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...

An Ornstein-Uhlenbeck process is the most basic mean-reversion model and has been used in various fields such as finance and biology. In some instances, reflecting boundary conditions are needed to restrict the state space of this process. We study an Ornstein-Uhlenbeck diffusion process with a reflecting boundary and its application to finance and neuroscience. In the financial application, th...

A stochastic process of Vasicek type describing the short rate is considered, where the three governing parameters {φ,α, σ}, with φ for the market fitting, α for the reversion and σ for the volatility, would depend on the macro-economic condition modeled as an independent birth-death process on a finite state space. Computational algorithms are developed for evaluating the prices of European ca...

We present a new class of estimators for approximating the entropy of multi-dimensional probability densities based on a sample of the density. These estimators extend the classic ”m-spacing” estimators of Vasicek and others for estimating entropies of one-dimensional probability densities. Unlike plug-in estimators of entropy, which £rst estimate a probability density and then compute its entr...

We present recently developed geometric methods for the analysis of finite dimensional term structure models of the interest rates. This includes an extension of the Frobenius theorem for Fréchet spaces in particular. This approach puts new light on many of the classical models, such as the Hull-White extended Vasicek and Cox-Ingersoll-Ross short rate models. The notion of a finite dimensional ...

We introduce a new exotic option to be used within structured products address key disadvantage of standard time-invariant portfolio protection: the well-known cash-lock risk. Our approach suggests enriching framework by including threshold in allocation mechanism so that guaranteed minimum equity exposure (GMEE) is ensured at any point time. To able offer such solution still with hard capital ...

In this paper, we try to model the dynamics of short term interest rate using the fractional nonhomogeneous differential equation with stochastic free term. This type of equation is similar to one which represents the viscoelastic behavior of certain materials from rheologic point of view. As a final result we obtain the closed formula for prices of zero-coupon bonds. They are analogous to thos...

Abstract The paper considers the pricing of credit default swaps (CDSs) using a revised version risk model proposed in Cathcart and El-Jahel (2003). Default occurs either first time signaling process breaches threshold barrier or unexpectedly at jump Cox process. intensity depends on risk-free interest rate, which follows Vasicek process, instead Cox-Ingersoll-Ross as original model. This offer...

A parsimonious autoregressive model that is globally mean-reverting but locally driven by momentum is proposed. The local-momentum autoregression (LM-AR) model carries one extra parameter, and depending on the sign of this extra parameter, it can be either local momentumpreserving or momentum-building. The LM-AR model is motivated by observing US interest rate movement over many decades, which ...

This paper deals with the effects of concentration (single name and sectoral) and contagion risk on credit portfolios. Results are obtained for the value at risk of the portfolio loss distribution, in the analytical framework originally developed by Vasicek in 1991 [1]. V aR is expressed as a sum of terms: the first contribution represents the value at risk of a hypothetical single-factor homog...