On valuing corporate debt with the volatility of corporate assets evolving according to an Ornstein-Uhlenbeck process

In this paper the problem of valuing corporate debt with possibility of default is considered. It is assumed that the volatility of the value of a firm's assets evolves according to an Ornstein-Uhlenbeck process and default occurs only if the value of corporate assets falls below an exogenously specified, time dependent barrier. In the case of a particular choice of default barrier the explicit formulas for the present value of a corporate debt, the total value of the firm, the value of equity, the expected default time and the variation of default time are derived.Coporate debt, Ornstein-Uhlenbeck process, default time

Sequential Detection of US Business Cycle Turning Points: Performances of Shiryayev-Roberts, CUSUM and EWMA Procedures

In this paper we consider the problem of sequential detecting change points in economic time series. We compare the performances of three well known procedures, Shiryayev-Roberts, CUSUM and EWMA, in the problem of early detection of the US business cycle turning points using leading indicators or some financial series. The comparison was done separately for detecting recessions and expansions during the period of 1955-2003. We found that in most cases the Shiryayev-Roberts procedure is superior to the other two in detecting turning points with leading indicators. At the same time the CUSUM procedure performs better in detecting turning points with stock price indices.Business cycles, change point detection, leading indicators

A note on a generalized Black-Scholes formula

A generalized Black-Scholes formula is presented for the case when the volatility part of the percentage changes in a stock price obeys a mean reverting Ornstein-Uhlenbeck process. When the parameter of the Ornstein-Uhlenbeck process converges to zero the generalized formula converges to the Black-Scholes formula.Black_Scholes formula; Option pricing; Ornstein-Uhlenbeck processes

On a CAPM monitoring based on the EWMA process control

CAPM, EWMA, Statistical process control, asymptotic expansions