strategien im Rahmen dieser allgemeinen Szenar- ien. Der zweite Teil beshäftigt sich mit die Pricing und Hedging von inflation- sindexierten Derivaten. In diesem Teil, vorausgesetzt, dass die foreign cur- rency analogy hält betrachten wir eine Drei-Faktor-Gauss-affine Modell für die Preisgestaltung der nominalen und inflationsindexierten Anleihen. Mit Hilfe der Theorie der affine Prozesse, die wir bekommen Anleihenkurse in der geschlossenen Form. No-Arbitrage-Annahme führt zu drift Bedingungen, die den Faktor Prozess hat zu befriedigen. Insbesondere ist eine der Bedingungen der bekannte Fisher-Gleichung. Dann unter der Annahme diagonalisierbar Drift-Matrix finden wir Bedingungen an die Eigenwerte und die Eigenvektoren der Drift Matrix, die die Hedging einer inflationsindexierten Anleihe nur durch den Handel mit nominalen Anleihen mit unterschiedlichen Laufzeiten zu gewährleisten. Die Kombination No-Arbitrage- Einschränkungen mit der Hedging Bedingungen auf dem diagonalisierbar Drift-Matrix 1 und die Nutzung des Marktes Vollständigkeit Kriterium gegeben in Davis und Obloj (2008) finden wir, dass die Hedging von inflationsindexierten An- leihen mit nominalen Anleihen ist möglich, wenn und nur wenn der Markt durch die nominale Anleihen aufgespannt wird. Schliesslich betrachten wir eine Multi-Country Modell, wo in-und ausländis- chen nominalen und realen Anleihen gehandelt werden. Wir nehmen zuerst an, dass die realen und nominellen Kurs der Anleihe, Preisindex und Wech- selkurs einem Itô Prozess folgen. Dann haben wir vorausgesetzten, dass der Markt Arbitrage-frei ist. No-Arbitrage-Annahme ergibt sich unmittelbar die übliche Definition des realen Wechselkurses (RW) zwischen den ausländis- chen und inländischen Economies. Darüber hinaus erhalten wir drift Be- dingungen für reale und nominale Zinsstrukturen des in-und auslŁndischen Economies. Unter der Annahme, Martingal Eigenschaft f§r RW finden wir eine Beziehung auf die reale Zinsdifferenz zwischen den Economies. Motiviert durch die Bedeutung der Informationen über die RW für die Zentralbanken, führen wir einen Forward-Kontrakt auf RW geschrieben. Daraus ergibt sich die Forward realen Wechselkurs, die in Bezug auf den Preis der inländis- chen und ausländischen Inflation Anleihen geschrieben werden konnen. Wir näher vorstellen Multi-Country inflationsindexierten Derivaten, wie Foreign Exchange Inflation-Optionen und die Inflation RW-Swaps mit der Idee, einen Schutz für die ausländischen Kaufkraft der inländischen Einkünfte. Wir ver- wenden die change of numeraire Technik, um die Preise für diese Derivate zu erhalten und unter der Annahme von deterministischen Volatilität an den inflationsindexierten Anleihen Preisdynamik, bekommen wir die Derivate Preisen in der geschlossenen Form.The objective of this study is twofold. One of them is the pricing and hedging of collateralized debt obligations (CDOs) and the other is the modeling of inflation linked derivatives. In the first part, we first review the framework introduced in Filipović et al. (2009) for the pricing and hedging of CDOs. As a first step towards the investigation of the market incompleteness, we examine the uniqueness of the martingale measure in the defaultable (T,x)-bonds market introduced in Filipović et al. (2009) and show that the equivalent local martingale measure (ELMM) is unique. Following this we specify an affine two factor stochastic drift model for the pricing and hedging of single tranche synthetic CDOs. We estimate the affine factor model on the iTraxx Europe data. The novelty of this part lies in the fact that the data covers a period, which witnessed different market conditions such as the recent credit crises. As the main tool for the estimation of the affine factor model we use quasi maximum likelihood based on a Kalman filter. Estimation results show that the two factor stochastic drift model is successful in terms of fitting the market data even for super-senior tranches. Apart from estimating the model, we analyze the real world performance of two hedging strategies, namely the variance minimizing and regression based hedging. We also run a simulation analysis where normal and extreme loss scenarios are generated via method of importance sampling. Finally we assess the hedging strategies under these more general scenarios. The second part of this thesis deals with the pricing and hedging of inflation-indexed derivatives. Assuming that the foreign currency analogy holds we first consider a three-factor Gaussian affine model for the pricing of nomi- nal and inflation indexed bonds. By using the theory of affine processes we get closed form bond prices. Imposing no-arbitrage assumption leads to drift restrictions that the factor process has to satisfy. In particular, one of the conditions the drift matrix of the factor process has to satisfy is the well known Fisher equation. Then, under the assumption of diagonalizable drift matrix we find conditions on the eigenvalues and the eigenvectors of the drift matrix which guarantee the hedge of an inflation indexed bond of a given maturity only by trading nominal bonds of different maturities. Combining no-arbitrage restrictions with the hedging conditions on the diagonalizable drift matrix and utilizing the market completeness criterion given in Davis and Obloj (2008) we find that cases in which it is possible to hedge inflation bonds by using nominal bonds coincide with cases where the market is spanned by the continuum of nominal bonds. That is, we show that under the assumption of diagonalizable drift matrix, hedging of inflation bonds by using nominal bonds is possible if and only if the market is spanned by the nominal bonds. Finally, we consider a multi-country setting where domestic and foreign nominal and real bonds are traded. We first specify the real and nominal bond prices, price index and exchange rate dynamics as Itô processes and assume that there is no- arbitrage in the market. Imposing no-arbitrage assumption immediately yields the usual definition of real exchange rate (RER) between the foreign and domestic economies. Moreover, we get drift conditions for real and nominal term structures of the domestic and foreign economies. Assuming martingale property for RER we find a relation on the real interest rate differential of the two economies. More importantly, we find that the martingale assumption on RER is equivalent to the condition that the nominal interest rate differentials between the two economies is given by the sum of appreciation rate of the exchange rate and the risk premium arising from exchange rate uncertainty. Motivated by the importance of the information on RER for central banks, we introduce a forward contract written on RER. This yields the forward real exchange rate whose value can be expressed in terms of the price of the domestic and foreign inflation indexed bonds. We further construct multi-country inflation linked derivatives such as foreign exchange inflation options and real exchange rate swaps with the idea of providing a protection for the foreign purchasing power of a domes- tic income. We use the change of numeraire technique to get the prices of these derivatives and under the assumption of deterministic volatility in the inflation indexed bond price dynamics, we get closed form formulae

