Fixed Income

Enhancing path-integral approximation for non-linear diffusion with neural network ArXiv ID: 2404.08903 “View on arXiv” Authors: Unknown Abstract Enhancing the existing solution for pricing of fixed income instruments within Black-Karasinski model structure, with neural network at various parameterisation points to demonstrate that the method is able to achieve superior outcomes for multiple calibrations across extended projection horizons. Keywords: Black-Karasinski Model, Fixed Income Pricing, Neural Networks, Interest Rate Models, Fixed Income Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper employs advanced mathematical concepts including path integrals, Taylor series expansions, and PDE approximations, but lacks empirical validation with backtests or statistical metrics, focusing instead on theoretical model formulation. flowchart TD A["Research Goal"] --> B["Data & Calibration"] A --> C["Methodology"] B --> D["Path-Integral Approx."] C --> D D --> E["Neural Network Enh."] E --> F["Computational Process"] F --> G["Key Outcomes"] subgraph Inputs A B C end subgraph Processing D E F end subgraph Results G end

The PEAL Method: a mathematical framework to streamline securitization structuring ArXiv ID: 2404.05372 “View on arXiv” Authors: Unknown Abstract Securitization is a financial process where the cash flows of income-generating assets are sold to institutional investors as securities, liquidating illiquid assets. This practice presents persistent challenges due to the absence of a comprehensive mathematical framework for structuring asset-backed securities. While existing literature provides technical analysis of credit risk modeling, there remains a need for a definitive framework detailing the allocation of the inbound cash flows to the outbound positions. To fill this gap, we introduce the PEAL Method: a 10-step mathematical framework to streamline the securitization structuring across all time periods. The PEAL Method offers a rigorous and versatile approach, allowing practitioners to structure various types of securitizations, including those with complex vertical positions. By employing standardized equations, it facilitates the delineation of payment priorities and enhances risk characterization for both the asset and the liability sides throughout the securitization life cycle. In addition to its technical contributions, the PEAL Method aims to elevate industry standards by addressing longstanding challenges in securitization. By providing detailed information to investors and enabling transparent risk profile comparisons, it promotes market transparency and enables stronger regulatory oversight. In summary, the PEAL Method represents a significant advancement in securitization literature, offering a standardized framework for precision and efficiency in structuring transactions. Its adoption has the potential to drive innovation and enhance risk management practices in the securitization market. ...

Revisiting Elastic String Models of Forward Interest Rates ArXiv ID: 2403.18126 “View on arXiv” Authors: Unknown Abstract Twenty five years ago, several authors proposed to describe the forward interest rate curve (FRC) as an elastic string along which idiosyncratic shocks propagate, accounting for the peculiar structure of the return correlation across different maturities. In this paper, we revisit the specific “stiff’’ elastic string field theory of Baaquie and Bouchaud (2004) in a way that makes its micro-foundation more transparent. Our model can be interpreted as capturing the effect of market forces that set the rates of nearby tenors in a self-referential fashion. The model is parsimonious and accurately reproduces the whole correlation structure of the FRC over the time period 1994-2023, with an error around 1% and with only one adjustable parameter, the value of which being very stable across the last three decades. The dependence of correlation on time resolution (also called the Epps effect) is also faithfully reproduced within the model and leads to a cross-tenor information propagation time on the order of 30 minutes. Finally, we confirm that the perceived time in interest rate markets is a strongly sub-linear function of real time, as surmised by Baaquie and Bouchaud (2004). In fact, our results are fully compatible with hyperbolic discounting, in line with the recent behavioral Finance literature (Farmer and Geanakoplos, 2009). ...

A Unifying Approach for the Pricing of Debt Securities ArXiv ID: 2403.06303 “View on arXiv” Authors: Unknown Abstract We propose a unifying framework for the pricing of debt securities under general time-inhomogeneous short-rate diffusion processes. The pricing of bonds, bond options, callable/putable bonds, and convertible bonds (CBs) is covered. Using continuous-time Markov chain (CTMC) approximations, we obtain closed-form matrix expressions to approximate the price of bonds and bond options under general one-dimensional short-rate processes. A simple and efficient algorithm is also developed to price callable/putable debt. The availability of a closed-form expression for the price of zero-coupon bonds allows for the perfect fit of the approximated model to the current market term structure of interest rates, regardless of the complexity of the underlying diffusion process selected. We further consider the pricing of CBs under general bi-dimensional time-inhomogeneous diffusion processes to model equity and short-rate dynamics. Credit risk is also incorporated into the model using the approach of Tsiveriotis and Fernandes (1998). Based on a two-layer CTMC method, an efficient algorithm is developed to approximate the price of convertible bonds. When conversion is only allowed at maturity, a closed-form matrix expression is obtained. Numerical experiments show the accuracy and efficiency of the method across a wide range of model parameters and short-rate models. ...

