General Quadratic Term Structures of Bond, Futures and Forward Prices

For finite dimensional factor models, the paper studies general quadratic term structures. These term structures include as special cases the affine term structures and the Gaussian quadratic term structures, previously studied in the literature. We show, however, that there are other, non-Gaussian, quadratic term structures and derive sufficient conditions for the existence of these general quadratic term structures for bond, futures and forward prices. As forward prices are martingales under the T-forward measure, their term structure equation depends on properties of bond prices' term structure. We exploit the connection with the bond prices term structure and show that even in quadratic short rate settings we can have affine term structures for forward prices. Finally, we show how the study of futures prices is naturally embedded in a study of forward prices and show that the difference between the two prices have to do with the correlation between bond prices and the price process of the underlying to the forward contract and this difference may be deterministic in some (non-trivial) stochastic interest rate settings.term structure; bond price; futures price; forward price; affine term structure; quadratic term structure

Correlation Between Intensity and Recovery in Credit Risk Models

We start by presenting a reduced-form multiple default type of model and derive abstract results on the influence of a state variable X on credit spreads, when both the intensity and the loss quota distribution are driven by X. The aim is to apply the results to a concrete real life situation, namely, to the influence of macroeconomic risks on credit spreads term structures. There has been increasing support in the empirical literature that both the probability of default (PD) and the loss given default (LGD) are correlated and driven by macroeconomic variables. Paradoxically, there has been very little effort from the theoretical literature to develop credit risk models that would include this possibility. A possible justification has to do with the increase in complexity this leads to, even for the "treatable" default intensity models. The goal of this paper is to develop the theoretical framework needed to handle this situation and, through numerical simulation, understand the impact on credit risk term structures of the macroeconomic risks. In the proposed model the state of the economy is modeled trough the dynamics of a market index, that enters directly on the functional form of both the intensity of default and the distribution of the loss quota given default. Given this setup, we are able to make periods of economic depression, periods of higher default intensity as well as periods where low recovery is more likely, producing a business cycle effect. Furthermore, we allow for the possibility of an index volatility that depends negatively on the index level and show that, when we include this realistic feature, the impacts on the credit spread term structure are emphasized.Credit risk; sistematic risk; intensity models; recovery; credit spreads

Quadratic Portfolio Credit Risk models with Shot-noise Effects

We propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds. Further on, we study a model for portfolio credit risk where we consider both firm specific and systematic risks. The model generalizes the attempt from Duffie and Garleanu (2001). We find that the model produces realistic default correlation and clustering of defaults. Then, we show how to price first-to-default swaps, CDOs, and draw the link to currently proposed credit indices.Credit risk; reduced-form models; CDS; CDO; quadratic term structures; shot-noise

General quadratic term structures of bond, futures and forward prices

For finite dimensional factor models, the paper studies general quadratic term structures. These term structures include as special cases the affine term structures and the Gaussian quadratic term structures, previously studied in the literature. We show, however, that there are other, non-Gaussian, quadratic term structures and derive sufficient conditions for the existence of these general quadratic term structures for bond, futures and forward prices. As forward prices are martingales under the T-forward measure, their term structure equation depends on properties of bond prices’ term structure. We exploit the connection with the bond prices term structure and show that even in quadratic short rate settings we can have affine term structures for forward prices. Finally, we show how the study of futures prices is naturally embedded in a study of forward prices and show that the difference between the two prices have to do with the correlation between bond prices and the price process of the underlying to the forward contract and this difference may be deterministic in some (non-trivial) stochastic interest rate settings..info:eu-repo/semantics/publishedVersio

Portfolio performance of european target prices

This paper explores the performance of actively managed portfolios constructed based on target price recommendations provided by analysts. We propose two methods for constructing portfolios using Bloomberg’s 12-month target price consensus, which we use as a signal to buy or sell assets. Using a sample of 50 European stocks over a 15-year period (2004-2019), we compare the performance of target price-based portfolios to traditional alternatives such as a naive homogeneous portfolio and the Eurostoxx 50 index, as well as to passive portfolios based on mean recommendations. We also examine the mean-variance efficiency of these portfolios and find that they all exhibit similar levels of efficiency, with theoretical tangent portfolios vastly outperforming all others. Our results indicate that target price-based portfolios show performance very close to that of the naive homogeneous portfolio. Even the passive ”mean” portfolios, which require pre-knowledge of targets for the entire investment period, are unable to outperform the naive portfolio. We also investigate the impact of rebalancing on portfolio performance and find that it does pay off in the long run (over an 8-year investment period), but that the frequency of rebalancing matters. Rebalancing only once a year is as detrimental to performance as not rebalancing at all. However, it is unclear whether the transaction costs associated with frequent rebalancing would offset any relative outperformance. Overall, our study contributes to the literature on portfolio management by showing the potential benefits and limitations of using target price recommendations to construct portfolios, and highlighting the importance of carefully considering rebalancing strategies in order to achieve optimal performance.info:eu-repo/semantics/publishedVersio

