Pricing options on mean reverting underliers

For mean reverting base probabilities, option pricing models are developed, using an explicit measure change induced by the selection of a terminal time and a terminal random variable. The models employed are the square root process and an OU equation driven by centred variance gamma shocks. VIX options are calibrated using the square root process. The OU equation driven by centred variance gamma shocks is applied in pricing options on the ratio of the stock price for J. P. Morgan Chase (JPM) to the Exchange Traded Fund for the financial sector with ticker XLF. For the purposes of calibrating the ratio option pricing model to market data, we indirectly infer the prices for stock options on JPM from the prices for options on the ratio, by hedging the conditional value of JPM options given XLF, using options on XLF. The implied volatilities for the options on the ratio are then indirectly observed to be fairly flat. This suggests that for JPM, the use XLF as a benchmark is a possibly good choice. It is shown to perform better than the use of the S&P 500 index. Furthermore, though the use of an unrelated stock price like Johnson and Johnson as a benchmark for JPM provides as a good fit as does the use of XLF, this comes at the cost of requiring a considerable smile for the implied volatilities on the ratio options and hence a more complex model for the implied distribution on the ratio.     

The Impact of the Automatic Balancing Mechanism for the Public Pension in Japan on the Extreme Elderly

Abstract

Most developed countries are seeking ways to maintain a sustainable social security system. Japan is no exception. The old-age dependency ratio in Japan is currently 35% and is expected to be 74% in 2050. Recently the Japanese government has adopted an automatic balancing mechanism, which gradually reduces the real price of the public pension through a reduction of inflation adjustments. The reduction, depending on future demographics, is a random process, so the elderly, in particular the extreme elderly, have to take the risk of receiving an inadequate public pension. The objectives of this paper are threefold. First, we review the recent trends in Japanese mortality and explain the underlying longevity issues that led to the automatic balancing mechanism. Second, by means of stochastic mortality and fertility modeling, we analyze how demographic changes will affect the future of public pensions in Japan. Third, we demonstrate, on the basis of the stochastic projections we made, how the automatic balancing mechanism will affect the financial security for people who live beyond age 100.     

Jackknife Empirical Likelihood Intervals for Spearman’s Rho

Abstract

In connection with copulas, rank correlation such as Kendall’s tau and Spearman’s rho has been employed in risk management for summarizing dependence between two variables and estimating parameters in bivariate copulas and elliptical models. In this paper a jackknife empirical likelihood method is proposed to construct confidence intervals for Spearman’s rho without estimating the asymptotic variance. A simulation study confirms the advantages of the proposed method.     

A Computationally Efficient Algorithm for Estimating the Distribution of Future Annuity Values Under Interest-Rate and Longevity Risks

Abstract

This paper proposes a computationally efficient algorithm for quantifying the impact of interestrate risk and longevity risk on the distribution of annuity values in the distant future. The algorithm simulates the state variables out to the end of the horizon period and then uses a Taylor series approximation to compute approximate annuity values at the end of that period, thereby avoiding a computationally expensive “simulation-within-simulation” problem. Illustrative results suggest that annuity values are likely to rise considerably but are also quite uncertain. These findings have some unpleasant implications both for defined contribution pension plans and for defined benefit plan sponsors considering using annuities to hedge their exposure to these risks at some point in the future.     

Efficient Pricing of Ratchet Equity-Indexed Annuities in a Variance-Gamma Economy

Abstract

In this paper we propose a new method for approximating the price of arithmetic Asian options in a Variance-Gamma (VG) economy, which is then applied to the problem of pricing equityindexed annuity contracts. The proposed procedure is an extension to the case of a VG-based model of the moment-matching method developed by Turnbull and Wakeman and Levy for the pricing of this class of path-dependent options in the traditional Black-Scholes setting. The accuracy of the approximation is analyzed against RQMC estimates for the case of ratchet equityindexed annuities with index averaging.     

The Second Fundamental Theorem of Asset Pricing

This paper presents a resolution of the paradox proposed by the example of an economy with complette markets and a multiplicityof martingale measures constructed by Artzner and Heath (1995). The resolution lies in noting that completeness is with respect to a topology on the space of cash flows and is connected with uniqueness of the price functional in the topological dual space. Uniqueness may be lost outside the dual and this is what occurs in the counterexample of Artzner and Heath.     

Lessons from the Snowy Slope: Vision and Politics in American Social Insurance

The enactment of social insurance, a fundamental departure from means‐tested welfare programs, was born out of the crisis of the Great Depression. Policy options to strengthen Social Security are mathematically simple, but ideologically contentious. Arguments against the program, remarkably consistent since its inception, have been gaining traction in the current political climate. As the debate proceeds, it is useful to examine the history of opposition and review the case for universal social insurance.     

Sports injuries and injury-preventive behavior related to hockey and volleyball in the Netherlands

Abstract

In a survey of hockey and volleyball players, the number and nature of sports injuries, the percentage of players taking injury-preventive measures (warming up before and cooling down after playing and the use of gum-shields and knee caps) and the main reasons for taking these measures have been assessed by self-reports in a questionnaire. The questionnaire for hockey players was answered by 635 respondents, the questionnaire for volleyball players by 711 players. For both hockey players and volleyball players, an incidence of about 500 injuries per 1000 players per year was found. Almost all volleyball players warmed-up before the last game played and 86% wore knee caps. About 25% of all hockey- and volleyball players took part in cooling down after this game. A gum-shield was used by 25% of the hockeyplayers. Surprisingly, players who took part in cooling down appeared to have a higher number of injuries than those who did not.