Paper: arXiv 2409.12783

Authors: Mohamed Ben Alaya, Ahmed Kebaier, Djibril Sarr

Abstract

This research presents a comprehensive framework for transitioning financial diffusion models from the risk-neutral (RN) measure to the real-world (RW) measure, leveraging results from probability theory, specifically Girsanov’s theorem. The RN measure, fundamental in derivative pricing, is contrasted with the RW measure, which incorporates risk premiums and better reflects actual market behavior and investor preferences, making it crucial for risk management. We address the challenges of incorporating real-world dynamics into financial models, such as accounting for market premiums, producing realistic term structures of market indicators, and fitting any arbitrarily given market curve. Our framework is designed to be general, applicable to a variety of diffusion models, including those with non-additive noise such as the CIR++ model. Through case studies involving Goldman Sachs’ 2024 global credit outlook forecasts and the European Banking Authority (EBA) 2023 stress tests, we validate the robustness, practical relevance and applicability of our methodology. This work contributes to the literature by providing a versatile tool for better risk measures and enhancing the realism of financial models under the RW measure. Our model’s versatility extends to stress testing and scenario analysis, providing practitioners with a powerful tool to evaluate various what-if scenarios and make well-informed decisions, particularly in pricing and risk management strategies.

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 mathematically solid framework using Girsanov’s theorem and Lamperti transforms to shift diffusion models from risk-neutral to real-world measures. It extends existing interest-rate literature to credit spreads and non-additive noise models like CIR++, backed by practical case studies using Goldman Sachs credit forecasts and EBA stress tests.

Research Flowchart

  flowchart TD
    A[Research Goal: Transition Diffusion Models from Risk-Neutral to Real-World Measure] --> B[Inputs: Market Curves & Stress Data<br><i>GS 2024 Outlook, EBA 2023 Tests</i>]
    B --> C[Theoretical Framework: Apply Girsanov's Theorem]
    C --> D[Computational Engine: Measure Transformation for Models<br><i>e.g., CIR++ with Non-Additive Noise</i>]
    D --> E[Outcomes: Real-World Scenarios & Risk Management<br><i>Stress Testing, Market Premiums, Term Structures</i>]

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0 of 55 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.