Portfolio optimization of credit risky bonds: a semi-Markov process approach

Abstract This article presents a semi-Markov process based approach to optimally select a portfolio consisting of credit risky bonds. The criteria to optimize the credit portfolio is based on l ∞ -norm risk measure and the proposed optimization model is formulated as a linear programming problem. The input parameters to the optimization model are rate of returns of bonds which are obtained using credit ratings assuming that credit ratings of bonds follow a semi-Markov process. Modeling credit ratings by semi-Markov processes has several advantages over Markov chain models, i.e., it addresses the ageing effect present in the credit rating dynamics. The transition probability matrices generated by semi-Markov process and initial credit ratings are used to generate rate of returns of bonds. The empirical performance of the proposed model is analyzed using the real data. Further, comparison of the proposed approach with the Markov chain approach is performed by obtaining the efficient frontiers for the two models

Topological data analysis in investment decisions

2020 Elsevier Ltd This article explores the applications of Topological Data Analysis (TDA) in the finance field, especially addressing the primordial problem of asset allocation. Firstly, we build a rationale on why TDA can be a better alternative to traditional risk indicators such as standard deviation using real data sets. We apply Takens embedding theorem to reconstruct the time series of returns in a high dimensional space. We adopt the sliding window approach to draw the time-dependent point cloud data sets and associate a topological space with them. We then apply the persistent homology to discover the topological patterns that appear in the multidimensional time series. The temporal changes in the persistence landscapes, which are the real-valued functions that encode the persistence of topological patterns, are captured via Lp norm. The time series of the Lp norms shows that it is better at measuring the dynamics of returns than the standard deviation. Inspired by our findings, we explore an application of TDA in Enhanced Indexing (EI) that aims to build a portfolio of fewer assets than that in the index to outperform the latter. We propose a two-step procedure to accomplish this task. In step one, we utilize the Lp norms of the assets to propose a filtration technique of selecting a few assets from a larger pool of assets. In step two, we propose an optimization model to construct an optimal portfolio from the class of filtered assets for EI. To test the efficiency of this enhanced algorithm, experiments are carried out on ten data sets from financial markets across the globe. Our extensive empirical analysis exhibits that the proposed strategy delivers superior performance on several measures, including excess mean returns from the benchmark index and tail reward-risk ratios than some of the existing models of EI in the literature. The proposed filtering strategy is also noted to be beneficial for both risk-seeking and risk-averse investors

A note on the calculation of default probabilities in Structural credit risk modeling with Hawkes jump-diffusion processes

2020 Elsevier B.V. Ma and Xu (2016) proposed a Hawkes jump-diffusion model for the firm\u27s value to describe the unexpectedness of default and default clustering in the framework of Merton\u27s structural default. However, the authors resorted to Monte-Carlo simulations for the calculation of the default probability and the default correlation, as no other solution method was available in the literature. In this note, we present a closed-form solution for the probability of default and the default correlation using the characteristic function. Our new solution can substantially improve the computational efficiency for the problem

Gluteal Thigh Flap Coverage In Pressure Sores

Single stage successful and easy closure of Ischial and trochantric pressure sores is now possible with use of a gluteal thigh flap. Experience of six cases, so treated is presented