Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy

In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of anyon condensation in the context of Abelian Chern-Simons theory, which is then generalized to more non-Abelian theories whose edge RCFTs are known. Then we apply these results to computing the entanglement entropy of different topological orders. We consider cases where the system resides on a cylinder with gapped boundaries and that the entanglement cut is parallel to the boundary. We also consider cases where the entanglement cut coincides with the interface on a cylinder. In either cases, we find that the topological entanglement entropy is determined by the anyon condensation pattern that characterizes the interface/boundary. We note that conditions are imposed on some non-universal parameters in the edge theory to ensure existence of the conformal interface, analogous to requiring rational ratios of radii of compact bosons.Comment: 38 pages, 5 figure; Added referenc

Direct inversion for the Heston model

The Heston stochastic volatility model is commonly used in financial mathematics. While closed form solutions for pricing vanilla European options are available, this is not the case for other exotic options, especially for path dependent ones, where Monte Carlo methods are often applied. In this thesis, we develop an accurate and efficient simulation method for the Heston model, which is then employed in the pricing of options that are computationally challenging. We consider the problem of sampling the asset price based on its exact distribution. One key step is to sample from the time integrated variance process conditional on its endpoints. We construct a new series expansion for this integral in terms of infinite weighted sums of exponential and gamma random variables through measure transformation and decompositions of squared Bessel bridges. This representation has exponentially decaying truncation errors, which allows efficient simulations of the Heston model. We develop direct inversion algorithms combined with series truncations, leading to an almost exact simulation for the model. The direct inversion is based on approximating the inverse distribution functions by Chebyshev polynomials. We derive asymptotic expansions for the corresponding distribution functions to evaluate the Chebyshev coefficients. We also design feasible strategies such that those coefficients are independent of any model parameters, whence the resulting Chebyshev polynomials can be used under any market conditions. Efficiency of our method is confirmed by numerical comparisons with existing methods

Determinants of Credit Spreads on Asset-Backed Securities: A British Case Study in the Context of the COVID-19 Pandemic

The determinants of credit spreads on asset-backed securities are an active topic of discussion in the literature. This study is aimed to close the gap in research regarding the impact of the COVID pandemic on the determinants of credit spreads of the asset-backed securities in the United Kingdom. The pandemic, as a crucial event, is a key factor influencing the economy. Furthermore, other relevant factors for tranches are considered in the analysing as well. This paper focuses on asset-backed securities excluding MBS. The sample of this study was collected from 201 asset-backed securities and their tranches issued from January 2010 to July 2021 and traded in the United Kingdom (in British pounds). The collected data were analysed by the ordinary least squares (OLS) method in the multiple cross-sectional models. This study explores the factors that impact credit spreads in the context of the COVID-19 pandemic and encourages financial market participants to make appropriate investment strategies on asset-backed securities. This paper provides two main contributions to the literature. First, the credit spreads of non-prime tranches have more positive changes than prime ones during COVID. Second, the link between the maturity of consumer tranches and credit spreads shifts from negative to positive after the COVID break-out. This means that if investors are risk-averse, they should invest in short-term asset-backed securities to reduce credit risk during COVID. This study is modest to fill the literature gap with the COVID-19 factor in analysing the determinants of credit spreads on asset-backed securities. The study also adds to a better understanding of the behaviour of investing in asset-backed securities, both from the perspective of investors and academics. Keywords: Asset-backed Securities (ABS); COVID-19; Ordinary Least Squares (OLS

MNER-QG: An End-to-End MRC framework for Multimodal Named Entity Recognition with Query Grounding

Multimodal named entity recognition (MNER) is a critical step in information extraction, which aims to detect entity spans and classify them to corresponding entity types given a sentence-image pair. Existing methods either (1) obtain named entities with coarse-grained visual clues from attention mechanisms, or (2) first detect fine-grained visual regions with toolkits and then recognize named entities. However, they suffer from improper alignment between entity types and visual regions or error propagation in the two-stage manner, which finally imports irrelevant visual information into texts. In this paper, we propose a novel end-to-end framework named MNER-QG that can simultaneously perform MRC-based multimodal named entity recognition and query grounding. Specifically, with the assistance of queries, MNER-QG can provide prior knowledge of entity types and visual regions, and further enhance representations of both texts and images. To conduct the query grounding task, we provide manual annotations and weak supervisions that are obtained via training a highly flexible visual grounding model with transfer learning. We conduct extensive experiments on two public MNER datasets, Twitter2015 and Twitter2017. Experimental results show that MNER-QG outperforms the current state-of-the-art models on the MNER task, and also improves the query grounding performance.Comment: 13 pages, 6 figures, published to AAA