Contagion on Financial Networks: An Introduction ArXiv ID: 2402.08071 “View on arXiv” Authors: Unknown Abstract This mini-project models propagation of shocks, in time point, through links in connected banks. In particular, financial network of 100 banks out of which 15 are shocked to default (that is, 85.00% of the banks are solvent) is modelled using Erdos and Renyi network – directed, weighted and randomly generated network. Shocking some banks in a financial network implies removing their assets and redistributing their liabilities to other connected ones in the network. The banks are nodes and two ranges of probability values determine tendency of having a link between a pair of banks. Our major finding shows that the ranges of probability values and banks’ percentage solvency have positive correlation. ...

Structured factor copulas for modeling the systemic risk of European and United States banks ArXiv ID: 2401.03443 “View on arXiv” Authors: Unknown Abstract In this paper, we employ Credit Default Swaps (CDS) to model the joint and conditional distress probabilities of banks in Europe and the U.S. using factor copulas. We propose multi-factor, structured factor, and factor-vine models where the banks in the sample are clustered according to their geographic location. We find that within each region, the co-dependence between banks is best described using both, systematic and idiosyncratic, financial contagion channels. However, if we consider the banking system as a whole, then the systematic contagion channel prevails, meaning that the distress probabilities are driven by a latent global factor and region-specific factors. In all cases, the co-dependence structure of bank CDS spreads is highly correlated in the tail. The out-of-sample forecasts of several measures of systematic risk allow us to identify the periods of distress in the banking sector over the recent years including the COVID-19 pandemic, the interest rate hikes in 2022, and the banking crisis in 2023. ...

Improved Data Generation for Enhanced Asset Allocation: A Synthetic Dataset Approach for the Fixed Income Universe ArXiv ID: 2311.16004 “View on arXiv” Authors: Unknown Abstract We present a novel process for generating synthetic datasets tailored to assess asset allocation methods and construct portfolios within the fixed income universe. Our approach begins by enhancing the CorrGAN model to generate synthetic correlation matrices. Subsequently, we propose an Encoder-Decoder model that samples additional data conditioned on a given correlation matrix. The resulting synthetic dataset facilitates in-depth analyses of asset allocation methods across diverse asset universes. Additionally, we provide a case study that exemplifies the use of the synthetic dataset to improve portfolios constructed within a simulation-based asset allocation process. ...

Enhanced Local Explainability and Trust Scores with Random Forest Proximities ArXiv ID: 2310.12428 “View on arXiv” Authors: Unknown Abstract We initiate a novel approach to explain the predictions and out of sample performance of random forest (RF) regression and classification models by exploiting the fact that any RF can be mathematically formulated as an adaptive weighted K nearest-neighbors model. Specifically, we employ a recent result that, for both regression and classification tasks, any RF prediction can be rewritten exactly as a weighted sum of the training targets, where the weights are RF proximities between the corresponding pairs of data points. We show that this linearity facilitates a local notion of explainability of RF predictions that generates attributions for any model prediction across observations in the training set, and thereby complements established feature-based methods like SHAP, which generate attributions for a model prediction across input features. We show how this proximity-based approach to explainability can be used in conjunction with SHAP to explain not just the model predictions, but also out-of-sample performance, in the sense that proximities furnish a novel means of assessing when a given model prediction is more or less likely to be correct. We demonstrate this approach in the modeling of US corporate bond prices and returns in both regression and classification cases. ...

Robust Asset-Liability Management ArXiv ID: 2310.00553 “View on arXiv” Authors: Unknown Abstract How should financial institutions hedge their balance sheets against interest rate risk when managing long-term assets and liabilities? We address this question by proposing a bond portfolio solution based on ambiguity-averse preferences, which generalizes classical immunization and accommodates arbitrary liability structures, portfolio constraints, and interest rate perturbations. In a further extension, we show that the optimal portfolio can be computed as a simple generalized least squares problem, making the solution both transparent and computationally efficient. The resulting portfolio also reduces leverage by implicitly regularizing the portfolio weights, which enhances out-of-sample performance. Numerical evaluations using both empirical and simulated yield curves support the feasibility and accuracy of our approach relative to existing methods. ...

DeFi: Shadow Banking 2.0? ArXiv ID: ssrn-4038788 “View on arXiv” Authors: Unknown Abstract The growth of so-called “shadow banking” was a significant contributor to the financial crisis of 2008, which had huge social costs that we still grapple with t Keywords: shadow banking, financial crisis, systemic risk, regulatory arbitrage, non-bank financial intermediation, Fixed Income Complexity vs Empirical Score Math Complexity: 0.5/10 Empirical Rigor: 1.0/10 Quadrant: Philosophers Why: The paper is a legal/regulatory analysis using historical case studies and conceptual arguments, with no mathematical modeling or empirical backtesting. flowchart TD A["Research Goal"] --> B["DeFi as Shadow Banking?"] B --> C["Methodology"] C --> D["Empirical Analysis"] D --> E["Data: Tether Reserves & Fixed Income"] E --> F["Computational Process"] F --> G["Correlation & Stress Tests"] G --> H["Findings"] H --> I["Systemic Risk & Regulatory Arbitrage"]