Lognormal price dynamics and passage to the continuum limit. After a brief recap of our pricing formula, this section introduces the lognormal model of stock price dynamics, and explains how it can be approximated using binomial trees. Then we use these binomial trees to price contingent claims. The Black-Scholes analysis is obtained in the limit δt → 0. As usual, Baxter–Rennie captures the cen...

The pricing models of American-type path-dependent options are of degenerate parabolic obstacle problems. The binomial tree method is the most popular approach to pricing options. For some special cases, this method is modified in order to make it feasible. The main purpose of this paper is, using numerical analysis and the notion of viscosity solutions, to show the uniform convergence of the b...

Let A = {a1, . . . , am} ⊂ Z be a vector configuration and IA ⊂ K[x1, . . . , xm] its corresponding toric ideal. We completely determine the number of different minimal systems of binomial generators of IA. We also prove that generic toric ideals are generated by indispensable binomials. We associate to A a simplicial complex ∆ind(A). We show that the vertices of ∆ind(A) correspond to the indis...

Lognormal price dynamics and passage to the continuum limit. After a brief recap of our pricing formula, this section introduces the lognormal model of stock price dynamics, and explains how it can be approximated using binomial trees. Then we use these binomial trees to price contingent claims. The Black-Scholes analysis is obtained in the limit δt→ 0. As usual, Baxter–Rennie captures the cent...

Modern networks typically limit the size of the largest packet for efficient communication. Thus, long messages are packetized and transmitted. Such networks also provide network interface support for nodes, which typically includes a coprocessor and memory, to implement the lower layers of the communication protocol. This paper presents a concept of smart network interface support for packetiz...

In a variety of research domains, data are generated as a consequence of the count process and may possess an ‘excess’ of zeros. There have been many attempts to analyse such data using different statistical methods, including the zero-inflated Poisson (ZiP) and zero-inflated binomial (ZiB) models. The interpretation of these models is however problematic if the covariates considered for the no...

Stochastic differential equations and the Black-Scholes PDE. We derived the BlackScholes formula by using arbitrage (risk-neutral) valuation in a discrete-time, binomial tree setting, then passing to a continuum limit. This section explores an alternative, continuoustime approach via the Ito calculus and the Black-Scholes differential equation. This material is very standard; I like Wilmott-How...

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mell...

In this paper we consider partnership deals under uncertainty but with downstream flexibility. We confine ourselves to bilateral deals and focus on the effect of options on the synergy set, the ‘core’, of a partnership deal. We distinguish between cooperative options, which are exercised jointly and in the interest of maximizing the total deal value, and non-cooperative options, which are exerc...

Binomial trees have been used extensively for broadcasting in clusters of workstations. In the case of heterogeneous nondedicated clusters and grid environments, the broadcasting occurs over a heterogeneous network, and the performance obtained by the broadcast algorithm will depend on the organization of the nodes onto the binomial tree. The organization of the nodes should take into account t...