MATHEMATICAL SCIENCES
Year:2012 | Volume:6 | Issue:-|Papers Count:4

Purpose: This paper develops new fast and accurate computational schemes for pricing European and American bond options under generalised Chan-Karoyli-Longstaff-Sanders term structure models.Methods: We use high-order compact discretisations of the pricing equations and an operator splitting method for American options.Results: Highly accurate numerical solutions can be computed using relatively coarse grid sizes and numerical solutions exhibiting fourth-order convergence are obtained for bond and bond option prices. The scheme is also stable and efficient for pricing financial problems with time dependent parameters.Conclusions: The new schemes are efficient alternatives to schemes based on the Crank-Nicolson discretisation for the pricing of interest rate derivatives.

Purpose: The purpose of this paper is to study a common fixed point theorem for two pairs of weakly compatible maps in dislocated metric spaces.Methods: Using familiar techniques, we extend the results of Hitzler and Kang et al. in dislocated metric spaces.

The purpose of the present paper is to establish some important fractional difference inequalities of Gronwall-Bellman type that have a wide range of applications in the study of fractional difference equations.

LetG be a group. Let R be a G -graded commutative ring with identity, and let M be a G -graded module over R. Two graded submodulesN and K of graded module M are called graded coprime whenever N+K=M. In this paper, some properties of graded coprime submodules are discussed. For example, we show that ifM is a graded finitely generated module, then two graded submodulesN and K of M are graded coprime if and only if gradM (N) and gradM (K)are graded coprime.