Theory and Calibration of Swap Market Models

This paper introduces a general framework for market models, named Market Model Approach, through the concept of admissible sets of for-ward swap rates spanning a given tenor structure. We relate this concept to results in graph theory by showing that a set is admissible if and only if the associated graph is a tree. This connection enables us to enumerate all admissible models for a given tenor structure. Three main classes are identified within this framework, and correspond to the co-terminal, co-initial, and co-sliding model. We prove that the LIBOR market model is the only admissible model of a co-sliding type. By focusing on the co-terminal model in a lognormal setting, we develop and compare several approximating analytical formulae for caplets, while swaptions can be priced by a simple Black-type formula. A novel calibration technique is introduced to allow simultaneous calibration to caplet and swaption prices. Empirical calibration of the co-terminal model is shown to be faster, more robust and more efficient than the same procedure applied to the LIBOR market model. We then argue that the co-terminal approach is the simplest and most convenient market model for pricing and hedging a large variety of exotic interest-rate derivatives.Swap Market Model, Cap, Swaption, Calibration, Graph Theory

Variance Optimal Cap Pricing Models

We propose new closed-form pricing formulas for interest rate options which guarantee perfect compatibility with volatility smiles. These cap pricing formulas are computed under variance optimal measures in the framework of the market model or the Gaussian model and achieve an exact calibration of observed market prices. They are presented in a general setting allowing to study model and numéraire choice effects on the computed prices. Numéraire dependence is particularly emphasized. A numerical example and an empirical application on market data are given to illustrate the practical use of the calibration procedure.Discount bond option; cap pricing formula; volatility smile; variance optimal measure; implied pricing model

Multiregime Term Structure Models

The Ho and Lee model is the analogue for the study of the term structure of interest rates of the binomial tree introduced by Cox, Ross and Rubinstein in the one risky asset case. This model allows only for a small number of deformations of the term structure between two successive dates, and is therefore incompatible with available data. We propose here to reconcile tree approaches and statistical inference. We consider regime models for which the deformation of the term structure may behave randomly in each regime. Questions about constraints induced by no arbitrage are also addressed in a context of asymmetric information between traders and the econometrician in charge with the estimation.binomial model; term structure; interest rate; asymmetric information

Testing for symmetry and conditional symmetry using asymmetric kernels

The final publication is available at Springer via http://dx.doi.org/10.1007/s10463-014-0469-6.e financial support from the ESRC under the grant RES-062-23-0311 (Fernandes), from the ARC grant DP0988579 (Mendes), and from the SNSF through the NCCR Finrisk (Scaillet).ESRC under the grant RES-062-23-0311 (Fernandes), from the ARC grant DP0988579 (Mendes), and from the SNSF through the NCCR Finrisk (Scaillet)

An Empirical Investigation in Credit Spread Indices

We study the dynamics of the spread between U.S. corporate and Treasury bonds. We focus on Aaa and Baa corporate yield indices and estimate nonparametrically the dynamics of the spreads assuming that they follow a univariate diffusion process. Using techniques developed for interest rate processes we try to infer from the data what acceptable process can be used to model aggregate credit spreads for option pricing or risk management purposes. We find that there is significant evidence of mean reversion especially for higher rated spreads and that the volatility of Aaa spreads exhibit a U-shape while the volatility of Baa spreads is monotonically increasing in the level of spreads. Based on these observations and on the evidence of jumps in the series, we propose a new model for credit spread indices (an Ornstein-Uhlenbeck with jumps) and estimate it by maximum likelihood.Credit spread; risk management; jump diffusion; volatility; nonparametric

