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Dynamic Hedging Of Longevity Risk
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Book Synopsis Dynamic Hedging of Longevity Risk by : Hong Li
Download or read book Dynamic Hedging of Longevity Risk written by Hong Li and published by . This book was released on 2015 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates dynamic hedging strategies for liabilities that are exposed to longevity risk. In particular, we consider the case where a hedger wishes to minimize the variance of her hedging error using longevity-linked derivatives. Time-consistent, closed-form solutions of optimal hedging strategies are obtained under a forward mortality framework. To cope with the fact that liquidity of longevity-linked derivatives is still limited, we also consider a liquidity constrained case where the hedger can only trade longevity-linked derivatives at a low frequency. The performance of the hedging strategies is evaluated in a numerical study with parameter estimates from the existing literature. We show that lowering the trading frequency of the longevity-linked derivatives only leads to a slight loss of the hedging performance. Even when the longevity-linked derivatives can only be traded at a very low frequency, dynamic hedging strategies still significantly outperform the static hedging strategies.
Book Synopsis A Study on Longevity Risk Hedging in the Presence of Population Basis Risk by : Kenneth Qian Zhou
Download or read book A Study on Longevity Risk Hedging in the Presence of Population Basis Risk written by Kenneth Qian Zhou and published by . This book was released on 2015 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Longevity risk refers to uncertainty surrounding the trend in human life expectancy. Standardized hedging instruments that are linked to broad-based mortality indexes can be used to offload longevity risk from pension plans and annuities. However, hedges that are based on such instruments are subject to population basis risk, which arises from the difference in mortality improvements between the hedger's population and the reference population to which the hedging instruments are linked. This thesis attempts to address some issues that are related to longevity risk hedging in the presence of population basis risk. In the first chapter, a graphical risk metric is proposed to intuitively measure population basis risk, which is believed to be a major obstacle to market development. It allows market participants to not only visually evaluate the extent of population basis risk, but also determine the most appropriate reference population. Compared to existing population basis risk metrics which are mostly numerical, the proposed graphical risk metric is more informative in that it captures more aspects of population basis risk. Along with the existing numerical risk metrics, the proposed graphical risk metric may help hedgers better understand population basis risk and hence make their risk management decisions. In the second chapter, the feasibility of dynamic longevity hedging with standardized hedging instruments is studied. To this end, the dynamic hedging strategy developed by Cairns (2011) is generalized to incorporate the situation when the hedger's population and the reference population are different. The empirical results indicate that dynamic hedging can effectively reduce the longevity risk exposures of a typical pension plan, even if population basis risk is taken into account. Further, by considering data from a large group of national populations, it is found that population basis risk and small sample risk can possibly be diversified across different hedgers. Hedgers may therefore be able to completely eliminate their longevity risk exposures by removing the underlying trend risk with a dynamic index-based hedge and transferring the residual risks through a reinsurance mechanism.
Book Synopsis Optimal Dynamic Longevity Hedge with Basis Risk by : Chengguo Weng
Download or read book Optimal Dynamic Longevity Hedge with Basis Risk written by Chengguo Weng and published by . This book was released on 2020 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes an optimal dynamic strategy for hedging longevity risk in a discrete-time setting. Our proposed hedging strategy relies on standardized mortality-linked securities and minimizes the variance of the hedging error as induced by the population basis risk. While the formulation of our proposed hedging strategy is quite general, we use a stylized pension plan, together with a specified "yearly rolling” trading strategy involving q-forwards and a specified stochastic mortality model, to illustrate our proposed strategy. Under these specifications, we show that the resulting hedging problem can be formulated as a stochastic optimal control framework and that a semi-analytic solution can be derived through the Bellman equation. Extensive Monte Carlo studies are conducted to highlight the effectiveness of our proposed hedging strategy. We also consider a scheme to approximate the semi-analytic solution in order to reduce the computational time significantly while still retaining its hedging effectiveness. We benchmark our strategy against the "delta” hedging strategy as well as its robustness to q-forwards' maturity, reference age, and stochastic mortality models. The proposed strategy has many appealing features, including its discrete-time setting which is consistent with market practice and hence conducive to practical implementation, and its generality in that the underlying hedging principle can be applied to other standardized mortality-linked securities and other stochastic models.
