Valuation of Participating Life Insurance Liabilities

Surrender and paid-up states are incorporated in the valuation of guaranteed benefits and payments of a level premium paying life insurance policy.

We present different valuation methods and examine to what extent they avoid capitalizing and releasing future loadings which are associated with the payment of future premiums.

We demonstrate how to avoid capital being required in the future to cover valuation strains. The paid-up benefit valuation method is being extended so that it does not require the premium basis to be on the safe-side of the valuation basis. We obtain a unification and integration of the level premium and paid-up valuation principles.     

The Optimal Choice for Lenders Facing Defaults: Short Sale,Foreclose, or REO

When mortgage borrowers default and have no desire or ability to keep their property, then loss mitigation involves a sale of the property via one of the following options: (1) the lender allows pre-foreclosure “short sale” by the borrower, (2) the lender institutes the foreclosure process under a notice of default and the property is sold during the process by the borrower, and (3) the lender forecloses on the property, takes title, and sells the property in the market as real estate owned (REO). Sale of the property in the above three options is conducted by a motivated seller, either the owner or the lender, who desires to sell the property as quickly as possible. Thus, relative to a no-default sale, the house is most likely to be sold at a discounted price. It is generally expected that the discount would be lower in the case of a “short sale.” This option, however, may result in a longer marketing time, thus a higher total loss, than the other two options. We developed a model that allows simultaneous estimation of price and time-on-market effects of “short sales,” foreclosures, and REO options. We find that the short-sale option has the lowest-price discount, but significantly higher costs associated with marketing time. The pattern of price discount and marketing time reverses as we move to a sale while in the process of foreclosure and to a sale with an REO status.     

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.     

Variable Purchase Options

This paper examines the design and pricing of an innovative derivative asset known as a variable purchase option (“VPO“). A VPO is a call option issued by a corporation on a stochastic number of shares of its common stock. The key feature of the security is that it is ex-ante certain to be exercised by rational investors at maturity, at which time the corporation is certain to issue a fixed dollar amount of new equity capital. A VPO therefore provides a corporation with an alternative to underwriting as a means to guarantee the success of a future equity offering. This revised version was published online in November 2006 with corrections to the Cover Date.     

Home Price,Time-on-Market,and Seller Heterogeneity Under Changing Market Conditions

This paper develops a formal model to examine the effect of changing market conditions and individuals’ selling constraints on selling price and time-on-market. Using the concept of Relative Liquidity Constraint (RLC)—a stochastic variable that captures the randomness of future individual constraints and market conditions—the study presents the first ex ante analysis that extends the investigation of the issue of seller heterogeneity to the point of the buying decision, that is, from the perspective of the buyer’s (future seller’s) point of view. We show that seller constraint, as well as the uncertainty of such a constraint, significantly depresses the expected selling price and increases risk. Our closed-form formulas provide a set of simple quantitative tools that enable buyers and sellers to adjust the “market average” to their ex ante “individual expectations”.     

Failed delivery and daily Treasury bill returns

If the seller of a Treasury bill does not provide timely and correct delivery instructions to the clearing bank, the bank does not deliver the security. Furthermore, the seller is not paid until this failed delivery is rectified. Since the purchase price is not changed, these fails generate interest-free loans from the seller to the buyer. This article studies the effect of failed delivery on Treasury bill prices. We find that investors bid prices to a premium to reflect the possibility of obtaining the interest-free loans that fails represent. This premium is a function of the opportunity cost of the fail. We also find that the bid-ask spread varies directly with the length of the fail. We rule out that our results are due to liquidity premiums, or to a general weekly pattern in short-term interest rates or the bid-ask spread.     

Die prämienbegünstigte Zukunftsvorsorge in Österreich

Due to the predictable demographic developments and the budgetary restrictions in the Stability Pact of the Treaty of Maastricht the big pay-as-you-go public sector pension systems in many western European countries seem to have reached their limits. Since 2003 the Austrian government has put its trust in strengthening the third pillar of the pension system and supports private provision with state-aided premiums. In this paper this state-aided private provision system with its capital guarantee is presented, evaluated and analyzed. Moreover we point out the dilemma of this pension provision product: in the case of low asset returns the state premiums will be eroded by the expenses of the issuers. Furthermore it will be clarified that the issuers, in contrast to the clients, have no interest in investing in volatile assets since in that case the probability of exercising the capital guarantee will increase.     

