Continuously Paying Options (CPOs) form a very natural class of derivatives for hedging risks coming from adverse movements of a continuously traded asset. We study the rate of convergence of CPOs evaluated under the binomial tree scheme when the payout function φ is piecewise C subject to some boundedness conditions. We show that if φ is continuous, the rate of convergence is n−1 while it is n...

Mathematical models have been used to understand the transmission dynamics of infectious diseases and to assess the impact of intervention strategies. Traditional mathematical models usually assume a homogeneous mixing in the population, which is rarely the case in reality. Here, we construct a new transmission function by using as the probability density function a negative binomial distributi...

The theory of modular binomial lattices enables the simultaneous combinatorial analysis of finite sets, vector spaces, and chains. Within this theory three generalizations of Stifling numbers of the second kind, and of Lah numbers, are developed. 1. Stirling numbers and their formal generalizations The nota t ional convent ions of this paper are as follows: N = {0,1,2 . . . . }, P = {1,2,. . . ...

This paper deals with modeling heterogeneous volumetric objects as point sets with attributes using trivariate B-splines. In contrast to homogeneous volumes with uniform distribution of material and other properties, a heterogeneous volumetric object has a number of variable attributes assigned at each point. An attribute is a mathematical model of an object property of arbitrary nature (materi...

This article discusses convergence problems when calculating Vega (option sensitivity to volatility) that arise from discretization errors embedded in the lattice approach. Four alternative improvements to the traditional binomial method are discussed and investigated for performance. We also propose a new Modified Binomial (MB) Method to calculate Vegas. Numerical results show that although th...

Software pricing has traditionally been focused on the vendor’s internal business objectives of covering costs, achieving specified margins, and meeting the competition. Pricing methods such as flat price, tiered pricing, MIPS-based, usage-based, per user, per seat, and pay as you go, are often tactical in nature and easily matched by competitors, which can undermine profitability by accelerati...

A special inequality between the tail probabilities of certain related hypergeometrics was shown by Seneta and Phipps [19] to suggest useful ‘quasi-exact’ alternatives to Fisher’s [5] Exact Test. With this result as motivation, two inequalities of Hájek and Havránek [6] are investigated in this paper and are generalised to produce inequalities in the form required. A parallel inequality in bino...

In this paper we provide a closed-form approximation as well as a measure of the error for the price of several twodimensional derivatives under the assumptions of stochastic correlation and constant volatility. The method is applied to the pricing of Spread Options and Quantos Options, while three models for the stochatsic correlation are considered.

We study Lissajous curves in the 3-cube that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications co...

In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that W 3 – the best-possible lower bound for the set of trivariate quasicopulas (and copulas) – is the limit member of this family, showing how the mass of W 3 is distributed on the plane x + y + z = 2 of [0, 1] in an easy manner, and providing the generalization of this result to n dimensions.