Book Synopsis Basis Risk in Static Vs. Dynamic Longevity Risk Hedging by : Clemente De Rosa
Download or read book Basis Risk in Static Vs. Dynamic Longevity Risk Hedging written by Clemente De Rosa and published by . This book was released on 2015 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a simple model for basis risk in a longevity framework, by separating common and idiosyncratic risk factors. Basis risk is captured by a single parameter, that measures the co-movement between the portfolio and the reference population. In this framework, the paper sets out the static, swap-based hedge for an annuity, and compares it with the dynamic, delta-based hedge, achieved using longevity bonds. We assume that the longevity intensity is distributed according to a CIR-type process and provide closed-form derivatives prices and hedges, also in the presence of an analogous CIR process for interest rate risk.
Book Synopsis Longevity Risk Management by : Kenneth Qian Zhou
Download or read book Longevity Risk Management written by Kenneth Qian Zhou and published by . This book was released on 2019 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Longevity risk management is becoming increasingly important in the pension and life insurance industries. The unexpected mortality improvements observed in recent decades are posing serious concerns to the financial stability of defined-benefit pension plans and annuity portfolios. It has recently been argued that the overwhelming longevity risk exposures borne by the pension and life insurance industries may be transferred to capital markets through standardized longevity derivatives that are linked to broad-based mortality indexes. To achieve the transfer of risk, two technical issues need to be addressed first: (1) how to model the dynamics of mortality indexes, and (2) how to optimize a longevity hedge using standardized longevity derivatives. The objective of this thesis is to develop sensible solutions to these two questions. In the first part of this thesis, we focus on incorporating stochastic volatility in mortality modeling, introducing the notion of longevity Greeks, and analysing the properties of longevity Greeks and their applications in index-based longevity hedging. In more detail, we derive three important longevity Greeks--delta, gamma and vega--on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility. We also study the properties of each longevity Greek, and estimate the levels of effectiveness that different longevity Greek hedges can possibly achieve. The results reveal several interesting facts. For example, we found and explained that, other things being equal, the magnitude of the longevity gamma of a q-forward increases with its reference age. As with what have been developed for equity options, these properties allow us to know more about standardized longevity derivatives as a risk mitigation tool. We also found that, in a delta-vega hedge formed by q-forwards, the choice of reference ages does not materially affect hedge effectiveness, but the choice of times-to-maturity does. These facts may aid insurers to better formulate their hedge portfolios, and issuers of mortality-linked securities to determine what security structures are more likely to attract liquidity. We then move onto delta hedging the trend and cohort components of longevity risk under the M7-M5 model. In a recent project commissioned by the Institute and Faculty of Actuaries and the Life and Longevity Markets Association, a two-population mortality model called the M7-M5 model is developed and recommended as an industry standard for the assessment of population basis risk. We develop a longevity delta hedging strategy for use with the M7-M5 model, taking into account of not only period effect uncertainty but also cohort effect uncertainty and population basis risk. To enhance practicality, the hedging strategy is formulated in both static and dynamic settings, and its effectiveness can be evaluated in terms of either variance or 1-year ahead Value-at-Risk (the latter is highly relevant to solvency capital requirements). Three real data illustrations are constructed to demonstrate (1) the impact of population basis risk and cohort effect uncertainty on hedge effectiveness, (3) the benefit of dynamically adjusting a delta longevity hedge, and (3) the relationship between risk premium and hedge effectiveness. The last part of this thesis sets out to obtain a deeper understanding of mortality volatility and its implications on index-based longevity hedging. The volatility of mortality is crucially important to many aspects of index-based longevity hedging, including instrument pricing, hedge calibration, and hedge performance evaluation. We first study the potential asymmetry in mortality volatility by considering a wide range of GARCH-type models that permit the volatility of mortality improvement to respond differently to positive and negative mortality shocks. We then investigate how the asymmetry of mortality volatility may impact index-based longevity hedging solutions by developing an extended longevity Greeks framework, which encompasses longevity Greeks for a wider range of GARCH-type models, an improved version of longevity vega, and a new longevity Greek known as `dynamic delta'. Our theoretical work is complemented by two real-data illustrations, the results of which suggest that the effectiveness of an index-based longevity hedge could be significantly impaired if the asymmetry in mortality volatility is not taken into account when the hedge is calibrated.
Book Synopsis Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk by : Elisa Luciano
Download or read book Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk written by Elisa Luciano and published by . This book was released on 2015 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article provides natural hedging strategies for life insurance and annuity businesses written on a single generation or on different generations in the presence of both longevity and interest-rate risks. We obtain closed-form solutions for delta and gamma hedges against cohort-based longevity risk. We exploit the correlation between the mortality intensities of different generations and hedge the longevity risk of one cohort with products on other cohorts. An application with UK data on survivorship and bond dynamics shows that hedging is effective, even when rebalancing is infrequent.