Convexity adjustments for ATS models

Practitioners are used to value a broad class of exotic interest rate derivatives simply by adjusting for what is known as convexity adjustments (or convexity corrections). We start by exploiting the relations between various interest rate models and their connections to measure changes. As a result we classify convexity adjustments into forward adjustments and swaps adjustments. We, then, focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward ad¬justments, we show how to obtain exact formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. Based upon the ideas of Schrager and Pelsser (2006) we are also able to derive general swap adjustments useful, in particular, when dealing with constant maturity swaps (CMS). Our approach bypasses the need for Taylor approximations or unrealistic assumptions. They include exact convexity adjustments previously derived, such as the adjustments associated with Gaussian models, but are far more general as they provide solutions for the entire ATS class of models.Financial support of FCT under grant PTDC/MAT/64838/2006 and Jan Wallander's Foundatio

On the pricing of CDOs

This chapter addresses the pricing of two popular portfolio credit derivatives: first-to-default swaps and collateralized debt obligations (CDOs). We use the recent model of Gaspar and Schmidt (2007) for the pricing of theses portfolio credit derivatives. This approach combines general quadratic models for term structures with shot-noise models and therefore naturally solves a number of important issues in credit portfolio risk. First, resulting pricing formulas are in closed form and therefore the model implementation is straightforward. Second, this class of models is able to incorporate well-known features of credit risky markets: realistic default correlations, default clustering and correlation between short-rate and credit spreads. Third, the recent turbulence in credit spreads caused by the U.S. subprime mortgage turmoil can be captured well.info:eu-repo/semantics/publishedVersio

CDOs in the light of the current crisis

This paper proposes a top-down model for pricing Collateralized Debt Obligation (CDOs). Our proposal is both treatable and realistic, in the sense we are able to obtain closed-form solutions to single tranche CDOs and capturing extreme credit events. We use as key ingredients the so-called (T, x)-bonds, as proposed in Filipovic, Overbeck, and Schmidt (2008), but generalize their affine specificationby including shot-noise processes. Our claim is that affine diffusions combined with shot-noise processes lead to an improved modeling of CDO spreads in comparison to existing affine jump-diffusion models. The proposed approach allows in particular for better capturing the possibility of extreme events, like the ones underlying the current crisis. We illustrate our results with a very concrete (simple) instance of our class of models. Finally, we identify the connections between the top-down and bottom-up approaches for modeling credit risk, within our class of models. Concretely, we show that even when taking a bottom-up approach the aggregate loss process would be a process of affine shot-noise type

Consumer Confidence and Stock Markets' Returns

This study provides new insights on the relationship between changes in consumer con dence indices worldwide and the performance of European, United States and Chinese stock markets, during the period from 2007 to 2021. We look both into global and industry returns. For the full-time period, we nd stock market returns tend to be positively correlated with changes in consumer con dence indices, with signi cant two-way Granger causal impacts between the two variables for Europe and the United States. For the Chinese stock market we nd less pronounced and only one-way impact { changes in consumer con dence indices can Granger explain Chinese stock returns, but not vice versa. In fact, Chinese stock returns only help explaining changes in East Asian consumer con dence index. These results are robust across industries. For the Covid pandemic sub-period, we nd some negative correlations between stock market returns and changes in consumer con dence indices. This is particularly evident in China, but it also happens in Europe and United States, at least for some industries, including Health Care. Overall, the connection between the stock market performance and changes in consumer con dence is lower for USA and European stock markets, but it is higher for the Chinese stock market, in terms of the number of signi cant outcomes.info:eu-repo/semantics/publishedVersio

On recovery and intensity's correlation : a new class of credit risk models

There has been increasing support in the empirical literature that both the probability of default (PD) and the loss given default (LGD) are correlated and driven by macroeconomic variables. Paradoxically, there has been very little effort from the theoretical literature to develop credit risk models that would include this possibility. The goals of this paper are: first, to develop the theoretical reduced-form framework needed to handle stochastic correlation of recovery and intensity, proposing a new class of models; and, second, to use concrete instance of our class to study the impact of this correlation in credit risk term structures. Our class of models is able to replicate and explain empirically observed features. For instance, we automatically get that periods of economic depression are periods of higher default intensity and where low recovery is more likely - the well-know credit risk business cycle effect. Finally, we show how to calibrate this class of models to market data, and illustrate the technique using our concrete instance using US market data on corporate yields.Financial support from Jan Wallander and Tom Hedelius foundation. This research was also partially supported by the Austrian Science Foundation project P18022 at the Vienna University of Technolog