Solvency II. A comparison of the standard model with internal models to calculate the Solvency Capital Requirements (SCR)

Table of Contents

1 Introduction

2 Solvency II

2.1 The need for a new solvency regime

2.2 Basic architecture of Solvency II

2.2.1 Pillar I: Quantitative Requirements

2.2.2 Pillar II: Qualitative Requirements

2.2.3 Pillar III: Transparency Requirements

3 Solvency Capital Requirements

3.1 The Solvency Balance Sheet

3.2 Definition of SCR

3.3 Standard Model

3.3.1 Basic Solvency Capital Requirements

3.3.2 Market Risk Module

3.3.2.1 Interest Rate Risk

3.3.2.2 Equity Risk

3.3.2.3 Property Risk

3.3.2.4 Currency Risk

3.3.2.5 Spread Risk

3.3.2.6 Concentration Risk

3.3.2.7 Illiquidity Risk

3.3.3 Life Module

3.3.3.1 Mortality Risk

3.3.3.2 Longevity Risk

3.3.3.3 Disability and Morbidity Risk

3.3.3.4 Lapse Risk

3.3.3.5 Expense Risk

3.3.3.6 Revision Risk

3.3.3.7 CAT Risk

3.3.4 Non-Life Module

3.3.4.1 Premium and Reserve Risk

3.3.4.2 Non-Life Lapse Risk

3.3.4.3 Non-Life CAT Risk

3.3.5 Counterparty Default Risk

3.3.6 Intangible Asset Risk Module

3.3.7 Operational Risk

3.4 Internal Model

3.4.1 The Internal Model Approval Process

3.5 Summary

4 Current Topics on Solvency II

4.1 Long Term Guarantee Assessments

5 Quantitative Comparison

5.1 Literature Review

5.2 Research Question

5.3 Model Framework

5.3.1 Calculating SCR in the standard approach

5.3.2 Calculating SCR in the internal approach

5.4 Input parameter and calibration

5.5 Results

6 Conclusion

Objectives and Core Topics

This thesis examines the regulatory framework of Solvency II, specifically focusing on the methodologies for calculating the Solvency Capital Requirements (SCR). The primary objective is to perform a quantitative comparison between the standardized model provided by the regulator and internally developed stochastic models, analyzing how different asset portfolio compositions impact capital requirements for life insurers.

• Comparison of the Standard Model versus Internal Models under Solvency II.
• Detailed analysis of the Market Risk Module and its components.
• Scenario-based analysis of asset classes including stocks, real estate, and bonds.
• Impact of asset quality and portfolio weighting on calculated risk capital.
• Discussion of the internal model approval process and regulatory governance.

Excerpt from the Book

Summary of Chapters

1 Introduction: Provides an overview of the Solvency II Directive, its background, and the goal of establishing a market-consistent risk management framework for European insurers.

2 Solvency II: Details the necessity for a new regulatory regime and explains the three-pillar architecture including quantitative, qualitative, and transparency requirements.

3 Solvency Capital Requirements: Defines the Solvency Balance Sheet and the SCR, describing both the standard model and internal model approaches to quantifying risks.

4 Current Topics on Solvency II: Discusses the Long Term Guarantee Assessments (LTGA) and various measures implemented to address volatility and market stress.

5 Quantitative Comparison: Presents the literature review, research methodology, model framework, and the numerical results comparing the standard and internal models.

6 Conclusion: Summarizes the key findings, highlighting that while internal models often result in lower SCRs, they require significant expertise and supervisory approval.

Keywords

Solvency II, Solvency Capital Requirements, SCR, Standard Model, Internal Model, Market Risk, Life Insurance, Value-at-Risk, Asset Management, Risk Governance, Quantitative Impact Studies, QIS5, Capital Adequacy, Financial Regulation, Risk Sensitivity.

Frequently Asked Questions

What is the core focus of this master thesis?

The thesis focuses on comparing the standard model and internal models for calculating the Solvency Capital Requirements (SCR) under the Solvency II Directive for European life insurers.

What are the primary areas of risk addressed?

The work primarily addresses market risks, including interest rate, equity, property, currency, and spread risks, while also touching upon life underwriting and operational risks.

What is the main objective of the research?

The objective is to identify in which portfolio constellations the SCR varies between the standard and internal model approaches, and how sensitive these models are to changes in asset allocation.

What scientific methods are utilized?

The author uses a stochastic simulation approach, applying the Cox-Ingersoll-Ross (CIR) model for interest rates and Geometric Brownian Motion (GBM) for other asset classes to perform numerical scenario analyses.

What content is covered in the main section?

The main section covers the architecture of Solvency II, the definition of SCR, detailed breakdown of standard formula sub-modules, the internal model approval process, and the quantitative analysis of asset portfolios.

Which keywords best characterize this research?

Key terms include Solvency II, SCR, Market Risk, Standard Model, Internal Model, Life Insurance, Value-at-Risk, and Capital Allocation.

Why are internal models considered more complex than the standard model?

Internal models require advanced mathematical modeling, significant IT resources, expert personnel, and a rigorous, time-consuming approval process by national supervisory authorities.

How do the results typically differ between the two models?

The research indicates that the standard model often overestimates risk compared to internal models, though internal models are highly sensitive to specific asset quality and volatility parameters.