Book Synopsis Risk Management with Basis Risk by : Jingong Zhang
Download or read book Risk Management with Basis Risk written by Jingong Zhang and published by . This book was released on 2018 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basis risk occurs naturally in a variety of financial and actuarial applications, and it introduces additional complexity to the risk management problems. Current literature on quantifying and managing basis risk is still quite limited, and one class of important questions that remains open is how to conduct effective risk mitigation when basis risk is involved and perfect hedging is either impossible or too expensive. The theme of this thesis is to study risk management problems in the presence of basis risk under three settings: 1) hedging equity-linked financial derivatives; 2) hedging longevity risk; and 3) index insurance design. First we consider the problem of hedging a vanilla European option using a liquidly traded asset which is not the underlying asset but correlates to the underlying and we investigate an optimal construction of hedging portfolio involving such an asset. The mean-variance criterion is adopted to evaluate the hedging performance, and a subgame Nash equilibrium is used to define the optimal solution. The problem is solved by resorting to a dynamic programming procedure and a change-of-measure technique. A closed-form optimal control process is obtained under a general diffusion model. The solution we obtain is highly tractable and to the best of our knowledge, this is the first time the analytical solution exists for dynamic hedging of general vanilla European options with basis risk under the mean-variance criterion. Examples on hedging European call options are presented to foster the feasibility and importance of our optimal hedging strategy in the presence of basis risk. We then explore the problem of optimal dynamic longevity hedge. From a pension plan sponsor's perspective, we study dynamic hedging strategies for longevity risk using standardized securities in a discrete-time setting. The hedging securities are linked to a population which may differ from the underlying population of the pension plan, and thus basis risk arises. Drawing from the technique of dynamic programming, we develop a framework which allows us to obtain analytical optimal dynamic hedging strategies to achieve the minimum variance of hedging error. For the first time in the literature, analytical optimal solutions are obtained for such a hedging problem. The most striking advantage of the method lies in its flexibility. While q-forwards are considered in the specific implementation in the paper, our method is readily applicable to other securities such as longevity swaps. Further, our method is implementable for a variety of longevity models including Lee-Carter, Cairns-Blake-Dowd (CBD) and their variants. Extensive numerical experiments show that our hedging method significantly outperforms the standard “delta” hedging strategy which is commonly adopted in the literature. Lastly we study the problem of optimal index insurance design under an expected utility maximization framework. For general utility functions, we formally prove the existence and uniqueness of optimal contract, and develop an effective numerical procedure to calculate the optimal solution. For exponential utility and quadratic utility functions, we obtain analytical expression of the optimal indemnity function. Our results show that the indemnity can be a highly non-linear and even non-monotonic function of the index variable in order to align with the actuarial loss variable so as to achieve the best reduction in basis risk. Due to the generality of model setup, our proposed method is readily applicable to a variety of insurance applications including index-linked mortality securities, weather index agriculture insurance and index-based catastrophe insurance. Our method is illustrated by a numerical example where weather index insurance is designed for protection against the adverse rice yield using temperature and precipitation as the underlying indices. Numerical results show that our optimal index insurance significantly outperforms linear-type index insurance contracts in terms of reducing basis risk.
Book Synopsis Immunization and Hedging of Longevity Risk by : Changyu Liu
Download or read book Immunization and Hedging of Longevity Risk written by Changyu Liu and published by . This book was released on 2015 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pension funds and life insurers offering annuities hold long term liabilities linked to longevity. Risk management of life annuity portfolios aims to immunize or hedge both interest rate and mortality risks. Standard fixed interest duration-convexity hedging must be adapted to allow for both interest rate and longevity risk. We develop an immunization approach along with a delta-gamma based approach allowing for both risks incorporating models for mortality and interest rate risk. The immunization and hedge effectiveness of fixed-income coupon bonds, annuity bonds, as well as longevity bonds, is compared and assessed using simulations of portfolio surplus outcomes for an annuity portfolio. Fixed-income annuity bonds can more effectively match cash flows and provide additional hedge effectiveness over coupon bonds. Longevity bonds, including deferred longevity bonds, reduce risk significantly compared to coupon and annuity bonds, reflecting the long duration of the typical life annuity and the exposure to longevity risk. Longevity bonds are shown to be effective in immunizing surplus over short and long horizons. Delta gamma hedging is shown to only be effective over short horizons.
