Pricing Participating Inflation Retirement Funds Through Option Modeling and Copulas

Abstract

Pension plans and life insurances offering minimum performance guarantees are very common worldwide. In the Brazilian market, the customers of a common type of defined contribution plan have the right to receive, over their savings, the positive difference between the return of a specified investment fund, usually a fixed income fund, and the minimum guaranteed rate, commonly defined as the composition of a fixed interest rate and a floating inflation rate. This instrument can be characterized as an option to exchange one asset, the minimum guaranteed rate, for another, the return of the specified investment fund. In this paper we provide a closed formula to evaluate this liability that depends on two stochastic rates assuming bivariate normality. We also explore the use of copulas for the modeling of the dependence structure and price the options using Monte Carlo simulation to compare the effects of the copula specification in their values. An application with real data is provided. The model makes use of a one-factor Vasicek framework for the term structures of interest rate and inflation rate.     

An Exact Bond Option Formula

This paper derives a closed-form solution for European options on pure discount bonds, assuming a mean-reverting Gaussian interest rate model as in Vasicek [8]. The formula is extended to European options on discount bond portfolios.     

Option Pricing under Stochastic Interest Rates: An Empirical Investigation

Using daily data of the Nikkei 225 index, call option prices and call money rates of the Japanese financial market,a comparison is made of the pricing performance of stock option pricing modelsunder several stochastic interest rate processes proposedby the existing term structure literature.The results show that (1) one option pricing modelunder a specific stochastic interest ratedoes not significantly outperformanother option pricing model under an alternative stochasticinterest rate, and (2) incorporating stochastic interest ratesinto stock option pricing does not contribute to the performanceimprovement of the original Black–Scholes pricing formula.     

佣金制度的改革:渐进市场化

固定佣金制度作为金融约束框架下的结构性制度安排，在市场初创时期起了重要作用，但与日前加剧的市场竞争不相适应，需要进行改革；在我国，最佳的改革方式可能是渐进的佣金市场化。     

缓行渐进与制度准备:央行支农再贷款淡出策略探讨

支农再贷款作为一项非常政策安排,对农村尤其是对贫困地区的“政策扶贫”和“政策补贴”的倾向性效应十分显著,但同时存在着诸多实践偏差和理论缺陷,已经对央行货币政策有效实施构成钳制,有必要对其未来取向进行建设性研究。     

Recent Superannuation Reforms: Choice and Flexibility in Retirement

This introduction to AAR's Forum on superannuation surveys the increased choice and flexibility available to retirement savers, with particular emphasis on the proposals announced in the May 2006 commonwealth budget. In an environment of greater reliance on defined-contribution superannuation arrangements, increased member choice means an increased responsibility on individual fund members to make active and appropriate decisions. As indicated in the analysis of papers in the Forum, some guidance may be required to ensure an adequate standard of living in retirement for all.     

Self-Annuitization and Ruin in Retirement

Abstract

At retirement, most individuals face a choice between voluntary annuitization and discretionary management of assets with systematic withdrawals for consumption purposes. Annuitization–buying a life annuity from an insurance company–assures a lifelong consumption stream that cannot be outlived, but it is at the expense of a complete loss of liquidity. On the other hand, discretionary management and consumption from assets–self-annuitization–preserves flexibility but with the distinct risk that a constant standard of living will not be maintainable.

In this paper we compute the lifetime and eventual probability of ruin (PoR) for an individual who wishes to consume a fixed periodic amount–a self-constructed annuity–from an initial endowment invested in a portfolio earning a stochastic (lognormal) rate of return. The lifetime PoR is the probability that net wealth will hit zero prior to a stochastic date of death. The eventual PoR is the probability that net wealth will ever hit zero for an infinitely lived individual.

We demonstrate that the probability of ruin can be represented as the probability that the stochastic present value (SPV) of consumption is greater than the initial investable wealth. The lifetime and eventual probabilities of ruin are then obtained by evaluating one minus the cumulative density function of the SPV at the initial wealth level. In that eventual case, we offer a precise analytical solution because the SPV is known to be a reciprocal gamma distribution. For the lifetime case, using the Gompertz law of mortality, we provide two approximations. Both involve “moment matching” techniques that are motivated by results in Arithmetic Asian option pricing theory. We verify the accuracy of these approximations using Monte Carlo simulations. Finally, a numerical case study is provided using Canadian mortality and capital market parameters. It appears that the lifetime probability of ruin–for a consumption rate that is equal to the life annuity payout–is at its lowest with a well-diversified portfolio.     

