We propose a fault-tolerant broadcasting algorithm for hypercubes with link faults. This algorithm is based on an extended spanning binomial tree structure that still keeps the simplicity of conventional binomial-tree-based broadcasting. In addition, it is optimal in the sense that exactly n steps are required to complete a broadcast in an n-dimensional injured hypercube with up to n 2 faulty l...

We present an algorithm and its software implementation that computes implied volatilities for exchangetraded stock options. The LR (Leisen-Reimer) binomial tree is used for the underlying option pricing, which is adjusted for dollar cash dividends. The Brent’s method is used as the root-finding procedure. The option pricing procedure that is at the core of the root-finding is optimised to maxi...

This paper proposes an envelope rejection method for computer sampling from the negative binomial distribution, with index parameter α and probability parameter p, based on a simple probability distribution inequality. Comparative timings with existing methods of generating NB variates show that the proposed method is comparable or faster when α is not too large (α < 11), and it is fastest for ...

We present new families of lower bounds for the price of the American put option on a dividend paying stock when the stock follows a log normal process and the option can be exercised continuously to a finite horizon . By put call parity, these bounds can be easily converted to bounds on the price of the Ameican call option on a dividend paying stock. By numerically optimizing these bounds, we ...

A binomial lattice approach is proposed for valuing options whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two simple ideas: a log-transformation of the underlying processes, which is step by step consistent with the continuous-time diffusions, and a change of basis of the asset span, to transform asset prices ...

A new family of binomial trees as approximations to the Black–Scholes model is introduced. For this class of trees, the existence of complete asymptotic expansions for the prices of vanilla European options is demonstrated and the first three terms are explicitly computed. As special cases, a tree with third order convergence is constructed and the conjecture of Leisen and Reimer that their tre...

In this paper, we develop a decision model of a firm’s optimal strategy for investment in security process innovations (SPIs) when confronted with a sequence of malicious attacks. The model incorporates real options as a methodology to capture the flexibility embed ded in such investment decisions. SPIs, when seamlessly integrated with the organization’s overall business dynamics, induce organi...

In this work, we present a model to value capacity investment decisions based on real options. In the problem considered we incorporate partial reversibility by letting the firm reverse its capital investment at a cost, both fully or partially. The standard RO approach considers the stochastic variable to be normally distributed and then approximated by a binomial distribution, resulting in a b...

We propose using a real options framework to quantify the financial value of cross training. We model the investment decision in cross training as a series of European call options with the same exercise price but with different maturity dates. We use the Black-Scholes formula and the binomial tree approach to find the value of having the option to cross train. A case study shows the applicatio...

Consider the following network subscription pricing problem. We are given a graph G = (V,E) with a root r, and potential customers are companies headquartered at r with locations at a subset of nodes. Every customer requires a network connecting its locations to r. The network provider can build this network with a combination of backbone edges (consisting of high capacity cables) that can rout...