Hybrid Derivatives Hedge Engine for Variable Annuity Cross-Gamma Risk

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Solution Overview

Problem

Current hedging programs for variable annuity guarantees are incomplete and uncertain, particularly in managing higher-order and cross-gamma exposures, leading to inefficiencies and increased risk for insurance companies due to the high correlation among contracts, which has resulted in reinsurers withdrawing from covering such risks.

Innovation Solution

The use of hybrid derivatives that embed equity and interest rate exposure to mitigate cross-gamma exposure, combined with a hedging engine that calculates and adjusts hedge positions based on first-order, higher-order, and cross-gamma values to effectively manage risks associated with variable annuity contracts.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If traditional hedging programs are used for variable annuity guarantees, then basic risk coverage is provided, but higher-order and cross-gamma exposures remain unmanaged leading to hedge inefficiency

Engineering Contradiction:

Improverisk coverage completenessVSAvoidhedge inefficiency

Core Design Contradiction:

ReliabilityVSLoss of energy

Solution Approach 1:

The patent applies parameter changes by transitioning from traditional first-order hedging parameters to include higher-order and cross-gamma parameters. The hedging system dynamically adjusts hedge ratios based on calculated higher-order derivatives and cross-gamma exposures, transforming the hedging approach to account for non-linear risk factors that traditional methods overlook, thereby eliminating hedge inefficiency while maintaining reliability.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent introduces an intermediary hedging engine that calculates higher-order and cross-gamma exposures and uses hybrid derivatives as intermediate instruments to bridge the gap between traditional hedging and comprehensive risk coverage. This intermediary system processes complex risk measurements and translates them into actionable hedge positions, enabling management of previously unmanageable risk factors.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If variable annuity guarantees are issued, then customer protection is enhanced, but insurance companies face increased economic losses due to high correlation among contracts

Engineering Contradiction:

Improvecustomer protectionVSAvoideconomic losses

Core Design Contradiction:

ReliabilityVSLoss of energy

Solution Approach 1:

The patent applies dynamics by implementing a dynamic hedging system that continuously recalibrates hedge positions based on changing market conditions and contract correlations. The system dynamically adjusts hedge ratios to account for the high correlation among variable annuity contracts, transforming static risk exposure into manageable dynamic positions that adapt to market movements, thereby reducing economic losses while maintaining customer protection.

Inventive Principle:

Principle #15Dynamics

Solution Approach 2:

The patent employs composite materials by combining multiple hedging instruments including equity derivatives, interest rate derivatives, and hybrid derivatives into a composite hedging portfolio. This composite approach diversifies the hedging strategy across different asset classes and risk factors, reducing the impact of high contract correlations and minimizing economic losses while preserving the protective function of variable annuity guarantees.

Inventive Principle:

Principle #40Composite materials

3Adaptability or versatility

If reinsurers withdraw from covering variable annuity risks, then insurance companies must self-insure, but this increases risk concentration and reduces ability to cover liabilities

Engineering Contradiction:

Improverisk transfer capabilityVSAvoidliability coverage ability

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The patent introduces an intermediary hybrid derivative instrument that mediates between insurance companies and the broader financial markets. These hybrid derivatives serve as intermediaries that translate variable annuity risk exposures into tradable financial instruments, enabling insurance companies to transfer risk to capital markets participants who can price and manage the correlated risk, thereby restoring risk transfer capability and enhancing liability coverage ability.

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent applies universality by designing hybrid derivatives with multi-functional characteristics that can serve multiple hedging objectives simultaneously. These instruments provide both protection against equity market movements and interest rate changes, while also addressing the specific needs of variable annuity guarantees, making them versatile tools that can be used across different risk management scenarios and enhancing the insurance company's overall risk transfer capability.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS9171332B2Equity/interest rate hybrid risk mitigation system and method

Publication Date: 2015.10.27 HARTFORD FIRE INSURANCE CO

AI summary

The present invention provides a method and system for determining hedging transactions to meet required characteristics of risks associated with an insurance instrument, and mitigating the risks associated with the insurance instrument by executing hedging transactions. The hedging transactions utilize hybrid derivatives. In general, the equity/interest rate hybrid derivative concept encapsulates any derivative, or any investment vehicle with an embedded derivative, that contains a payoff formula(s). At a minimum the formula(s), is/are a function of two items: equities, and any interest rates.