Partial Hedging for Equity-Linked Products Using Risk-Minimizing Strategies

In this article, we consider the pricing and hedging of equity-indexed annuities (EIAs) using local risk-minimizing strategies as well as evaluating the capital requirement for these products. Since these products involve mortality as well as financial risks, we integrate mortality risk and propose partial hedging strategies that protect the insurer based on risk measures. The framework we present makes use of sequential local risk-minimizing strategies to take into account all intermediate requirements. To demonstrate the flexibility of this framework we present numerical examples featuring point-to-point EIAs with a two-state regime-switching equity model.     

Bayesian Risk Management for Equity-Linked Insurance

This paper describes how to apply Markov Chain Monte Carlo (MCMC) techniques to a regime switching model of the stock price process to generate a sample from the joint posterior distribution of the parameters of the model. The MCMC output can be used to generate a sample from the predictive distribution of losses from equity linked contracts, assuming first an actuarial approach to risk management and secondly a financial economics approach. The predictive distribution is used to show the effect of parameter uncertainty on risk management calculations. We also explore model uncertainty by assuming a GARCH model in place of the regime switching model. The results indicate that the financial economics approach to risk management is substantially more robust to parameter uncertainty and model uncertainty than the actuarial approach.     

The Effect of Risk Aversion and Loss Aversion on Equity-Linked Life Insurance With Surrender Guarantees

We price equity-linked life insurance with surrender guarantees and account for risk preferences in the form of risk-averse and loss-averse policyholders in continuous time. Risk-averse policyholders surrender their policy for higher equity index values. Compared to optimally surrendered policies, this behavior creates substantial policy value losses. In contrast, loss-averse policyholders surrender once the surrender benefit realizes a gain but keep under-performing policies. This disposition effect reduces the policy value relative to both optimally surrendered policies and policies surrendered by risk-averse policyholders. Insurers in competitive markets need to estimate their policyholders’ risk preferences accurately.     

On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Bühlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.     

Analysis of Participating Life Insurance Contracts: A Unification Approach

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk‐neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk‐neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk‐neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance company's risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.     

Fair Valuation of Participating Life Insurance Contracts with Jump Risk

The purpose of this article is to value participating life insurance contracts when the linked portfolio is modeled by a jump-diffusion. More precisely, this process has a Brownian component and a compound Poisson one, where the jump size is driven by a double exponential distribution. Specifically here, the bankruptcy risk of the insurance company is considered. Thus, market and credit risks are taken into account. A quasi-closed-form formula is obtained in fair value for the price of the considered life insurance contract. This allows us to investigate the impact of strategic parameters as well as structural ones, as is shown in the numerical section of this paper. In particular, we study the impact on the contract of the volatility, jump intensity, jump asymmetry, company leverage, guaranteed rate, participation rate and level of the default barrier, and comment on how they are likely to increase the probability of early default of the issuer.     

Valuation of Equity-Linked Insurance and Annuity Products with Binomial Models

Abstract

In this paper we develop a valuation method for equity-linked insurance products. We assume that the premium information of term life insurances, pure endowment insurances, and endowment insurances at all maturities is obtainable within a company or from the insurance market. Using a method similar to that of Jarrow and Turnbull (1995), we derive three martingale probability measures associated with these basic insurance products. These measures are agedependent, include an adjustment for the mortality risk, and reproduce the premiums of the respective insurance products. We then extend the martingale measures to include the financial market information using copulas and use them to evaluate equity-linked insurance contracts and equity-indexed annuities in particular. This is different from the traditional approach under which diversification of mortality risk is assumed. A detailed numerical analysis is performed for various existing equity-indexed annuities in the North American market.     

