A stochastic interest rate generator is a valuable actuarial tool. The parameters that specify a stochastic model of interest rates can be adjusted to make the model arbitrage-free, or they can be adjusted to accommodate an individual investor's subjective views. The arbitrage-free settings of the parameters must be used when pricing streams of interest-rate-contingent cash flows, for example, ...

There is a massive amount of study deals with the stochastic modelling of the interest rates. The first approach to specify the interest rate movements as continuoustime Ito process was introduced by Merton in 1973. But his approach had many shortcomings including possibility of negative interest rates. In his seminal work in 1977, Vasicek developed Merton’s model by introducing mean-reverting ...

We extend the Cox-Ingersoll-Ross (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the long-term return by using the theory of generalised Bessel-square p...

In this paper, we study optimal investment, consumption and portfolio choice in a framework where the pension planner member (PPM) embarks on an investment policy to cover up for some certain life targets. The aim of plan manager is maximize expectation total wealth at time retirement. return process comprises risk free asset two risky assets, PPM benefit lies complete market that constrained b...

For the pricing of interest rate derivatives, various stochastic interest rate models are used. The shape of such a model can take very different forms, such as direct modeling of the probability distribution (e.g. a generalized beta function of second kind), a short rate model (e.g. a Hull-White model), or a forward rate model (e.g. a LIBOR market model). This paper describes the general struc...

In this paper we formulate the Risk Management Control problem in the interest rate area as a constrained stochastic portfolio optimization problem. The utility that we use can be any continuous function and based on the viscosity theory, the unique solution of the problem is guaranteed. The numerical approximation scheme is presented and applied using a single factor interest rate model. It is...

Abstract: This paper presents a one factor and a two factor arbitrage-free interest rate models with parsimonious implied volatility functions. The models are empirically tested on the entire swaption surface in three currencies (U. S. dollar, Euro and Japanese yen) over a five year period. They are shown to be robust in explaining the swaption values, and the implied volatility functions are s...

We investigate a portfolio optimization problem under the threat of a market crash, where the interest rate of the bond is modeled as a Vasicek process, which is correlated with the stock price process. We adopt a non-probabilistic worst-case approach for the height and time of the market crash. On a given time horizon [0, T ], we then maximize the investor’s expected utility of terminal wealth...