Interest rate dynamics, derivatives pricing, and risk management
This book is a revised version of the author's Ph.D. thesis, hence less general than might appear from the title. It studies in detail the following particular term structure model: \(\theta\) and \(v\) are Feller square-root (CIR) processes driven by two correlated Brownian motions, and the short rate \(r\) under \(P\) satisfies \[ dr_t= k(\theta_t-r_t)dt+ \sqrt{v_t}\sqrt{r_t} dW_t \] for a third Brownian motion also correlated with the other two. This is a generalization of the Cox-Ingersoll-Ross model to random volatility \(v\) and short-term mean \(\theta\) of \(r\). To specify the model completely, a pricing measure \(Q\) is chosen to obtain a \(Q\)-Markovian model. Thus prices of interest rate derivatives are functions of the three factors \(r\), \(v\), \(\theta\) and satisfy a PDE whose terminal condition depends on the chosen derivative. The fundamental solution for this PDE is given fairly explicitly and used to price derivatives via integration instead of solving the PDE with a boundary condition. This approach is presented in Chapter 1 and illustrated in a large number of examples in Chapters 2 and 3. The second half of the book is considerably less thorough. It briefly mentions fitting to a given term structure, explains in some more detail a discretization of the model, gives a rough overview of possible methods for estimating the model's ten parameters, discusses some elements of interest rate risk management and shortly mentions extensions of the model obtained by adding jump components. As all these topics are only dealt with rather summarily, their treatment is not very satisfactory. Moreover, the practical aspects of working with the model remain unclear: There are neither empirical studies on the claimed realism of the model, nor results to substantiate the asserted efficient numerical computability of option prices. On the whole, the book can be recommended only for someone who is very interested in this particular model and ready to make a substantial effort in additional applied work.
scientific article; zbMATH DE number 862990