Hedging with Two Futures Contracts: Simplicity Pays

We propose to use two futures contracts in hedging an agricultural commodity commitment to solve either the standard delta hedge or the roll‐over issue. Most current literature on dual‐hedge strategies is based on a structured model to reduce roll‐over risk and is somehow difficult to apply for agricultural futures contracts. Instead, we propose to apply a regression based model and a naive rules of thumb for dual‐hedges which are applicable for agricultural commodities. The naive dual strategy stems from the fact that in a large sample of agricultural commodities, De Ville, Dhaene and Sercu (2008) find that GARCH‐based hedges do not perform as well as OLS‐based ones and that we can avoid estimation error with such a simple rule. Our semi‐naive hedge ratios are driven from two conditions: omitting exposure to spot price and minimising the variance of the unexpected basis effects on the portfolio values. We find that, generally, (i) rebalancing helps; (ii) the two‐contract hedging rules do better than the one‐contract counterparts, even for standard delta hedges without rolling‐over; (iii) simplicity pays: the naive rules are the best one–for corn and wheat within the two‐contract group, the semi‐naive rule systematically beats the others and GARCH performs worse than OLS for either one‐contract or two‐contract hedges and for soybeans the traditional naive rule performs nearly as well as OLS. These conclusions are based on the tests on unconditional variance ( Diebold and Mariano, 1995 ) and those on conditional risk ( Giacomini and White, 2006 ).     

Hedging and Reserving for Single-Premium Segregated Fund Contracts

Abstract

Three methods for determining suitable provision for maturity guarantees for single-premium segregated fund contracts are compared. Actuarial reserving assumes funds are held in risk-free assets, to give a prescribed probability of meeting the guarantee liability. Dynamic hedging uses the Black-Scholes framework to determine the replicating portfolio. Static hedging assumes a counterparty is willing to sell the options required to meet the guarantee. Using a stochastic cash flow projection, we consider how to assess which approach is most profitable. The example given assumes a typical Canadian segregated fund contract.     

Assessing the Risk Potential of Premium Payment Options in Participating Life Insurance Contracts

Most life insurance contracts embed the right to stop premium payments during the term of the contract (paid-up option). Thereby, the contract is not terminated but continues with reduced benefits and often provides the right to resume premium payments later, thus increasing the previously reduced benefits (resumption option). In our analysis, we start with a basic contract with two standard options, namely, an interest rate guarantee and annual surplus participation. Next, in addition to the features of the basic contract, a paid-up and resumption option is included in the framework. The valuation process is not based on assumptions about a particular policyholders' exercise strategy but instead assesses the risk potential from the insurer's viewpoint by providing an upper bound for any possible exercise behavior. This approach provides important information to the insurer about the potential hazard of offering the paid-up and resumption option. Further, the approach allows an analysis of the impact of guaranteed interest rate, annual surplus participation, and investment volatility on the values of the premium payment options.     

Corporate Hedging in the Insurance Industry

Abstract

In this paper we investigate the extent to which insurance companies utilize financial derivatives contracts in the management of risks The data set we employ allows us to observe the universe of individual insurer transactions for a class of contracts, namely, those normally thought of as off-balance-sheet (OBS) We provide information on the number of insurers using various types of derivatives contracts and the volume of transactions in terms of notional amounts and the number of counterparties. Life insurers are most active in interest rate and foreign exchange derivatives, while property/casualty insurers tend to be active in trading equity option and foreign exchange contracts Using a multivariate probtt analysis, we explore the factors that potentially influence the existence of OBS activities. We also investigate questions relating to whether certain subsets of OBS transactions (for example, exchange traded) are related to such things as interest rate risk measures, organizational form and other characteristics that may discriminate between desired risk/return profiles across a cross-section of insurers. We find evidence consistent with the use of derivatives by insurers to hedge risks posed by guaranteed investment contracts (GICs), coilater-alized mortgage obligations (CMOs), and other sources of financial risk     

Finding Pareto Optimal Insurance Contracts

This paper deals with on-line computation—or step-wise learning—of Pareto optimal insurance contracts. Our approach tolerates that the loss distribution might be unknown, intractable, or not well specified. Thus we accommodate fairly inexperienced parties. Losses are here simulated or observed, one at a time, and they cause iterated revisions of the premium. The mechanical and global nature of probability calculus thereby yields to more tentative, myopic procedures, possibly closer to how humans operate or reason in face of risk. Sequential revisions may also reduce the expense of insurers' time and money in seeking sufficient statistics. Emphasized below is the remarkable simplicity and stability of the resulting adaptive procedures. Special attention goes to catastrophic risks, and to subsidized or competitive insurance.     