Author :International Monetary Fund. Monetary and Capital Markets Department Publisher :International Monetary Fund ISBN 13 :1616352477 Total Pages :94 pages Book Rating :4.6/5 (163 download)
Book Synopsis Global Financial Stability Report, April 2012 by : International Monetary Fund. Monetary and Capital Markets Department
Download or read book Global Financial Stability Report, April 2012 written by International Monetary Fund. Monetary and Capital Markets Department and published by International Monetary Fund. This book was released on 2012-04-18 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The April 2012 Global Financial Stability Report assesses changes in risks to financial stability over the past six months, focusing on sovereign vulnerabilities, risks stemming from private sector deleveraging, and assessing the continued resilience of emerging markets. The report probes the implications of recent reforms in the financial system for market perception of safe assets, and investigates the growing public and private costs of increased longevity risk from aging populations.
Book Synopsis A Simple Hedge for Longevity Risk and Reimbursement Risk Using Research-Backed Obligations by : Roger Stein
Download or read book A Simple Hedge for Longevity Risk and Reimbursement Risk Using Research-Backed Obligations written by Roger Stein and published by . This book was released on 2016 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Longevity risk is the risk that the promised recipient of lifetime cashflows ends up living much longer than originally anticipated, thus causing a shortfall in funding. A related risk, reimbursement risk is the risk that providers of health insurance face when new and expensive drugs are introduced and the insurer must cover their costs. Longevity and reimbursement risks are particularly acute in domains in which scientific breakthroughs can increase the speed of new drug development. An emerging asset class, research-backed obligations or RBOs (cf., Fernandez et al., 2012), provides a natural mechanism for hedging these risks: RBO equity tranches gain value as new life- extending therapies are developed and do so in proportion to the number of successful therapies introduced. We use the stylized case of annuity underwriting to show how RBO equity could be used to hedge some forms longevity risk on a retirement portfolio. Using the same framework, we then show how RBO securities may be used to hedge a much broader class of reimbursement risks faced by health insurance firms. We demonstrate how to compute hedge ratios to neutralize specific exposures. Although our analytic results are stylized, our simulation results suggest substantial potential for this asset class to reduce financial uncertainty for those institutions exposed to either longevity or reimbursement risks. For example, our simulation results indicate that the correlation between the return on RBO equity and the reimbursement shortfall for a health insurer is about 0.66 under reasonable assumptions. Even under extremely conservative assumptions, this correlation is still 0.34, suggesting that RBO equity offers substantial hedging benefits, producing more favorable outcomes in about 87% of scenarios.
Book Synopsis Longevity Hedge Effectiveness Using Socioeconomic Indices by : Malene Kallestrup Lamb
Download or read book Longevity Hedge Effectiveness Using Socioeconomic Indices written by Malene Kallestrup Lamb and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper evaluates socioeconomic basis risk in longevity hedging. Using data for a full population stratified into socioeconomic groups, we explore the benefits and costs of two alternative hedging strategies, with and without basis risk, in the capital market. The benefit of the longevity hedge is represented by the risk reduction in the variability of a life annuity, whereas the cost is the notional amount of hedging contracts times the actuarial risk premium. We find that hedging is more cost-effective for the annuity provider when basis risk is eliminated. Moreover, it allows for a higher degree of hedge effectiveness at a cost that is equivalent to a hedge where basis risk is present. Finally, the yearly expenses related to hedging longevity risk requires, at most, an extra added rate of return of no more than 0.2%.
Book Synopsis Hedging Longevity Risk by Issuing Mortality Bonds by : Xilin Li
Download or read book Hedging Longevity Risk by Issuing Mortality Bonds written by Xilin Li and published by . This book was released on 2012 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis How Effective is Natural Hedging of Longevity Risk? by : Silvan Bienz
Download or read book How Effective is Natural Hedging of Longevity Risk? written by Silvan Bienz and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The consideration of longevity risk is increasingly important to insurance companies and pension plans due to the demographic development. In recent years, the capital market has developed a variety of longevity risk related securities. As the capital market solutions are just about to emerge, the only viable longevity risk management strategy to date remains natural hedging. Authors with different points of view are debating about the effectiveness of natural hedging in the academic literature. Therefore, this work tries to add to the discussion by examining natural hedging in comparison to longevity bonds and survivor swaps. This comparison is achieved through a comprehensive theoretical discussion and a numerical analysis. Hereby, longevity risk is assessed by modelling a mortality shock on a fictitious insurance portfolio and analysing the financial implications thereof under the three longevity risk management solutions. This paper demonstrates that natural hedging can provide a partial hedge against longevity risk. The combination of our analysis' result and estimates in the academic literature leads to the conclusion that natural hedging is semi-effective. In comparison to longevity bonds and survivor swaps, natural hedging proves less effective as these capital market instruments are able to provide a perfect hedge. However, natural hedging convinces with the highest level of practicability.