The Cost of Employee Stock Option Grants: An Empirical Analysis

This study presents empirical evidence on the ex post costs of employee stock option (ESO) grants to issuing firms and examines whether the Black–Scholes [1973] model provides reasonable estimates of these values. Because there are no market prices for ESOs, the traditional avenues for testing option–pricing models are unavailable. This research relies instead on techniques from the economic forecasting literature, viewing model values as forecasts of the options' payoff. The theoretically appropriate rate at which to discount ESO payoffs is derived under the maintained hypothesis that the Black–Scholes model is valid. This rate is used in estimating ex post ESO costs at the time of grant, which are then compared with Black–Scholes estimates using Theil's [1966] tests of forecast rationality. Based on a sample of 966 ESO grants over 1963–1984, the results suggest that the Black–Scholes model, adjusted for concavity in the time to exercise using the Hemmer, Matsunaga, and Shevlin [1994] procedure, appears to provide reasonable estimates of ex post ESO costs for the average ESO grant. However, there is significant variability in the amount of model error on an individual grant basis.     

Aging and Retirement: Evidence Across Countries

How do demographic factors influence retirement? Using a large cross-country data set, I show that in countries with a larger share of elderly in their population the length of retirement is longer. This result holds true if I control for wealth effects, and when the effective labor force participation rate of the elderly is used instead of the official retirement age. Retirement policies and the social security size are strictly related: a new variable, representing the aggregate relevance of retirement policies, turns out to be significant in explaining the size of social security. Finally, the total amount of social security transfers is positively related with the increase of the elderly population, while in per capita terms this relation is not significant.     

Industrial Production in Germany: Recovery Only Gradual

Original Papers

Industrial Production in Germany: Recovery Only Gradual     

The Quality Option and Timing Option in Futures Contracts

Often futures contracts contain quality options whereby the short position has the choice of delivering one of an acceptable set of assets. We explore the implications of the quality option on the futures price. We develop a method for pricing the quality option for the general case of n deliverable assets and provide numerical illustrations of its significance. Even when the asset prices are very highly correlated, this option can have nontrivial value, especially when there is a large number of deliverable assets. We analyze the impact of the timing option and its interaction with the quality option. A procedure is developed for valuing the timing option in the presence of the quality option, and some numerical estimates are obtained.     

我国二元期权交易的法律规制路径研究

境外二元期权存在场内交易、场外交易两种形式。场内二元期权由交易所提供,具有一定风险管理职能,受到监管当局的严格监管;场外二元期权依托互联网传播,多为发行机构与投资者的对赌交易,交易风险不容忽视。二元期权业务在我国的发展过程中有意省略了合约设计的原理说明,并割裂了其服务国民经济功能,与我国期货市场的目标、宗旨及发展思路相悖,极易沦为赌博、诈骗之工具。现阶段放开二元期权管制的条件尚不成熟,但可结合特定领域风险管理的现实需要,引导其由场外对赌回归场内交易,以发挥交易所中央对手方的制度优势,强化投资者保护,实现产品创新与规范发展的法治路径。     

An Empirical Portfolio Perspective on Option Pricing Anomalies

We empirically study the economic benefits of giving investorsaccess to index options in the standard portfolio problem, analyzingboth expected-utility and nonexpected-utility investors in orderto understand who optimally buys and sells options. Using dataon S&P 500 index options, CRRA investors find it alwaysoptimal to short out-of-the-money puts and at-the-money straddles.The option positions are economically and statistically significantand robust to corrections for transaction costs, margin requirements,and Peso problems. Loss-averse and disappointment-averse investorsalso optimally hold short option positions. Only with highlydistorted probability assessments can we obtain positive portfolioweights for puts (cumulative prospect theory and anticipatedutility) and straddles (anticipated utility).     

Retirement and Healthy Eating

This paper investigates the effect of retirement on healthy eating using data drawn from the Survey of Health, Ageing and Retirement in Europe (SHARE). We estimate the causal effect of retiring from work on daily fruit or vegetable consumption by exploiting policy changes in eligibility rules for early and statutory retirement. Our results show that changes in eating behaviour upon retirement are gender-specific: retirement induces men to reduce healthy eating; it has no effect on women. We further show that, for men, retirement increases the probability of becoming obese.     

我国职工退休年龄影响因素的实证研究

当前我国劳动力逐渐短缺,职工退休年龄直接关系到我国劳动力供给的数量和结构。使用2011年在广东省21个地市的问卷调查数据,研究影响职工退休年龄问题的影响因素。实证研究表明,工资、工龄对职工退休年龄的影响显著为正。养老金对男职工退休年龄的影响显著为负。机关事业单位职工的退休年龄更晚。教育年限对女职工的影响显著为正。已婚、...     

Option Delisting of Stocks That Continue Trading: An Examination of Welfare Effects

This paper addresses the resulting effects from the delisting of options on underlying stocks that continue to trade. The evidence generally supports the argument that options in this sample are delisted as a result of financial difficulty and/or a lack of interest. An insignificant average abnormal return and a small significantly negative average standardized abnormal return are observed around the delisting date, but the average price effect is determined to be considerably less than the normal discrete trading intervals at which stocks trade on exchanges. There are no effects found on volatility measures directly attributable to option delisting.