On the Calculation of Risk Measures for Variable Annuities with Guaranteed Benefits PDF Download
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Author: Lei Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
With the development of the life insurance industry, different types of life insurance products, in addition to the traditional ones, are being developed. A common and well-known life insurance product is the variable annuity with different types of guaranteed benefit riders, which provides policyholders a high rate of investment return with downside risk protections. Two typical distortion risk measures, VaR (value at risk) and CTE (conditional tail expectation), are widely used to manage insurers' future liabilities to avoid the potential of insolvency. In this project, we consider variable annuities with certain types of guaranteed benefits and various asset price processes, and focus on the calculation of the two risk measures of insurers' net and gross liabilities at the maturity date. Specifically, we consider two types of guaranteed benefit riders, the guaranteed minimum death benefit (GMDB) and the guaranteed minimum maturity benefit (GMMB), and assume that the logarithm of underlying asset returns follows a Cauchy or a skew-normal distribution. Analytical expressions of VaR and CTE for insurers' future liabilities are obtained, and numerical calculation algorithms are proposed. Comparisons of the calculated risk measure results with that under the normal distribution are also presented.
Author: Lei Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
With the development of the life insurance industry, different types of life insurance products, in addition to the traditional ones, are being developed. A common and well-known life insurance product is the variable annuity with different types of guaranteed benefit riders, which provides policyholders a high rate of investment return with downside risk protections. Two typical distortion risk measures, VaR (value at risk) and CTE (conditional tail expectation), are widely used to manage insurers' future liabilities to avoid the potential of insolvency. In this project, we consider variable annuities with certain types of guaranteed benefits and various asset price processes, and focus on the calculation of the two risk measures of insurers' net and gross liabilities at the maturity date. Specifically, we consider two types of guaranteed benefit riders, the guaranteed minimum death benefit (GMDB) and the guaranteed minimum maturity benefit (GMMB), and assume that the logarithm of underlying asset returns follows a Cauchy or a skew-normal distribution. Analytical expressions of VaR and CTE for insurers' future liabilities are obtained, and numerical calculation algorithms are proposed. Comparisons of the calculated risk measure results with that under the normal distribution are also presented.
Author: Zhenyu Cui
Publisher:
ISBN:
Category :
Languages : en
Pages : 35
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Book Description
In this paper, we propose an efficient approach to the calculation of risk measures for an insurer's liability from writing a variable annuity with guaranteed benefits. Our approach is based on a novel application of the Hermite series expansions on the transition density of a diffusion process to the insurance setting. We compare our method with existing methods in the literature, including the analytical method, the spectral method and the Green's function method, and illustrate its substantial advantages in calculating risk measures for variable annuities with different guarantee structures. The gained efficiency makes our method flexible to practical implementation in reporting risk measures on a daily basis. We also conduct sensitivity analysis of the risk measures with respect to key parameters.
Author: Runhuan Feng
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benefits. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so much time that they cannot obtain information and take actions in a timely manner. In an attempt to find low-cost and efficient alternatives, we explore the techniques of comonotonic bounds to produce closed-form approximation of the risk measures for variable annuity guaranteed benefits. The techniques are further developed in this paper to address in a systematic way risk measures for death benefits with the consideration of dynamic policyholder behavior.
Author: Claymore James Marshall
Publisher:
ISBN:
Category :
Languages : en
Pages : 276
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Book Description
A guaranteed minimum income benefit (GMIB) is a long-dated option that can be embedded in a deferred variable annuity. The GMIB is attractive because, for policyholders who plan to annuitize, it offers protection against poor market performance during the accumulation phase, and adverse interest rate experience at annuitization. The GMIB also provides an upside equity guarantee that resembles the benefit provided by a lookback option. We price the GMIB, and determine the fair fee rate that should be charged. Due to the long dated nature of the option, conventional hedging methods, such as delta hedging, will only be partially successful. Therefore, we are motivated to find alternative hedging methods which are practicable for long-dated options. First, we measure the effectiveness of static hedging strategies for the GMIB. Static hedging portfolios are constructed based on minimizing the Conditional Tail Expectation of the hedging loss distribution, or minimizing the mean squared hedging loss. Next, we measure the performance of semi-static hedging strategies for the GMIB. We present a practical method for testing semi-static strategies applied to long term options, which employs nested Monte Carlo simulations and standard optimization methods. The semi-static strategies involve periodically rebalancing the hedging portfolio at certain time intervals during the accumulation phase, such that, at the option maturity date, the hedging portfolio payoff is equal to or exceeds the option value, subject to an acceptable level of risk. While we focus on the GMIB as a case study, the methods we utilize are extendable to other types of long-dated options with similar features.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Runhuan Feng
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
The stochastic modeling and determination of reserves and risk capitals for variable annuity guarantee products are relatively new developments in the insurance industry. The current market practice is largely based on Monte Carlo simulations, which have great engineering flexibility but the demand for heavy computational power can be prohibitive in many cases. In this paper, we distinguish and compare two types of risk models to determine the commonly used risk measures for reserving and capital calculations. Using an example of the guaranteed minimum maturity benefit, we investigate alternative numerical methods that require less computational resources and yet achieves high accuracy and efficiency.