A rapid mechanism to remobilize and homogenize highly crystalline magma bodies

International audienceThe largest products of magmatic activity on Earth, the great bodies of granite and their corresponding large eruptions, have a dual nature: homogeneity at the large scale and spatial and temporal heterogeneity at the small scale1-4. This duality calls for amechanism that selectively removes the large-scale heterogeneities associated with the incremental assembly4 of these magmatic systems and yet occurs rapidly despite crystal-rich, viscous conditions seemingly resistant to mixing2,5. Here we show that a simple dynamic template can unify a wide range of apparently contradictory observations from both large plutonic bodies and volcanic systems by a mechanism of rapid remobilization (unzipping) of highly viscous crystalrich mushes. We demonstrate that this remobilization can lead to rapid overturn and produce the observed juxtaposition ofmagmatic materials with very disparate ages and complex chemical zoning. What distinguishes our model is the recognition that the process has two stages. Initially, a stiff mushy magma is reheated from below, producing a reduction in crystallinity that leads to the growth of a subjacent buoyant mobile layer. When the thickening mobile layer becomes sufficiently buoyant, it penetrates the overlying viscous mushy magma. This second stage rapidly exports homogenized material from the lower mobile layer to the top of the system, and leads to partial overturn within the viscous mush itself as an additional mechanism of mixing. Model outputs illustrate that unzipping can rapidly produce large amounts of mobile magma available for eruption. The agreement between calculated and observed unzipping rates for historical eruptions at Pinatubo and at Montserrat demonstrates the general applicability of the model. This mechanism furthers our understanding of both the formation of periodically homogenized plutons (crust building) and of ignimbrites by large eruptions

Decadal to monthly timescales of magma transfer and reservoir growth at a caldera volcano

International audienceCaldera-forming volcanic eruptions are low-frequency, highimpact events capable of discharging tens to thousands of cubic kilometres of magma explosively on timescales of hours to days, with devastating effects on local and global scales1. Because no such eruption has been monitored during its long build-up phase, the precursor phenomena are not well understood. Geophysical signals obtained during recent episodes of unrest at calderas such as Yellowstone, USA, and Campi Flegrei, Italy, are difficult to interpret, and the conditions necessary for large eruptions are poorly constrained2,3. Here we present a study of pre-eruptive magmatic processes and their timescales using chemically zoned crystals from the 'Minoan' caldera-formingeruption of Santorini volcano,Greece4, which occurred in the late 1600s BC. The results provide insights into how rapidly large silicic systems may pass from a quiescent state to one on the edge of eruption5,6. Despite the large volume of erupted magma4 (40-60 cubic kilometres), and the 18,000-year gestation period between the Minoan eruption and the previous major eruption, most crystals in the Minoan magma record processes that occurred less than about 100 years before the eruption. Recharge of the magma reservoir by large volumes of silicic magma (and some mafic magma) occurred during the century before eruption, and mixing between different silicicmagmabatches was still taking place during the final months. Final assembly of large silicic magma reservoirs may occur on timescales that are geologically very short by comparison with the preceding repose period, with major growth phases immediately before eruption. These observations have implications for the monitoring of long-dormant, but potentially active, caldera systems

Empirical Bayes analysis of single nucleotide polymorphisms

<p>Abstract</p> <p>Background</p> <p>An important goal of whole-genome studies concerned with single nucleotide polymorphisms (SNPs) is the identification of SNPs associated with a covariate of interest such as the case-control status or the type of cancer. Since these studies often comprise the genotypes of hundreds of thousands of SNPs, methods are required that can cope with the corresponding multiple testing problem. For the analysis of gene expression data, approaches such as the empirical Bayes analysis of microarrays have been developed particularly for the detection of genes associated with the response. However, the empirical Bayes analysis of microarrays has only been suggested for binary responses when considering expression values, i.e. continuous predictors.</p> <p>Results</p> <p>In this paper, we propose a modification of this empirical Bayes analysis that can be used to analyze high-dimensional categorical SNP data. This approach along with a generalized version of the original empirical Bayes method are available in the R package siggenes version 1.10.0 and later that can be downloaded from <url>http://www.bioconductor.org</url>.</p> <p>Conclusion</p> <p>As applications to two subsets of the HapMap data show, the empirical Bayes analysis of microarrays cannot only be used to analyze continuous gene expression data, but also be applied to categorical SNP data, where the response is not restricted to be binary. In association studies in which typically several ten to a few hundred SNPs are considered, our approach can furthermore be employed to test interactions of SNPs. Moreover, the posterior probabilities resulting from the empirical Bayes analysis of (prespecified) interactions/genotypes can also be used to quantify the importance of these interactions.</p