Option Valuation in Life Insurance

Table of Contents

Introduction

The impact of the German Tax Raises on the Importance of Options

A. The Role of Bonus Payments in Capital Forming Life Insurance Contracts

B. A Model of Bonus Payments to attract New Customers

1. Legal Framework

2. Model

C. The influence of the change in law on the profit sharing in 2005

D. Numerical results

Implicit Options in Life Insurance

E. Options in Financial Theory

F. Implicit options

G. Classification of options in life insurance according to the risk type

1. Risk-free Options

2. Actuarial Risks

3. Financial Risks

H. Classification of the Most Common Options

1. Risk-free Options

2. Actuarial Options

3. Financial Options

Basic Models of Option Valuation.

I. Equity Option Models

1. Black-Scholes Model

2. Binomial Tree Model of Cox, Ross and Rubinstein

3. Risk neutral valuation

J. Interest Rate Option Models

1. Hull-White Model

Models of the Valuation of the American Options in Life Insurance

K. Tribinomial tree for the interest rate and asset process

L. Valuation of the Surrender Option in Capital Forming Life Insurance

1. The model

2. Numerical Results

M. Grosen-Jorgensen Approach

N. Longstaff and Schwartz Approach

Conclusion

Research Objectives and Key Topics

This master's thesis analyzes the valuation of implicit options in German life insurance contracts, particularly in the context of changing tax laws effective from 2005. It aims to determine how insurers adapt their bonus payment strategies in a competitive market and why the proper valuation of embedded options is essential for maintaining corporate solvency.

• The impact of tax legislative changes on German life insurance products.
• Mechanism and modeling of bonus payments as a marketing tool.
• Classification of implicit options based on actuarial and financial risk.
• Valuation models for American-style options using tree-based approaches.
• Sensitivity analysis of surrender options in capital-forming life insurance.

Excerpt from the Book

Summary of Chapters

Introduction: Outlines the challenges facing the capital-forming life insurance market in Germany due to the end of tax privileges and the resulting focus on implicit options.

The impact of the German Tax Raises on the Importance of Options: Explains the necessity of modeling bonus payments as an investment to attract new customers and how tax changes shift competitive focus.

Implicit Options in Life Insurance: Defines implicit options and classifies them into risk-free, actuarial, and financial categories based on their risk profiles for the insurer.

Basic Models of Option Valuation.: Introduces classical models including Black-Scholes and Binomial trees for equity and interest rate derivatives.

Models of the Valuation of the American Options in Life Insurance: Describes advanced tree-based modeling methods, specifically the tribinomial tree for estimating American options.

Conclusion: Synthesizes the findings, asserting that insurers must shift focus toward proper pricing of embedded options to avoid future liabilities.

Keywords

Life insurance, Option valuation, Implicit options, Bonus payments, Tax change 2005, Capital-forming insurance, Solvency, Actuarial risk, Financial risk, Surrender option, Hull-White model, Tribinomial tree, Risk-neutral valuation, Competitive market.

Frequently Asked Questions

What is the primary focus of this thesis?

The work examines how German life insurance companies manage and value implicit options within their contracts, especially in light of the 2005 tax law changes that reduced the attractiveness of traditional profit-sharing policies.

What are the main thematic fields?

The core themes include the economics of insurance bonus payments, the classification of contract-embedded options based on risk, and the application of financial mathematics to value these liabilities.

What is the central research question?

The research investigates how insurers can effectively price implicit options to remain competitive and solvent when traditional profit-sharing mechanisms (bonus payments) lose their effectiveness due to legislative shifts.

Which scientific methods are used?

The author utilizes standard option pricing theory, including Black-Scholes, Binomial trees, and advanced Tribinomial tree modeling, to conduct numerical analyses and sensitivity testing of insurance contract features.

What is covered in the main body of the work?

The main part covers the legal framework of profit sharing, the classification of various options, and detailed technical valuation methods for American options in life insurance settings.

Which keywords characterize this work?

The work is characterized by terms such as option valuation, implicit options, surrender options, and the impact of German tax regulations on life insurance strategy.

How does the tax change affect the bonus policy?

The 2005 tax reform forces insurers to decrease bonus rates because the tax-advantaged status of older contracts creates an intense, temporary competitive pressure that will fade, rendering current high bonus payments unsustainable.

What is the role of the "Tribinomial tree" in this study?

The tribinomial tree is used as a superior modeling tool that accounts for both interest rate and asset price processes simultaneously, allowing for more precise valuation of American options compared to simpler models.