Mathematical Modeling of Investors’ Savings Plan (ISP) with Stochastic Interest Rate via Numéraire Change

An Equity-Interest Rate hybrid model with Stochastic Volatility and the interest rate smile

We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main processes. By an appropriate change of measure the dimension of the corresponding pricing PDE can be gre...

Interest Rate Policies in Consumption - Savings Dynamic Models

We examine the effect of interest rate policies on an agent’s consumption and savings when her income is fluctuating. In each period a long-lived agent decides how much to save (i.e., invest in a risk-free bond) and how much to consume while her income is uncertain and depends on the state of the economy. The central bank, on the other hand, fixes a policy, called an interest rate policy, which...

Interest Rate Models Key Developments in the Mathematical Theory of Interest Rate Risk Management Presented By

CVaR hedging under stochastic interest rate

In this paper we assess the partial hedging problems by formulating hedging strategies that minimize conditional value-at-risk (CVaR) of the portfolio loss under stochastic interest rate environment. The combination of stochastic interest and CVaR hedging method makes the valuing approach more complex than the existing model with constant interest rate. We take up two issues in searching the op...

Stochastic interest rate modelling with continuous-time GARCH(1,1) model

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 ...