Binomial trees are widely used for both financial and real option pricing due to their ease of use, versatility and precision. However, the classic approach developed by Cox, Ross, and Rubinstein (1979) applies only to a Geometric Brownian Motion diffusion processes, limiting the modeling choices. Nelson and Ramaswamy (1990) provided a general method to construct recombining binomial lattices w...

Combinatorial methods prove extremely useful towards designing blazingly fast yet simple algorithms for pricing European-style barrier options. Closed-form formulae to standard European-style barrier options can then be easily derived. Combinatorial formulae under the trinomial model are also presented. The common practice in the literature compares algorithms based on their respective numbers ...

In this paper, we discuss statistical families P with the property that if the distribution of a random variable X is in P, then so is the distribution of ZwBi(X, p) for 0%p%1. (Here we take ZwBi(X, p) to mean that given XZx, Z is a draw from the binomial distribution Bi(x, p).) It is said that the family is closed under binomial subsampling. We characterize such families in terms of probabilit...

An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne’s test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it pe...

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 ...

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Statistical methods for the use of historical control data in testing for a trend in proportions in carcinogenicity rodent bioassays are reviewed. Asymptotic properties of the Hoel-Yanagawa exact conditional tests are developed and compared with the Tarone test. It is indicated that the Hoel-Yanagawa test is more powerful than the Tarone test. These tests depend on the beta-binomial parameters ...

A class of new type graded infinite posets with minimal element is introduced. These so called cobweb posets proposed recently by the present author constitute a wide range of new noncommutative and nonassociative prefab combinatorial schemes‘ examples with characteristic graded sub-posets as primes. These schemes are defined here via relaxing commutativity and associativity requirements impose...

We study the detailed convergence of the binomial tree scheme. It is known that the scheme is first order. We find the exact constants, and show it is possible to modify Richardson extrapolation to get a method of order three-halves. We see that the delta, used in hedging, converges at the same rate. We analyze this by first embedding the tree scheme in the Black-Scholes diffusion model by mean...

An edge-colored graph G is conflict-free connected if, between each pair of distinct vertices, there exists a path containing a color used on exactly one of its edges. The conflict-free connection number of a connected graph G, denoted by cfc(G), is defined as the smallest number of colors that are required in order to make G conflict-free connected. A coloring of vertices of a hypergraph H = (...