Book Synopsis Optimal Hedging with Basis Risk Under Mean-Variance Criterion by : Jingong Zhang
Download or read book Optimal Hedging with Basis Risk Under Mean-Variance Criterion written by Jingong Zhang and published by . This book was released on 2019 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basis risk occurs naturally in a number of financial and insurance risk management problems. A notable example is in the context of hedging a derivative where the underlying security is either non-tradable or not sufficiently liquid. Other examples include hedging longevity risk using index-based longevity instrument and hedging crop yields using weather derivatives. These applications give rise to basis risk and it is imperative that such a risk needs to be taken into consideration for the adopted hedging strategy. In this paper, we consider the problem of hedging a European option using another correlated and liquidly traded asset and we investigate an optimal construction of hedging portfolio involving such an asset. The mean-variance criterion is adopted to evaluate the hedging performance, and a subgame Nash equilibrium is used to define the optimal solution. The problem is solved by resorting to a dynamic programming procedure and a change-of-measure technique. A closed-form optimal control process is obtained under a diffusion model setup. The solution we obtain is highly tractable and to the best of our knowledge, this is the first time the analytical solution exists for dynamic hedging of general European options with basis risk under the mean-variance criterion. Examples on hedging European call options are presented to foster the feasibility and importance of our optimal hedging strategy in the presence of basis risk.
Book Synopsis Dynamic Hedging Strategies Based on Changing the Pricing Parameters for Compound Ratchets by : Samia El Khoury
Download or read book Dynamic Hedging Strategies Based on Changing the Pricing Parameters for Compound Ratchets written by Samia El Khoury and published by . This book was released on 2016 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equity-Indexed Annuity products (EIAs) are becoming increasingly popular as they are tax-deferred accumulation vehicles that offer participation in the equity market growth while keeping the initial capital protected. This thesis focuses in particular on a special type of EIAs; the Compound Ratchet (CR). Sellers of this product, such as insurance companies and banks, retain the right to change one of the pricing parameters on each contract anniversary date, while promising not to cross a certain predetermined threshold. Changing these parameters can sometimes have an impact on the value of the EIA, which makes them interesting to study, especially when the issuer's changing policy is not clear. In order to reproduce the pattern of these changing parameters, a new approach of dynamically hedging the CR EIA and simultaneously protecting the issuer from hedging risk is proposed and tested. Assuming the Black-Scholes Financial framework and in the absence of mortality risk, closed-form solutions for the price and value of the CR EIA at any time throughout the contract term are obtained and then used to find the Greeks, which are in turn used build the hedging strategies. In reality, trading can only be done in discrete time, which produces hedging errors. A detailed numerical example shows that the Gamma-hedging strategy outperforms the Delta-hedging strategy by reducing the magnitude of these errors. However hedging risk still exists, therefore, the new approach is applied to transfer the errors from the issuer to the buyer by dynamically changing the pricing parameters. Additionally in the numerical example, the distribution of these parameters is extracted and analyzed, as well as the resulting reduction in the hedging errors, which represent the reduced cost for the issuer.
Download or read book Pension Economics written by David Blake and published by John Wiley & Sons. This book was released on 2006-11-02 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: While not attempting to train readers as professional economists, this book aims to provide a secure grounding in the theory and practice of economics insofar as it deals with pension matters. From reading this book, the user will understand: * The key types of pension scheme * The role of pensions in maximizing individual lifetime welfare * The role of pensions in individual savings and retirement decisions * The role and consequences of the pension plan from the company's viewpoint * The role of pensions in promoting aggregate savings * The role of pensions and retirement in overlapping generations models * The economics of ageing and intergenerational accounting * The social welfare implications of pensions * The lessons of behavioural economics for pensions
Book Synopsis Risk Management for Pension Funds by : Francesco Menoncin
Download or read book Risk Management for Pension Funds written by Francesco Menoncin and published by Springer Nature. This book was released on 2021-02-09 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a consistent and complete framework for studying the risk management of a pension fund. It gives the reader the opportunity to understand, replicate and widen the analysis. To this aim, the book provides all the tools for computing the optimal asset allocation in a dynamic framework where the financial horizon is stochastic (longevity risk) and the investor's wealth is not self-financed. This tutorial enables the reader to replicate all the results presented. The R codes are provided alongside the presentation of the theoretical framework. The book explains and discusses the problem of hedging longevity risk even in an incomplete market, though strong theoretical results about an incomplete framework are still lacking and the problem is still being discussed in most recent literature.
