A unified pricing of variable annuity guarantees under the optimal stochastic control framework

In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the existing numerical methods. For numerical valuation of these contracts, we develop a direct integration method based on Gauss-Hermite quadrature with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is very efficient when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We also present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a benchmark for practitioners and researchers developing pricing of variable annuity guarantees.Comment: Keywords: variable annuity, guaranteed living and death benefits, guaranteed minimum accumulation benefit, optimal stochastic control, direct integration metho

The Elusiveness of Applied Management Knowledge: A Critical Challenge for Management Educators

A wealth of anecdotal data suggest that, despite sufficient conceptual knowledge of what constitutes effective management practice, managers may often lack the ability to apply that knowledge in context. We measured the applied managerial knowledge of 21,319 managers and 2,644 students and found a disturbingly low level of such capability in both groups. Moreover, our findings indicated little difference in demonstrated applied managerial knowledge across a wide range of management experience. In our student sample, we found only modest to small relationships between applied managerial knowledge and measures of cognitive aptitude, select personality characteristics, and academic performance. Despite an immense amount of educational resources devoted to its development, applied managerial knowledge is clearly elusive. We discuss implications for future research and more effective management education

Variable Annuities: Risk Identification and Risk Assessment

Life annuities and pension products usually involve a number of ‘guarantees’, such as, e.g., minimum accumulation rates, minimum annual payments and minimum total payout. Packaging different types of guarantees is the feature of the so-called Variable Annuities. Basically, these products are unit-linked investment policies providing deferred annuity benefits. The guarantees, commonly referred to as GMxBs (namely, Guaranteed Minimum Benefits of type ‘x’), include minimum benefits both in case of death and survival. Following a Risk Management-oriented approach, this paper first aims at singling out all sources of risk affecting Variable Annuities (‘risk identification phase’). Critical aspects arise from the interaction between financial and demographic issues. In particular, the longevity risk may have a dramatic impact on the technical equilibrium of a portfolio. Then, we deal with risk quantification (‘risk assessment phase’), mostly via stochastic simulation of financial and demographic scenarios. Our main contribution is to present an integrated approach to risks in Variable Annuity products, so providing a unifying and innovative point of view

Accounting and reporting by insurance enterprises for certain nontraditional long-duration insurance contracts and for separate accounts; Statement of position 03-01

https://egrove.olemiss.edu/aicpa_sop/1005/thumbnail.jp

Individual Welfare Gains from Deferred Life-Annuities under Stochastic Lee-Carter Mortality

A deferred annuity typically includes an option-like right for the policyholder. At the end of the deferment period, he may either choose to receive annuity payouts, calculated based on a mortality table agreed to at contract inception, or receive the accumulated capital as a lump sum. Considering stochastic mortality improvements, such an option could be of substantial value. Whenever mortality improves less than originally expected, the policyholder will choose the lump sum and buy an annuity on the market granting him a better price. If, however, mortality improves more than expected, the policyholder will choose to retain the deferred annuity. We use a realistically calibrated life-cycle consumption/saving/asset allocation model and calculate the welfare gains of deferred annuities under stochastic Lee- Carter mortality. Our results are relevant both for individual retirement planning and for policymakers, especially if legislation makes annuitization, at least in part, mandatory. Our results also indicate the maximal willingness to pay for the mortality option inherent in deferred annuities, which is of relevance to insurance pricing.Stochastic Mortality, Deferred Annuitization, Retirement Decisions, Annuity Puzzle, Intertemporal Utility Maximization

Financial Risk Management of Guaranteed Minimum Income Benefits Embedded in Variable Annuities

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

Exploring Mechanisms Insurers Employ to Set Premiums and Maximize Profitability

The insurance industry is a very complex segment of the macroeconomy. An explain will be given as to how these companies are able to maintain and maximize their profits, allowing them to remain in business. A key area in this process is the setting of premiums. This activity draws from many areas of the business model. This paper will start with a birds-eye view and telescope in, starting with standard business practices and ending with specific undertakings of insurance companies. Companies must keep adequate liquid funds. This is done mainly through forecasting cash outflows and investing their assets under management. Within the realm of investing, insurance companies also use hedging techniques to maintain a healthy cashflow

Object Position Labelling in Video Using PRBS Audio Multilateration

Supervised machine learning approaches for tracking objects’ positions in video typically require a large set of images in which the positions are labelled. Human labelling is time-consuming and automatic position labelling using visual markers is generally not possible because visible markers would corrupt the data. Here, we present an approach in which an object is tracked using a hidden tag that emits a PRBS audio signal. Four microphones arranged in a planar cross formation capture parallel recordings of the PRBS signal. Multilateration, using the time difference of arrival (TDoA) of the PRBS at each microphone, is used to estimate the position of the emitter. Here, we describe and evaluate the method by which the TDoAs are obtained and the emitter position is calculated. When evaluated, the approach yielded threedimensional position estimates with a mean error of 18.56cm. In its present form, the method is suitable for applications in which precision is not a priority, but three-dimensional object coordinates are required rather than two-dimensional camera view coordinates