We develop a singular stochastic control model for pricing variable annuities with the guaranteed minimum withdrawal benefit. This benefit promises to return the entire initial investment, with withdrawals spread over the term of the contract, irrespective of the market performance of the underlying asset portfolio. A contractual withdrawal rate is set and no penalty is imposed when the policyholder chooses to withdraw at or below this rate. Subject to a penalty fee, the policyholder is allowed to withdraw at a rate higher than the contractual withdrawal rate or surrender the policy instantaneously. We explore the optimal withdrawal strategy adopted by the rational policyholder that maximizes the expected discounted value of the cash flows generated from holding this variable annuity policy. An effcient finite difference algorithm using the penalty approximation approach is proposed for solving the singular stochastic control model. Optimal withdrawal policies of the holders of the variable annuities with the guaranteed minimum withdrawal benefit are explored. We also construct discrete pricing formulation that models withdrawals on discrete dates. Our numerical tests show that the solution values from the discrete model converge to those of the continuous model.

/pdf/guaranteed-minimum-withdrawal-benefit-in-variable-annuities-zryyq44w09.pdf

Guaranteed Minimum Withdrawal Benefit in Variable Annuities

Life annuities and pension products usually involve a number of guarantees, such as minimum accumulation rates, minimum annual payments or a minimum total payout. Packaging different types of guarantees is the feature of so-called variable annuities. Basically, these products are unit-linked investment policies providing a post-retirement income. The guarantees, commonly referred to as GMxBs (namely, Guaranteed Minimum Benefits of type ‘x’), include minimum benefits both in the case of death and survival. In this paper we propose a unifying framework for the valuation of variable annuities under quite general model assumptions. We compute and compare contract values and fair fee rates under ‘static’ and ‘mixed’ valuation approaches, via ordinary and least squares Monte Carlo methods, respectively.

Variable annuities: A unifying valuation approach

Life annuities and pension products usually involve a number of guarantees, such as minimum accumulation rates, minimum annual payments or a minimum total payout. Packaging different types of guarantees is the feature of so-called variable annuities. Basically, these products are unit-linked investment policies providing a post-retirement income. The guarantees, commonly referred to as GMxBs (namely, Guaranteed Minimum Benefits of type 'x'), include minimum benefits both in case of death and survival. In this paper we propose a unifying framework for the valuation of variable annuities under quite general model assumptions. We compute and compare contract values and fair fee rates under 'static' and 'mixed' valuation approaches, via ordinary and least squares Monte Carlo methods, respectively.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1810522_code437995.pdf?abstractid=1810522&type=2

Variable Annuities: A Unifying Valuation Approach

Purpose – The purpose of this paper is to review research on lapse in life insurance and to outline potential new areas of research in this field.Design/methodology/approach – The authors consider theoretical lapse rate models as well as empirical research on life insurance lapse and provide a classification of these two streams of research. More than 50 theoretical and empirical papers from this important field of research are reviewed. Challenges for lapse rate modeling, lapse risk mitigation techniques, and possible trends in future lapse behavior are discussed.Findings – Lapse rate modeling has been a very active field of research in the last years, as evidenced by the 44 papers on lapse modeling considered in this review. Moreover, a fair amount of empirical work (another 12 papers) has been done, especially on the issue of how environmental variables affect lapse. Research on individual policyholder and contract information is more scarce, since such information is typically treated as confidential....

/pdf/research-on-lapse-in-life-insurance-what-has-been-done-and-3kx5srcvh5.pdf

Research on lapse in life insurance: what has been done and what needs to be done?

Policyholder exercise behavior presents an important risk factor for pricing Variable Annuities. However, approaches presented in the literature—building on value-maximizing strategies akin to pricing American options—do not square with observed price and exercise patterns for popular withdrawal guarantees. We show that including taxes into the valuation closes this gap between theory and practice. In particular, we develop a subjective risk-neutral valuation methodology that takes into consideration differences in the tax structure between investment opportunities. We demonstrate that accounting for tax advantages significantly affects the value of the guarantees and produces results that are in line with empirical patterns.

Revisiting the Risk-Neutral Approach to Optimal Policyholder Behavior: A Study of Withdrawal Guarantees in Variable Annuities

In this article, an extensive study of the no-arbitrage fee for Guaranteed Minimum Withdrawal Benefit (GMWB) variable annuity riders is carried out. The value of the GMWB guarantee increases substantially when taking into account the separation of mutual fund fees and the fees earmarked for hedging the guarantee. In addition, the fee is also adversely affected if the underlying risky asset follows a jump diffusion process. We also explore the effects of various modelling assumptions on the optimal withdrawal strategy of the contract holder, as well as the impact on the guarantee value of sub-optimal withdrawal behaviour. Our general conclusions are that only if several unrealistic modelling assumptions are made is it possible to obtain GMWB fees in the same range as is normally charged. In all other cases, it would appear that typical fees are not enough to cover the cost of hedging these guarantees.

/pdf/the-effect-of-modelling-parameters-on-the-value-of-gmwb-54bepo7juz.pdf

The effect of modelling parameters on the value of GMWB guarantees

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Z. Chen

Author Tools

Chat about Author

Papers

The effect of modelling parameters on the value of GMWB guarantees