Risk-neutral compatibility with option prices

A common problem is to choose a “risk-neutral” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure” by completing the market with option prices. We do this by modeling the behavior of the stock price X, together with the behavior of the option prices for a relevant family of options which are (or can theoretically be) effectively traded. In doing so, we need to ensure a kind of “compatibility” between X and the prices of our options, and this poses some significant mathematical difficulties.     

The Enron Bankruptcy: When did the options market in Enron lose it’s smirk?

The Enron Corporation went from a $65 billion dollar market capitalization to bankruptcy in just 16 months. Using statistical techniques for extracting the implied probability distributions built into option prices, I examine the market’s expectation of Enron’s risk of collapse. I find that the options market remained far too optimistic about the stock until just weeks before their bankruptcy filing. I thank Oded Palmon and an anonymous referee for helpful comments. JEL Classification G13 · G14     

Pension funds with a minimum guarantee: a stochastic control approach

In this paper we propose and study a continuous-time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. We adopt the point of view of a fund manager maximizing the expected utility from the fund wealth over an infinite horizon. In our model the dynamics of wealth takes directly into account the flows of contributions and benefits, and the level of wealth is constrained to stay above a “solvency level.” The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. We concentrate the analysis on the effect of the solvency constraint, analyzing in particular what happens when the fund wealth reaches the allowed minimum value represented by the solvency level.     

The Dynamics of the S&P 500 Implied Volatility Surface

This empirical study is motivated by the literature on “smile-consistent” arbitrage pricing with stochastic volatility. We investigate the number and shape of shocks that move implied volatility smiles and surfaces by applying Principal Components Analysis. Two components are identified under a variety of criteria. Subsequently, we develop a “Procrustes” type rotation in order to interpret the retained components. The results have implications for both option pricing and hedging and for the economics of option pricing. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Upper Bound of a Call Option

Using only a weak set of assumptions, Merton (1973) shows that the upper bound of a European or American call option on a non-dividend paying stock is the underlying stock price: a result which is often extended to options on dividend paying stocks. In this short technical piece we show that the underlying stock price is in fact not the least upper bound of either a European or an American call option on a stock that pays one or more known dividends prior to maturity. Based on Merton's (1973) original framework, new upper bounds are established which depend on the size(s) of the dividend(s) compared to the size of the strike. JEL Classification: G12, G13     

The optimal asset allocation of the main types of pension funds: a unified framework

The existing literature deals with the optimal investment strategy of defined benefit (DB) or defined contribution (DC) pension plans. This article’s objective is to compare the optimal policies of different types of pension plans. This is done by first defining an original framework, which is based on the distinction between the nature of the guarantee—which can be internal or external—offered by or to a pension fund. This framework allows to establish links between optimization programs of DC, DB and targeted money purchase schemes. The case of an internal guarantee appears as a standard portfolio insurer’s problem. The second kind of guarantee, not analyzed in the literature yet with regard to the resulting optimal policy, is characterized by the existence of an option in the final wealth definition. Four funds are present in the internal guarantee optimal allocation: the speculative component, the preference independent guarantee- and contribution-hedge terms and the preference dependent state variable-hedge fund. The external guarantee program, solved with an original method using the principles of standard options theory, yields an optimal policy incorporating the delta of the option embodied in the final wealth definition. The conclusion is that the resulting optimal portfolio policy becomes riskier.

An Actuarial Analysis of Participating Life Insurance

An actuarial model is developed to reveal the intrinsic nature of participating life insurance. The basic safe-side criterion is examined. It is established how the first-order prospective net premium reserve includes safety margins or bonus loadings, and it is demonstrated how the bonus loadings are currently released. It is demonstrated how surplus may be distributed and accumulated as a terminal bonus in an equitable way. The level premium is divided into a variable recurrent single premium and a variable natural premium, and an alternative to the prospective net premium reserve is examined. A capitalization of future safety margins or bonus loadings, which are related to past premiums and the paid-up benefit, may allow the insurance company a considerable increase in investment freedom. The theory is illustrated by numerical results.     

