We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of ...

The aim of this paper is to develop a methodology to estimate the interest rates yield curve and its dynamics in the Tunisian bond market, which is considered as an illiquid market with a low trading volume. To achieve this, first, we apply the cubic spline interpolation method to deal with the missing observation problem. Second, we focus on the work of Vasicek (1977) and Cox-Ingersoll and Ros...

This paper investigates a continuous-time mean-variance portfolio selection problem based on log-return model. The financial market is composed of one risk-free asset and multiple risky assets whose prices are modelled by geometric Brownian motions. We derive sufficient condition for open-loop equilibrium strategies via forward backward stochastic differential equat...

In this paper, we study pricing of American put options on a nondividend-paying stock in the Black and Scholes market with stochastic interest rate finite-time maturity. We prove that option value is C1 function initial time, rate, price. By means Itô calculus, rigorously derive value's early exercise premium formula associated hedging portfolio. existence an optimal boundary splitting state sp...

We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval models. We show also that when the short-rate dynamics is given by a Brownian motion or a geometric Brownian motion, then the value function is infinite.