国际财务报告准则第4号:保险合同

目标 1.本国际财务报告准则的目标是在理事会完成保险合同项目第二阶段之前,规范所有签发保险合同的实体(本国际财务报告准则称之为承保人)对保险合同的财务报告.特别是,本国际财务报告准则要求:(1)承保人对保险合同的会计处理作有限的改进.(2)披露相关信息,明确和解释承保人财务报表中因保险合同而产生的金额,以帮助这些财务报表的使用者理解保险合同未来现金流量的金额、时间及其不确定性.     

Dynamic Insurance Contracts and Adverse Selection

We take a dynamic perspective on insurance markets under adverse selection and study a dynamic version of the Rothschild and Stiglitz model. We investigate the nature of dynamic insurance contracts by considering both conditional and unconditional dynamic contracts. An unconditional dynamic contract has insurance companies offering contracts where the terms of the contract depend on time, but not on the occurrence of past accidents. Conditional dynamic contracts make the actual contract also depend on individual past performance (such as in car insurances). We show that dynamic insurance contracts yield a welfare improvement only if they are conditional on past performance. With conditional contracts, the first‐best can be approximated if the contract lasts long. Moreover, this is true for any fraction of low‐risk agents in the population.     

Understanding Basis Risk in Insurance Contracts

There is a tremendous amount of resources being tied up in litigation between insurance companies and policyholders over things like the extent of coverage for various loss scenarios or allegedly bad faith delays in settlement payments. The fact that policyholders formally dispute insurer coverage positions or claims payment strategies gives credibility to the idea that mismatches exist between what policyholders expect insurance policies to cover and what the insurance contracts actually provide as loss indemnification. This mismatch essentially represents insurance basis risk, the analysis of which can more accurately reflect the value and overall efficiency of insurance contracts and suggest factors that may influence policyholder dissatisfaction and consequently insurance contract disputes. This article takes a detailed look at insurance basis risk and finds that subjectivity plays a prominent role in its definition. Using Bayesian inference, it is shown how factors can affect the magnitude of insurance basis risk depending on the individual situation in which the mismatch between losses and coverage exists.     

Dynamic Prevention in Short-Term Insurance Contracts

This article looks at the dynamic properties of insurance contracts when insurers have a better technology at preventing catastrophic losses than the insured. When the prevention technology is irreversible and its benefits last for all future periods although its cost is borne in the period in which it is made, a hold‐up problem occurs because the insured can change insurer after his initial insurer has invested in prevention. Investment in prevention is then delayed compared to the first best outcome. When the audit cost must be incurred by the insured when he wants to change insurer, the incumbent insurer has an informational advantage so that he can keep his client over the entire investment horizon, even though long‐term contracts are not possible. This does not avoid the delay in investment, however.     

Efficient Insurance Contracts under Epsilon-Contaminated Utilities

This paper analyses the qualitative properties of optimal contracts when agents have multiple priors and are uncertainty averse in an infinite state space framework. The case of the epsilon-contamination of a given prior, a basic tool in robustness theory is fully developped. It is shown that if both agents have strictly concave utility index, then if the insurer is less uncertainty averse than the insured, he provides a full insurance contract above a deductible for high values of the loss.     

保险合同的一些法律问题

我国保险法研究尚处于发展阶段,有关保险合同问题的认识比较混乱.本文针对争论比较多的保险合同的特征、保险合同中的要约与承诺、保险合同的形式以及保险利益等四个问题展开分析和讨论.文中充分利用了已有的研究成果,通过对比发现一些问题,并结合司法实践对相关问题进行再认识,从而提出了一些新的观点.     

Portfolio Insurance Strategies when Hedging Affects Share Prices

Option-based portfolio insurance can result in coordinated buying and selling, which destabilizes markets such that hedgers fail to achieve their objective. Gennotte and Leland (1990) show portfolio insurance strategies can have an impact on price movements. Ramanlal and Mann (1996) show how price movements, in turn, can alter hedging strategies. In this paper, we combine these separate effects and develop an equilibrium, executable hedging strategy. This hedging strategy requires less rebalancing than traditional portfolio insurance; more important, it achieves downside protection with a less destabilizing impact on security prices.