Poverty traps and intergenerational transfers

In this paper, by adopting an OLG neoclassical growth model, we show that intergenerational transfers may trigger the take off of an economy entrapped into poverty in a twofold way: (1) by eliminating the zero equilibrium, which, under technology with low factor substitutability, is always a “catching” point, so that the economy might start converging to a positive equilibrium. In this case, the appropriate instrument turns out to be a transfer from the old to the young, while there is no room for policies redistributing in the opposite direction (i.e., a pay-as-you-go pension scheme); (2) when the rich equilibrium is unstable—which can be the case under high intertemporal elasticity of substitution of individuals—the introduction of transfers may stabilize such an equilibrium, so that the economy starts converging to it. In the latter case, both policy programs such as pay-as-you-go pension schemes or subsidies to the young may help escaping from poverty. However, we point out that in either circumstance, the “size” of transfers should be sufficiently large (and, as for pensions, not even too large), in order to avoid ineffective and useless burden on the taxpayers without triggering the take off.      

The Pension Protection Fund*

We develop a model of the Pension Protection Fund (PPF), a defined benefit pension guarantee system for the UK, based on an analogy between pension liabilities and corporate debt obligations. We show that the PPF is likely to face many years of low claims interspersed irregularly with periods of very large claims. There is a significant chance that these claims will be so large that the PPF will default on its liabilities, leaving the government with no option but to bail it out. The cause of this problem is the double impact of a fall in equity prices on the PPF: it makes sponsor firms more likely to default and it makes defaulted plans more likely to be underfunded. We use our model to derive a fair premium for PPF insurance under different circumstances, to estimate the extent of cross‐subsidies in the PPF between strong and weak sponsors, and to show that risk‐rated premiums are unlikely to have a substantial effect on either the size or the lumpiness of claims. We argue that for the PPF to operate effectively, it should be introduced in tandem with strong minimum funding requirements and a lower level of benefit guarantee than at present.     

Yes We Can (Price Derivatives on Survivor Indices)

We propose a simulation approach to value derivatives when the underlying dynamics are estimated using the survivor indices directly. Our results show that survivor forward and swap premiums increase with maturity and with the market price of risk. Our results also confirm that taking the optionality into consideration is important from a pricing perspective, for both U.S. women and men. We compare our results to what is obtained using an alternative modeling approach in which a Lee–Carter model is used to indirectly model the survivor index. Compared to this method, our estimated premiums and prices are higher for all longevity products. Moreover, comparing American‐style with European‐style options we find that, although the early exercise option has value when using survivor indices directly, the relative value of the early exercise option is significantly less than when the Lee–Carter model is used to indirectly model the survivor index. It follows that the assumed mortality dynamics have important implications for the term structure of forward and swap premiums and for the effect that changes in the market price of risk has on them.     

浙江农村社会保障市场机制利用的调查报告

浙江省农村社会保障引入市场机制,在工作实践中创造出保险公司经办新农保业务的"衢江模式"、银行贷款垫交养老保险费用的"柯城模式"、引进市场机制提高医疗保障程度的"金华模式",这些创新在便民惠民的同时减轻了地方政府负担,提高了管理经办效率。浙江经验意味着,为促进我国农村社会保障的发展,可以从四个层次逐步深化对市场机制的利用。     

Skewness of Returns, Capital Adequacy, and Mortgage Lending

We calibrate a simulation model of credit value-at-risk for mortgage lending to UK experience. Simulations to capture the skewness of returns that might arise in the context of a financial crisis suggest that the IRB calculations of the new Basel Accord can substantially understate prudential capital adequacy. The same model shows that raising capital requirements has only a small impact on bank funding costs. We conclude that Pillar 2 supervisory review should increase capital requirements above IRB levels for secured bank assets—those whose returns can potentially fall furthest, relative to other, normally “riskier” assets, in extreme outcomes. JEL classification: G21, G28, R31. Presented at the December 2003 conference at the University of Tor Vegata, Rome. We are grateful for comments from William Lang, Mario Onarato, Larry Wall, and from an anonymous referee. All errors and omissions are our own responsibility. “The lady doth protest too much, methinks. The Queen's response to the players in Hamlet, Act 3, scene 2.