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...

This paper develops a simple technique for valuing European and American derivatives with underlying asset risk-neutral returns that depart from lognormal in terms of prespecified non-zero skewness and greater-than-three kurtosis. Instead of specifying the entire risk-neutral distribution by the riskless return and volatility (as in the Black-Scholes case), this distribution is specified by its...

Option pricing is a tool that investors often use for the purpose of arbitrage or hedging. However, both the BlackScholes model and the CRR model can only provide a theoretical reference value. The volatility in the CRR model cannot always appear in the precise sense because the financial markets fluctuate from time to time. Hence, the fuzzy volatility is naturally to be considered. The main pu...

We study several enumerative properties of the set of all binary strings without zigzags, i.e., without substrings equal to 101 or 010 . Specifically we give the generating series, a recurrence and two explicit formulas for the number wm,n of these strings with m 1’s and n 0’s and in particular for the numbers wn = wn,n of central strings. We also consider two matrices generated by the numbers ...

Let Fq be a finite field of q = pm elements with characteristic p. A polynomial P(x) ∈ Fq[x] is called a permutation polynomial of Fq if P(x) induces a bijective map from Fq to itself. In general, finding classes of permutation polynomials of Fq is a difficult problem (see [3, Chapter 7] for a survey of some known classes). An important class of permutation polynomials consists of permutation p...