Lognormal Approximation of Complex Path-dependent Pension Scheme Payoffs

This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation based numerical experiments, and we point to several other potential practical applications of the paper’s theoretical results.Account-based pension schemes; return smoothing; payoff distributions; density approximation; Monte Carlo simulation; Asian options

Weighted Sum of Correlated Lognormals: Convolution Integral Solution

Probability density function (pdf) for sum of n correlated lognormal variables is deducted as a special convolution integral. Pdf for weighted sums (where weights can be any real numbers) is also presented. The result for four dimensions was checked by Monte Carlo simulation

Interference and Deployment Issues for Cognitive Radio Systems in Shadowing Environments

In this paper we describe a model for calculating the aggregate interference encountered by primary receivers in the presence of randomly placed cognitive radios (CRs). We show that incorporating the impact of distance attenuation and lognormal fading on each constituent interferer in the aggregate, leads to a composite interference that cannot be satisfactorily modeled by a lognormal. Using the interference statistics we determine a number of key parameters needed for the deployment of CRs. Examples of these are the exclusion zone radius, needed to protect the primary receiver under different types of fading environments and acceptable interference levels, and the numbers of CRs that can be deployed. We further show that if the CRs have apriori knowledge of the radio environment map (REM), then a much larger number of CRs can be deployed especially in a high density environment. Given REM information, we also look at the CR numbers achieved by two different types of techniques to process the scheduling information.Comment: to be presented at IEEE ICC 2009. This posting is the same as the original one. Only author's list is updated that was unfortunately not correctly mentioned in first versio

Asymptotic tail behavior of phase-type scale mixture distributions

We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the scaling random variable. We investigate conditions for such a class of distributions to be either light- or heavy-tailed, we explore subexponentiality and determine their maximum domains of attraction. Particular focus is given to phase-type scale mixture distributions where the scaling random variable $S$ has discrete support --- such a class of distributions has been recently used in risk applications to approximate heavy-tailed distributions. Our results are complemented with several examples.Comment: 18 pages, 0 figur

Heterogeneous Basket Options Pricing Using Analytical Approximations

This paper proposes the use of analytical approximations to price an heterogeneous basket option combining commodity prices, foreign currencies and zero-coupon bonds. We examine the performance of three moment matching approximations: inverse gamma, Edgeworth expansion around the lognormal and Johnson family distributions. Since there is no closed-form formula for basket options, we carry out Monte Carlo simulations to generate the benchmark values. We perfom a simulation experiment on a whole set of options based on a random choice of parameters. Our results show that the lognormal and Johnson distributions give the most accurate results.Basket Options, Options Pricing, Analytical Approximations, Monte Carlo Simulation