Early Surrender Research Articles

Taxation and policyholder behavior: the case of guaranteed minimum accumulation benefits

AbstractThis paper considers variable annuity (VA) contracts embedded with guaranteed minimum accumulation benefit (GMAB) riders when policyholder’s proceeds are taxed upon early surrender or maturity. These contracts promise the return of the premium paid by the policyholder, or a higher rolled-up value, at the end of the investment period. A partial differential equation valuation framework which exploits the numerical method of lines is used to determine fair fees that render the policyholder and insurer breakeven. Two taxation regimes are considered: one where capital gains are allowed to offset losses and a second where gains do not offset losses. Most insurance providers highlight the tax-deferred features of VA contracts. We show that the regime under which the insured is taxed significantly impacts prices. If losses are allowed to offset gains then this enhances the market, increasing the policyholder’s willingness to participate in the market compared to the case when losses are not allowed to offset gains. With fair fees from the policyholder’s perspective, we show that the net profit is generally positive for insurance companies offering the contract as a naked option without any hedge. We also show how investment policy, as reflected in the Sharpe ratio, impacts and interacts with policyholder persistency.

Valuation of guaranteed minimum maturity benefits under mean reversion and jump models with surrender risk

We propose an efficient valuation approach for guaranteed minimum benefits embedded in variable annuity (VA) contracts, where the price of underlying asset is modeled by a mean reversion process with jumps. We consider the case in which early surrender is permitted, and an intensity-based framework is used to capture surrender behavior and other asset price volatilities. To analyze the contract within this complex stochastic setting, we rely on the Fourier cosine series expansion method to approximate the expectation of the value function, which serves as an estimation of the value of VA benefits. We conduct numerical examples to demonstrate the efficiency and accuracy of the proposed method. Sensitivity analysis of involved parameters is given.

Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees

This work studies the valuation and optimal surrender of variable (equity-linked) annuities under a Lévy-driven equity market with mortality risk. We consider a practical periodic fee structure which can vary over time and is assessed as a proportion of the fund value. At maturity, the fund value is returned to the policyholder according to a guaranteed minimum accumulation benefit (GMAB). Mortality risk is also modeled discretely, and the contract offers a guaranteed minimum death benefit (GMBD) prior to maturity. The benefits accommodate caps on the growth of funds (in addition to the rising floor) to reduce the fee level and as a disincentive to early surrender. Interest rates are modeled via a deterministic discounting term structure, which can be calibrated (bootstrapped) to the rates market, according to market convention. An efficient and accurate valuation framework is developed, along with closed form pricing formulas in the case where policy surrender is not permitted. Numerous experiments are conducted to illustrate the interplay between contract parameters and the decision to surrender, and we provide an extensive analysis that investigates how to structure contracts to disincentivize early surrender.

Efficient valuation of guaranteed minimum maturity benefits in regime switching jump diffusion models with surrender risk

We present an efficient valuation approach for guaranteed minimum maturity benefits (GMMBs) embedded in variable annuity (VA) contracts in a regime-switching jump diffusion model. We allow early surrender of the VA contract and impose surrender charges, which are important in practice to discourage early termination/lapse of the contract. We consider both continuously-monitored and discretely-monitored surrender behaviors before maturity, and utilize an intensity-based framework. Based on the continuous-time Markov chain (CTMC) approximation combined with the Fourier cosine series expansion method, we find that the valuation problem can be solved under a regime-switching jump diffusion framework. Both error analysis and numerical experiments demonstrate the accuracy and efficiency of the proposed method.

Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility

This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

Introduction

Abstract The Mongol empire (1206–1368) caused massive transformations in the composition and functioning of elites across Eurasia. While the Mongols themselves obviously became the new Eurasian elite, their small number as compared to the huge territory over which they ruled and their initial inexperience in administrating sedentary realms meant that many of their subjects also became part of the new multi-ethnic imperial elite. Mongol preferences, and the high level of mobility—both spatial and social—that accompanied Mongol conquests and rule, dramatically changed the characteristics of elites in both China and the Muslim world: While noble birth could be instrumental in improving one’s status, early surrender to Chinggis Khan; membership in the Mongol imperial guards (keshig); and especially, qualifications—such as excellence in warfare, administration, writing in Mongolian script or astronomy to name but a few—became the main ways to enter elite circles. The present volume translates and analyzes biographies of ten members of this new elite—from princes through generals, administrators, and vassal kings, to scientists and artists; including Mongols, Koreans, Chinese and Muslims—studied by researchers working at the project “Mobility, Empire and Cross Cultural Contacts in Mongol Eurasia” at the Hebrew University of Jerusalem. The annotated biographies assembled here not only add new primary sources—translated from Chinese, Persian and Arabic—to the study of the Mongol Empire. They also provide important insights into the social history of the period, illuminating issues such as acculturation (of both the Mongols and their subjects), Islamization, family relations, ethnicity, imperial administration, and scientific exchange.

Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates

In this paper we analyse how the policyholders’surrender behaviour is influenced by changes in various sources of risk impacting a variable annuity (VA) contract embedded with a guaranteed minimum maturity benefit rider that can be surrendered anytime prior to maturity. We model the underlying mutual fund dynamics by combining a Heston (1993) stochastic volatility model together with a Hull and White (1990) stochastic interest rate process. The model is able to capture the smile/skew often observed on equity option markets (Grzelak and Oosterlee 2011) as well as the influence of the interest rates on the early surrender decisions as noted from our analysis. The annuity provider charges management fees which are proportional to the level of the mutual fund as a way of funding the VA contract. To determine the optimal surrender decisions, we present the problem as a 4-dimensional free-boundary partial differential equation (PDE) which is then solved efficiently by the method of lines (MOL) approach. The MOL algorithm facilitates simultaneous computation of the prices, fair management fees, optimal surrender boundaries and hedge ratios of the variable annuity contract as part of the solution at no additional computational cost. A comprehensive analysis on the impact of various risk factors in influencing the policyholder’s surrender behaviour is carried out, highlighting the significance of both stochastic volatility and interest rate parameters in influencing the policyholder’s surrender behaviour. With the aid of the hedge ratios obtained from the MOL, we construct an effective dynamic hedging strategy to mitigate the provider’s risk and compare different hedging performances when the policyholders’ surrender behaviour is either optimal or sub-optimal.

Variable Annuities with High Water Mark Withdrawal Benefit

In this paper, we develop a continuous-time model for variable annuities allowing for periodic withdrawals proportional to the high water mark of the underlying account value as well as early surrender of the policy. We derive a HJB variational inequality characterizing the minimal superhedging price of such a contract and the worst-case policyholder behavior from an issuer's perspective. Based on these results, we construct a dynamic trading strategy which superreplicates the contract. In addition, we show how early surrender has to be penalized to disincentivize a worst-case policyholder from using this option. To treat the problem numerically, we develop a semi-Lagrangian scheme based on a discretization of the underlying noise process.

Pricing Ratchet Equity-Indexed Annuities with Early Surrender Risk in a CIR++ Model

In this article we propose a lattice algorithm for pricing simple Ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR++ stochastic interest rates. In addition we present an asymptotic expansion technique that permits us to obtain a first-order approximation formula for the price of simple Ratchet EIAs without early surrender risk and without a global minimum contract value. Numerical comparisons show the reliability of the proposed methods.

Covenants Without the Sword International Law and the Protection of Civilians in Times of War

Do the international laws of war effectively protect civilian populations from deliberate attack? In a statistical analysis of all interstate wars from 1900 to 2003 the authors find no evidence that signatories of The Hague or Geneva Conventions intentionally kill fewer civilians during war than do nonsignatories. This result holds for democratic signatories and for wars in which both sides are parties to the treaty. Nor do they find evidence that a state's regime type or the existence of ethnic or religious differences between combatants explains the variation in civilian targeting. They find strong support, however, for their theoretical framework, which suggests that combatants seek to kill enemy civilians when they believe that doing so will coerce their adversaries into early surrender or undermine their adversaries' war-related domestic production. The authors find that states fighting wars of attrition or counterinsurgency, states fighting for expansive war aims, and states fighting wars of long duration kill significantly more civilians than states in other kinds of wars.

Early surrender and the distribution of policy reserves

We extend the literature by incorporating early surrender into the distribution estimation for policy reserves. First, we employ the cointegrated vector autoregression technique to estimate an empirical relation between the lapse rate and interest rate. The tests indicate a significant cointegrated vector that implies a long-term relation between the lapse rate and interest rate. Based on the estimated error-correction model, we then simulate the policy reserve distribution with stochastic mortality, interest rate, and early surrender. We find that early surrender reduces the expected value as well as the risk for policy reserves due to surrenders in the low interest rate periods. Further analyses indicate that the early surrender effect depends on the sign and magnitude of the difference between the market interest rate and policy credit rate. When the credit rate is higher (lower) than the market interest rate, early surrender acts to decrease (increase) the mean reserve. This effect increases with the magnitude in the difference.

Ending the War with Japan: Paul Nitze's "Early Surrender" Counterfactual

The most important foundation for attacks on the decision of President Harry S. Truman to use atomic bombs againstJapan is the claim that conventional bombing and naval blockade had brought Japan to the point of by the summer of 1945, that Truman knew this, and that he dropped the bombs to intimidate the Soviet Union, not to end the war. This early surrender counterfactual hypothesis comes from publications of the United States Strategic Bombing Survey (USSBS). The USSBS was headed in Japan, and its official reports edited and controlled, by Paul H. Nitze. This article examines the evidence on which Nitze claims to have based his early surrender hypothesis. The USSBS began as an effort by strategic bombing advocates to establish their craft as the ultimate arbiter of all future

Peacemaking on the Dark Side of the Moon: Hungary 1943–1947

At the close of hostilities geography proved decisive in the mis-fortune of Hungary, a country that had been in the inner circle of the German power sphere. From this came the basic problem of Hungarian diplomacy—attempting to preserve Hungarian independence in an almost impossible situation. None of the Axis satellites was in so precarious a position. The peripheral location of Italy, Finland, Rumania and Bulgaria made possible their early surrender, but events in Hungary inevitably turned out differently. Hungary could hardly succeed in changing sides during the war. She did not enjoy the trust of the Germans, her supposed partners. She did not enjoy much sympathy in the West. And she was positively disliked by the Russians. Foreign Secretary Anthony Eden said to President Franklin D. Roosevelt that he “thought Stalin would want to be pretty arbitrary about Hungary.”