Pricing credit derivatives

The financial crisis set off by the default of Lehman Brothers in 2008 leading to disastrous consequences for the global economy has focused attention on regulation and pricing issues related to credit derivatives. Credit risk refers to the potential losses that can arise due to the changes in the credit quality of financial instruments. These changes could be due to changes in the ratings, market price (spread) or default on contractual obligations. Credit derivatives are financial instruments designed to mitigate the adverse impact that may arise due to credit risks. However, they also allow the investors to take up purely speculative positions. In this article we provide a succinct introduction to the notions of credit risk, the credit derivatives market and describe some of the important credit derivative products. There are two approaches to pricing credit derivatives, namely the structural and the reduced form or intensity-based models. A crucial aspect of the modelling that we touch upon briefly in this article is the problem of calibration of these models. We hope to convey through this article the challenges that are inherent in credit risk modelling, the elegant mathematics and concepts that underlie some of the models and the importance of understanding the limitations of the models.

Exploiting coherence for the simultaneous discovery of latent facets and associated sentiments

Facet-based sentiment analysis involves discovering the latent facets, sentiments and their associations. Traditional facet-based sentiment analysis algorithms typically perform the various tasks in sequence, and fail to take advantage of the mutual reinforcement of the tasks. Additionally,inferring sentiment levels typically requires domain knowledge or human intervention. In this paper, we propose aseries of probabilistic models that jointly discover latent facets and sentiment topics, and also order the sentiment topics with respect to a multi-point scale, in a language and domain independent manner. This is achieved by simultaneously capturing both short-range syntactic structure and long range semantic dependencies between the sentiment and facet words. The models further incorporate coherence in reviews, where reviewers dwell on one facet or sentiment level before moving on, for more accurate facet and sentiment discovery. For reviews which are supplemented with ratings, our models automatically order the latent sentiment topics, without requiring seed-words or domain-knowledge. To the best of our knowledge, our work is the first attempt to combine the notions of syntactic and semantic dependencies in the domain of review mining. Further, the concept of facet and sentiment coherence has not been explored earlier either. Extensive experimental results on real world review data show that the proposed models outperform various state of the art baselines for facet-based sentiment analysis.

IceCube: efficient targeted mining in data cubes

We address the problem of mining targeted association rules over multidimensional market-basket data. Here, each transaction has, in addition to the set of purchased items, ancillary dimension attributes associated with it. Based on these dimensions, transactions can be visualized as distributed over cells of an n-dimensional cube. In this framework, a targeted association rule is of the form {X -> Y} R, where R is a convex region in the cube and X. Y is a traditional association rule within region R. We first describe the TOARM algorithm, based on classical techniques, for identifying targeted association rules. Then, we discuss the concepts of bottom-up aggregation and cubing, leading to the CellUnion technique. This approach is further extended, using notions of cube-count interleaving and credit-based pruning, to derive the IceCube algorithm. Our experiments demonstrate that IceCube consistently provides the best execution time performance, especially for large and complex data cubes.

Quantum entropic ambiguities: Ethylene

In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are, in general, different. Therefore, one reaches the remarkable possibility that there may be many entropies for a given state R. Sorkin (private communication)]. This ambiguity in entropy can often be traced to a gauge symmetry emergent from the nontrivial topological character of the configuration space of the underlying system. It can also happen in finite-dimensional matrix models. In the present work, we discuss this entropy ambiguity and its consequences for an ethylene molecule. This is a very simple and well-known system, where these notions can be put to tests. Of particular interest in this discussion is the fact that the change of the density matrix with the corresponding entropy increase drives the system towards the maximally disordered state with maximum entropy, where Boltzman's formula applies. Besides its intrinsic conceptual interest, the simplicity of this model can serve as an introduction to a similar discussion of systems such as colored monopoles and the breaking of color symmetry.

Wireless bidirectional relaying and Latin squares

The design of modulation schemes for the physical layer network-coded two way relaying scenario is considered with the protocol which employs two phases: Multiple access (MA) Phase and Broadcast (BC) Phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA Phase and all these network coding maps should satisfy a requirement called the exclusive law. We show that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, and this relationship can be used to get the network coding maps satisfying the exclusive law. Using the structural properties of the Latin Squares for a given set of parameters, the problem of finding all the required maps is reduced to finding a small set of maps for M-PSK constellations. This is achieved using the notions of isotopic and transposed Latin Squares. Furthermore, the channel conditions for which the bit-wise XOR will perform well is analytically obtained which holds for all values of M (for M any power of 2). We illustrate these results for the case where both the end users use QPSK constellation.

From Selective-ID to Full-ID IBS without Random Oracles

Since its induction, the selective-identity (sID) model for identity-based cryptosystems and its relationship with various other notions of security has been extensively studied. As a result, it is a general consensus that the sID model is much weaker than the full-identity (ID) model. In this paper, we study the sID model for the particular case of identity-based signatures (IBS). The main focus is on the problem of constructing an ID-secure IBS given an sID-secure IBS without using random oracles-the so-called standard model-and with reasonable security degradation. We accomplish this by devising a generic construction which uses as black-box: i) a chameleon hash function and ii) a weakly-secure public-key signature. We argue that the resulting IBS is ID-secure but with a tightness gap of O(q(s)), where q(s) is the upper bound on the number of signature queries that the adversary is allowed to make. To the best of our knowledge, this is the first attempt at such a generic construction.