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.

Consistent Valuation Across Curves Using Pricing Kernels

The general problem of asset pricing when the discount rate differs from the rate at which an asset's cash flows accrue is considered. A pricing kernel framework is used to model an economy that is segmented into distinct markets, each identified by a yield curve having its own market, credit and liquidity risk characteristics. The proposed framework precludes arbitrage within each market, while the definition of a curve-conversion factor process links all markets in a consistent arbitrage-free manner. A pricing formula is then derived, referred to as the across-curve pricing formula, which enables consistent valuation and hedging of financial instruments across curves (and markets). As a natural application, a consistent multi-curve framework is formulated for emerging and developed inter-bank swap markets, which highlights an important dual feature of the curve-conversion factor process. Given this multi-curve framework, existing multi-curve approaches based on HJM and rational pricing kernel models are recovered, reviewed and generalised, and single-curve models extended. In another application, inflation-linked, currency-based, and fixed-income hybrid securities are shown to be consistently valued using the across-curve valuation method.Comment: 56 page

Model uncertainty in financial markets:Long run risk and parameter uncertainty

Uncertainty surrounding key parameters of financial markets, such as the in- flation and equity risk premium, constitute a major risk for institutional investors with long investment horizons. Hedging the investors’ inflation exposure can be challenging due to the lack of domestic inflation-linked securities. I show that inflation hedging investors can benefit from holding bonds that are linked to inflation in foreign countries. Investors can further improve their inflation hedge by incorporating the long term interactions between his own inflation exposure and the foreign inflation measures. Focusing on the major inflation-linked security markets, I find an increase of the inflation risk premium over the financial crisis in the UK, whereas in the US it decreased. Since the parameter uncertainty of these estimates is large, and increased over the financial crisis in both the UK and US markets, I present a framework in which investors can quantify and integrate it in their long term investment decisions. Finally, I demonstrate that the difficulty of estimating the equity risk premium is the largest source of parameter uncertainty in defined contribution pension contracts. I introduce a methodology to take parameter uncertainty into account, so that participants can set contributions that reflect the uncertainty about their replacement rate at retirement. Overall, this thesis demonstrates robust methods to incorporate the effects of parameter uncertainty and contributes to the literature on how parameter uncertainty of financial models can substantially affect the investors’ investment risk

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors

We consider the consumption and portfolio choice problem of a long-run investor when the term structure is affine and when the investor has access to nominal bonds and a stock portfolio. In the presence of unhedgeable inflation risk, there exist multiple pricing kernels that produce the same bond prices, but a unique pricing kernel equal to the marginal utility of the investor. We apply our method to a three-factor Gaussian model with a time-varying price of risk that captures the failure of the expectations hypothesis seen in the data. We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio for the long-run investor looks very different from the portfolio of a mean-variance optimizer. In particular, the desire to hedge changes in term premia generates large hedging demands for long-term bonds

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?

We solve the portfolio problem of a long-run investor when the term structure is Gaussian and when the investor has access to nominal bonds and stock. We apply our method to a three-factor model that captures the failure of the expectations hypothesis. We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio of a long-run investor looks very different from the portfolio of a mean-variance optimizer. In particular, time-varying term premia generate large hedging demands for long-term bonds

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?

We solve the portfolio problem of a long-run investor when the term structure is Gaussian and when the investor has access to nominal bonds and stock. We apply our method to a three-factor model that captures the failure of the expectations hypothesis. We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio of a long-run investor looks very different from the portfolio of a mean-variance optimizer. In particular, time-varying term premia generate large hedging demands for long-term bonds

A two-factor model of the German term structure of interest rates

In this paper we show that a two-factor constant volatility model provides an adequate description of the dynamics and shape of the German term structure of interest rates from 1972 up to 1998. The model also provides reasonable estimates of the volatility and term premium curves. Following the conjecture that the two factors driving the German term structure of interest rates represent the H[-DQWH real interest rate and the expected inflation rate, the identification of one factor with expected inflation is discussed. Our estimates are obtained using a Kalman filter and a maximum likelihood procedure including in the measurement equation both the yields and their volatilities JEL Classification: E43, G12affine model, expectations hypothesis, pricing kernels, term premiums