An accurate analytical approximation for the price of a European-style arithmetic Asian option.

For discrete arithmetic Asian options the payoff depends on the price average of the underlying asset. Due to the dependence structure between the prices of the underlying asset, no simple exact pricing formula exists, not even in a Black-Scholes setting. In the recent literature, several approximations and bounds for the price of this type of option are proposed. One of these approximations consists of replacing the distribution of the stochastic price average by an ad hoc distribution (e.g. Lognormal or Inverse Gaussian) with the same first and second moment. In this paper we use a different approach and combine a lower and upper bound into a new analytical approximation. This approximation can be calculated efficiently, turns out to be very accurate and moreover, it has the correct first and second moment. Since the approximation is analytical, we can also calculate the corresponding hedging Greeks and construct a replicating strategy.Options; Dependence; Structure; Prices; Hedging; Strategy;

Divulgation de l’orientation sexuelle, soutien de la famille d’origine et adaptation conjugale chez des mères lesbiennes ayant eu leur(s) enfant(s) dans le contexte d’une relation hétérosexuelle. Étude exploratoire

Les couples lesbiens se distinguent des couples hétérosexuels par le fait qu’ils sont contraints de développer leurs relations de couple dans un contexte de sanctions sociales, ce qui pourrait augmenter l’importance de la qualité des liens avec l’entourage. De plus, la divulgation de l’orientation sexuelle représente une caractéristique de cette population qui agit sur l’ajustement psychologique et qui pourrait influencer le soutien familial. Cette étude examine l’effet du coming-out et du soutien familial sur l’ajustement conjugal des mères lesbiennes ayant eu leur(s) enfant(s) dans le contexte d’une relation hétérosexuelle. Nous nous attendons à ce que le soutien familial soit un médiateur du lien entre le coming-out et l’ajustement conjugal. Cinquante-cinq mères lesbiennes en couple ont rempli des questionnaires portant sur la perception du soutien familial, le coming-out et l’ajustement conjugal. Les résultats révèlent un lien positif entre le coming-out et le soutien familial et entre le soutien familial et l’ajustement conjugal, mais aucun lien entre le coming-out et l’ajustement conjugal. Le modèle de médiation n’est pas confirmé. Les implications de ces résultats sont discutées.Lesbian couples differ from heterosexual couples in that they must develop their relationship within an environment that is generally unsympathetic to homosexuality, a fact that could accentuate the importance of family support. Furthermore, the disclosure of their sexual orientation by lesbian couples could also affect the support given by family members. The present study examines the effect of coming-out and family support on the relationship adjustment of lesbian mothers whose children were born within a heterosexual context. It was expected that family support would mediate the relationship between coming-out and relationship adjustment. Fifty-five lesbian mothers currently in a relationship answered questions about their perception of family support, on their coming-out behaviour and their relationship adjustment. Results revealed a positive relationship between coming-out and family support, and between family support and relationship adjustment, however no association was found between coming-out and relationship adjustment. The mediation model was therefore not confirmed. Finally, the authors discuss the implications of these results.Las parejas lesbianas se distinguen de las parejas heterosexuales por el hecho de que están restringidas a desarrollar sus relaciones de pareja en un contexto de sanciones sociales, lo que podría aumentar la importancia de la calidad de las relaciones con el entorno. Además, la divulgación de la orientación sexual representa una característica de esta población que actúa sobre el ajuste psicológico y que podría influir en el apoyo familiar. Este estudio examina el efecto de “salir del armario” y del apoyo familiar en el ajuste conyugal de las madres lesbianas que tienen hijo(s) en el contexto de una relación heterosexual. Esperamos que el apoyo familiar sea un mediador de la relación entre el “salir del armario” y el ajuste conyugal. Cincuenta y cinco madres lesbianas en pareja respondieron los cuestionarios acerca de la percepción del apoyo familiar, el “salir del armario” y el ajuste conyugal. Los resultados revelan una relación positiva entre el “salir del armario” y el apoyo familiar, y entre el apoyo familiar y el ajuste conyugal, pero no se confirmó ninguna relación entre el “salir del armario” y el ajuste conyugal. El modelo de mediación no ha sido confirmado. Se discuten las implicaciones de estos resultados.Os casais de lésbicas distinguem-se dos casais heterossexuais pelo fato que eles são forçados a desenvolver suas relações amorosas em um contexto de sanções sociais, o que poderia aumentar a importância da qualidade das relações com o meio. Além disto, a divulgação da orientação sexual representa uma característica desta população que age no ajustamento psicológico e que poderia influenciar o apoio familiar. Este estudo examina o efeito do “coming-out” e do apoio familiar no ajustamento conjugal das mães lésbicas que tiveram filhos no contexto de uma relação heterossexual. Esperamos que o apoio familiar seja um mediador da relação entre o “coming-out” e o ajustamento conjugal. 55 mães lésbicas em casal preencheram questionários sobre a percepção do apoio familiar, o “coming-out” e o ajustamento conjugal. Os resultados revelam uma relação positiva entre o “coming-out” e o apoio familiar e entre o apoio familiar e o ajustamento conjugal, mas nenhuma relação entre o “coming-out” e o ajustamento conjugal. O modelo de mediação não foi confirmado. As implicações destes resultados são discutidas

The concept of comonotonicity in actuarial science and finance : theory.

n an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic. We will determine approximations for sums of random variables, when the distributions of the terms are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. In this paper, the theoretical aspects are considered. Applications of this theory are considered in a subsequent paper. Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented.Risk; Actuarial; Science; Theory;

Bounds for present value functions with stochastic interest rates and stochastic volatility.

The distribution of the present value of a series of cash flows under stochastic interest rates has been investigated by many researchers. One of the main problems in this context is the fact that the calculation of exact analytical results for this type of distributions turns out to be rather complicated, and is known only for special cases. An interesting solution to this difficulty consists of determining computable upper bounds, as close as possible to the real distribution.In the present contribution, we want to show how it is possible to compute such bounds for the present value of cash flows when not only the interest rates but also volatilities are stochastic. We derive results for the stop loss premium and distribution of these bounds.Distribution; Value; Cash flow; Interest rates; Researchers; Problems;

How to Determine the Capital Requirement for a Portfolio of Annuity Liabilities

This paper illustrates an analytic method that can be used to determine the total capital requirements necessary to properly provide for the future obligations of a portfolio of annuity liabilities and to protect the enterprise from the related risks it faces. This example is based on the work of Kaas, Dhaene and Goovaerts (2000).

General closed-form basket option pricing bounds

This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms; hence, they do not suffer from the curse of dimensionality and can be applied also to high-dimensional problems where most existing methods fail. In particular, we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate