Pricing Derivatives the Martingale Way.

In recent years results from the theory of martingales has been successfully applied to problems in financial economics. In the present paper we show how efficient and elegant this "martingale technology" can be when solving for complex options. In particular we provide closed form solutions for several new classes of exotic options including the cliquet, the ladder, the discrete shout and the discrete lookback. We also provide a derivation of the price of an option on the maximum of n assets to demonstrate the power of the multi-dimensional Girsanov theorem. Although some of the results presented are well known, the treatment of the material in this paper is new in that it focuses on the application of the martingale technology to concrete problems in option pricing, methods that until now have mostly been used for purely theoretical purposes.

PHYMYCO-DB: A curated database for analyses of fungal diversity and evolution.

International audienceBackground: In environmental sequencing studies, fungi can be identified based on nucleic acid sequences, using either highly variable sequences as species barcodes or conserved sequences containing a high-quality phylogenetic signal. For the latter, identification relies on phylogenetic analyses and the adoption of the phylogenetic species concept. Such analysis requires that the reference sequences are well identified and deposited in public-access databases. However, many entries in the public sequence databases are problematic in terms of quality and reliability and these data require screening to ensure correct phylogenetic interpretation. Methods and Principal Findings: To facilitate phylogenetic inferences and phylogenetic assignment, we introduce a fungal sequence database. The database PHYMYCO-DB comprises fungal sequences from GenBank that have been filtered to satisfy stringent sequence quality criteria. For the first release, two widely used molecular taxonomic markers were chosen: the nuclear SSU rRNA and EF1-a gene sequences. Following the automatic extraction and filtration, a manual curation is performed to remove problematic sequences while preserving relevant sequences useful for phylogenetic studies. As a result of curation, ,20% of the automatically filtered sequences have been removed from the database. To demonstrate how PHYMYCO-DB can be employed, we test a set of environmental Chytridiomycota sequences obtained from deep sea samples. Conclusion: PHYMYCO-DB offers the tools necessary to: (i) extract high quality fungal sequences for each of the 5 fungal phyla, at all taxonomic levels, (ii) extract already performed alignments, to act as 'reference alignments', (iii) launch alignments of personal sequences along with stored data. A total of 9120 SSU rRNA and 672 EF1-a high-quality fungal sequences are now available. The PHYMYCO-DB is accessible through the URL http://phymycodb.genouest.org/

Term Structure Models with Shot-noise Effects

This work proposes term structure models consisting of two parts: a part which can be represented in exponential quadratic form and a shot noise part. These term structure models allow for explicit expressions of various derivatives. In particular, they are very well suited for credit risk models. The goal of the paper is twofold. First, a number of key building blocks useful in term structure modelling are derived in closed-form. Second, these building blocks are applied to single and portfolio credit risk. This approach generalizes Duffie & Garleanu (2001) and is able to produce realistic default correlation and default clustering. We conclude with a specific model where all key building blocks are computed explicitly

Liquidity risk premia : an empirical analysis of european corporate bond yields

In this study we highlight the importance of liquidity risk, especially in periods of market stress, and advocate in favour of an explicit consideration of a liquidity premium when using mark-to-model methodologies to value financial assets. For European corporate bonds, we show that the liquidity premium, calculated as the difference between the yield spread of corporate bonds and the spread of credit default swaps, grew significantly during the recent market turmoil not only in absolute terms but also in relative terms. Although liquidity premiums were far from stable during the time frame of analysis-from 1 January 2005 to 31 December 2009 - on average roughly 40% of corporate yield spreads can be interpreted in terms of liquidity premia. We propose direct matching between the CDS and the underlying reference assets when computing liquidity premia. This differs from what seems to be the industry standard, which is simply to use indices when trying to infer market implied liquidity premia. Although computationally more demanding, the method we use is sounder from a theoretical point of view and produces richer results and analysis. With this method we are able present an analysis of liquidity risk premia per sector of activity