Squared Bessel processes and their applications to the square root interest rate model
The author studies the extended Cox-Ingersoll-Ross (CIR) term structure model of the form \(dr_t=(\alpha_t-\beta_tr_t)dt+\sigma_t\sqrt{r_t}dW_t \), where \( \alpha_t, \beta_t \) and \( \sigma_t \) are time-varying deterministic functions. The object of the paper is to apply the basic properties of the squared Bessel processes with time-varying dimension for studying the extended CIR model with time-varying parameters in a purely probabilistic approach. It is established that there exists an equivalent martingale measure for the square root risk premium process. Then, the arbitrage free prices of pure discount bonds and their call options under this measure change are derived. At last, a special class of extended CIR models is studied which not only enables to fit every arbitrage free initial term structure, but also to give the extended CIR call option pricing formula.
scientific article; zbMATH DE number 2036994