We study a skew Ornstein–Uhlenbeck process with zero being a sticky reflecting boundary, which is defined as the weak solution to a stochastic differential equation (SDE) system involving local time. The main results obtained include: (i) the existence and uniqueness of solutions to the SDE system, (ii) the scale function and speed measure, and (iii) the distributional properties regarding the transition density and the first hitting times. On the application side, we apply the process to interest rate modeling and obtain the explicit pricing formula for zero-coupon bonds. Numerical examples illustrate the impacts on bond yields of skewness and stickiness parameters.

Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein–Uhlenbeck or fractional Cox–Ingersoll–Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.

In this paper we consider a structural form credit risk model with jumps. We investigate the credit spread, the price, and the fair premium of the zero-coupon bond for the proposed model. The price and the fair premium of the bond are associated with the Laplace transform of default time and the firm's expected present market value at default. We give sufficient conditions under which the Laplace transform and the expected present market value of a firm at default are twice continuously differentiable. We derive closed-form expressions for them when the jumps have a hyperexponential distribution. Using the closed-form expressions, we obtain numerical solutions for the default probability, the credit spread, and the fair premium of the bond.

In this paper, a finite-state mean-reverting model for the short rate, based on the continuous-time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and special symmetric cases. Its limiting relationship to the Vasicek model will be examined with some numerical results.