Author: Collectif
Publisher: OECD
ISBN: 9264267794
Category : Business & Economics
Languages : en
Pages : 108
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Book Description
This publication helps policy makers to better understand annuity products and the guarantees they provide in order to optimise the role that these products can play in financing retirement. Product design is a crucial factor in the potential role of annuity products within the pension system, along with the cost and demand for these products, and the resulting risks that are borne by the annuity providers. Increasingly complex products, however, pose additional challenges concerning consumer protection. Consumers need to be aware of their options and have access to unbiased and comprehensible advice and information about these products.
Author: Runhuan Feng
Publisher: CRC Press
ISBN: 1498742181
Category : Business & Economics
Languages : en
Pages : 382
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Book Description
The quantitative modeling of complex systems of interacting risks is a fairly recent development in the financial and insurance industries. Over the past decades, there has been tremendous innovation and development in the actuarial field. In addition to undertaking mortality and longevity risks in traditional life and annuity products, insurers face unprecedented financial risks since the introduction of equity-linking insurance in 1960s. As the industry moves into the new territory of managing many intertwined financial and insurance risks, non-traditional problems and challenges arise, presenting great opportunities for technology development. Today's computational power and technology make it possible for the life insurance industry to develop highly sophisticated models, which were impossible just a decade ago. Nonetheless, as more industrial practices and regulations move towards dependence on stochastic models, the demand for computational power continues to grow. While the industry continues to rely heavily on hardware innovations, trying to make brute force methods faster and more palatable, we are approaching a crossroads about how to proceed. An Introduction to Computational Risk Management of Equity-Linked Insurance provides a resource for students and entry-level professionals to understand the fundamentals of industrial modeling practice, but also to give a glimpse of software methodologies for modeling and computational efficiency. Features Provides a comprehensive and self-contained introduction to quantitative risk management of equity-linked insurance with exercises and programming samples Includes a collection of mathematical formulations of risk management problems presenting opportunities and challenges to applied mathematicians Summarizes state-of-arts computational techniques for risk management professionals Bridges the gap between the latest developments in finance and actuarial literature and the practice of risk management for investment-combined life insurance Gives a comprehensive review of both Monte Carlo simulation methods and non-simulation numerical methods Runhuan Feng is an Associate Professor of Mathematics and the Director of Actuarial Science at the University of Illinois at Urbana-Champaign. He is a Fellow of the Society of Actuaries and a Chartered Enterprise Risk Analyst. He is a Helen Corley Petit Professorial Scholar and the State Farm Companies Foundation Scholar in Actuarial Science. Runhuan received a Ph.D. degree in Actuarial Science from the University of Waterloo, Canada. Prior to joining Illinois, he held a tenure-track position at the University of Wisconsin-Milwaukee, where he was named a Research Fellow. Runhuan received numerous grants and research contracts from the Actuarial Foundation and the Society of Actuaries in the past. He has published a series of papers on top-tier actuarial and applied probability journals on stochastic analytic approaches in risk theory and quantitative risk management of equity-linked insurance. Over the recent years, he has dedicated his efforts to developing computational methods for managing market innovations in areas of investment combined insurance and retirement planning.
Author: Tigran Kalberer
Publisher:
ISBN: 9781906348212
Category : Annuities
Languages : en
Pages : 298
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Book Description
Variable Annuities provides an overview of all the relevant aspects of variable annuity (VA) products from an insurers perspective. It is a collection of contributions from several authors, co-ordinated in such a way that it covers all relevant areas with minimal overlap and a consistent level of detail.
Author: Jin Cheng
Publisher: Springer Nature
ISBN: 9811655766
Category : Technology & Engineering
Languages : en
Pages : 191
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Book Description
This volume includes selected technical papers presented at the Forum “Math-for-Industry” 2018. The papers written by eminent researchers and academics working in the area of industrial mathematics from the viewpoint of financial mathematics, machine learning, neural networks, inverse problems, stochastic modelling, etc., discuss how the ingenuity of science, technology, engineering and mathematics are and will be expected to be utilized. This volume focuses on the role that mathematics-for-industry can play in interdisciplinary research to develop new methods. The contents are useful for researchers both in academia and industry working in interdisciplinary sectors.
