The simplest model for pricing d erivative securities is the binomial model. It generalizes the o n e period \up-down" model of Chapte r 1 t o a m ulti-period setting, assuming t hat t he price of the u nderlying asset follows a random walk. In the binomial model, there are N trading periods and N+1 trading d ates, t 0 t 1 ::: t N when it is possible to i n vest in a risky security with p r i c...

We show for every k ≥ 1 that the binomial tree of order 3k has a vertex-coloring with 2k+1 colors such that every path contains some color odd number of times. This disproves a conjecture from [1] asserting that for every tree T the minimal number of colors in a such coloring of T is at least the vertex ranking number of T minus one.

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...

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market-implied probability distributions for commodity prices. Also, the existence of long-dated futures options means that good ...

An option is a nancial contract whose value depends on that of an underlying asset such as a company stock. The Black-Scholes model for option pricing, published in 1973, revolutionized the nancial industry by introducing a no-arbitrage paradigm for valuing uncertainty and hedging against risk. This simple model assumes that the underlying stock price follows a stochastic Brownian motion proces...

More than 60% of accidents in Iran occur within 30 kilometers of cities entrance roads. Therefore the number of accidents per kilometer in these regions, in contrast to the other parts of roads is very considerable. The city of Tehran, as the capital of Iran, is the cross point of major arterials of passenger and freight transportation. Thus the evaluation of road safety, entering and exiting t...

In this paper a univariate discrete distribution, denoted by GIT, is proposed as a generalization of the shifted inverse trinomial distribution, and is formulated as a first-passage time distribution of amodified randomwalk on the half-plane with five transition probabilities. In contrast, the inverse trinomial arises as a random walk on the real line with three transition probabilities. The pr...