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Binomial trees are very popular in both theory and applications of option pricing. As they often suffer from an irregular convergence behavior, improving this is an important task. We build upon a new version of the Edgeworth expansion for lattice models to construct new and quickly converging binomial schemes with a particular application to barrier options.

In a sequence of independent Bernoulli trials, by counting multidimensional lattice paths in order to compute the probability of a first-passage event, we derive and study a generalized negative binomial distribution of order k, type I, which extends to distributions of order k, the generalized negative binomial distribution of Jain and Consul (1971), and includes as a special case the negative...

Spatially explicit ecosystem models of all types require an initial allocation of biomass, often in areas where fisheries independent abundance estimates do not exist. A generalized additive modelling (GAM) approach is used to describe the abundance of 40 species groups (i.e. functional groups) across the Gulf of Mexico (GoM) using a large fisheries independent data set (SEAMAP) and climate sca...

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processes and take values in a two-dimensional binomial tree. The other two component...

Compound processes are proposed as models for the acquisition of hydatid cysts in sheep, caused by the parasite Echinococcus granulosus. The hypothesis of a clumped infection process against single ingestions is tested and it is shown that the clump-based approach provides a more accurate description of the two data sets investigated. Models with simple and mixed Poisson incidence processes and...

This paper proposes a new efficient algorithm for the computation of Greeks for options using the binomial tree. We also show that Greeks for European options introduced in this article are asymptotically equivalent to the discrete version of Malliavin Greeks. This fact enables us to show that our Greeks converge to Malliavin Greeks in the continuous time model. The computation algorithms of Gr...

Oscillatory behavior of cumulant moments obtained from the experimental data in pp collisions and p̄p collisions are analyzed by the modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Both distributions well describe the cumulant moments obtained from the data. This fact shows sharp contrast to the result in ee collisions, which is described by the the M...

We thank the editor and an anonymous referee. Any errors are our own. Abstract Using the WACC to Value Real Options We present a real option valuation using the weighted average cost of capital (WACC). This is an alternative to risk-neutral real option valuation. Using the WACC involves a marginal increase in mathematical complexity, but it is easy to implement in a spreadsheet, and it is easy ...

A new binomial approximation to the Black–Scholes model is introduced. It is shown that for digital options and vanilla European call and put options that a complete asymptotic expansion of the error in powers of n−1 exists. This is the first binomial tree for which such an asymptotic expansion has been shown to exist.