This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. Finally, the error analysis and some numerical examples are provided...

A convertible bond is defined to be (e.g., Jorion [10]) a bond issued by a corporation that can be converted into the equity of that corporation at certain times using a predetermined exchange ratio. This entails the creation of new shares issued by the corporation if and when conversion occurs, and the existing shares are diluted by the creation of the new shares. The option to convert is sole...

We characterize the solution to the consumption and investment problem of a timeadditive power utility investor in a continuous-time dynamically complete market with stochastic changes in the opportunity set. It is demonstrated that under stochastic interest rates the investor optimally hedges against changes in the term structure of interest rates by investing in a coupon bond, or portfolio of...

this paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (tfs) in combination with the collocation method. the method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. finally, the error analysis and some numerical examples are provided...

The concept of best-estimate, prescribed by regulators to value insurance liabilities for accounting and solvency purposes, has recently been discussed extensively in the industry and related academic literature. To differentiate hedgeable and non-hedgeable risks in a general case, recent literature defines best-estimates using orthogonal projections of a claim on the space of replicable payoff...

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be deriv...

The focus of this work is on numerical solutions to two-factor option pricing partial differential equations with variable interest rates. Two interest rate models, the Vasicek model and the Cox-Ingersoll-Ross model (CIR), are considered. Emphasis is placed on the definition and implementation of boundary conditions for different portfolio models, and on appropriate truncation of the computatio...

Three approaches in obtaining the closed-form solution of the Vasicek bond pricing problem are discussed in this exposition. A derivation based solely on the distribution of the short rate process is reviewed. Solving the bond price partial differential equation (PDE) is another method. In this paper, this PDE is derived via a martingale approach and the bond price is determined by integrating ...

In this paper, we focus on the calibration of affine stochastic mortality models using insurance contracts premiums. Viewing insurance contracts as “market products,” we propose fitting stochastic models on the quotes of insurance policies. For this purpose, insurance contracts are viewed as a “swap” in which policyholders exchange cash flows (premiums vs. benefits) with an insurer analogous to...

The paper provides a discussion of the most relevant aspects of yield curve modeling. Two classes of models are considered: stochastic and parsimonious function based, through the approaches developed by Vasicek (1977) and Nelson and Siegel (1987). Yield curve estimates for Croatia are presented and their dynamics analyzed and finally, a comparative analysis of models is conducted. Keywords—the...