Paper: arXiv 2410.02645

Authors: Ankush Agarwal, Ying Liao

Abstract

We derive a closed-form approximation for the credit default swap (CDS) spread in the two-dimensional shifted square-root diffusion (SSRD) model using asymptotic coefficient expansion technique to approximate solutions of nonlinear partial differential equations. Specifically, we identify the Cauchy problems associated with two terms in the CDS spread formula that lack analytical solutions and derive asymptotic approximations for these terms. Our approximation does not require the assumption of uncorrelated interest rate and default intensity processes as typically required for calibration in the SSRD model. Through several calibration studies using market data on CDS spread, we demonstrate the accuracy and efficiency of our proposed formula.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous analytical contribution by deriving closed-form asymptotic expansions for nonlinear PDEs in a correlated two-dimensional SSRD framework. It addresses a key limitation in previous literature by relaxing the uncorrelation assumption between interest rates and default intensity, validating the method via empirical calibration to CDS spread market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Efficient CDS Spread Calibration in 2D SSRD Model without Uncorrelated Assumptions] --> B[Data Inputs: Market CDS Spreads & Financial Parameters]
    B --> C[Formulate SSRD Model & Identify Intractable Cauchy Problems]
    C --> D[Apply Asymptotic Coefficient Expansion Technique]
    D --> E[Derive Closed-Form CDS Spread Approximation Formula]
    E --> F[Calibration Studies & Performance Evaluation]
    F --> G[Key Outcomes: High Calibration Accuracy, Speed & Support for Correlated Factors]