In
mathematics, the Chan–Karolyi–Longstaff–Sanders process (abbreviated as CKLS process) is a
stochastic process with applications to
finance. In particular it has been used to model the
term structure of
interest rates. The CKLS process can also be viewed as a generalization of the
Ornstein–Uhlenbeck process. It is named after K. C. Chan, G. Andrew Karolyi, Francis A. Longstaff, and Anthony B. Sanders, with their paper published in 1992.[1][2]
Many
interest rate models and
short-rate models are special cases of the CKLS process which can be obtained by setting the CKLS model parameters to specific values.[1][7] In all cases, is assumed to be positive.
Family of CKLS process under different parametric specifications.
In their original paper, CKLS argued that the elasticity of interest rate volatility is 1.5 based on historical data, a result that has been widely cited. Also, they showed that models with can model
short-term interest rates more accurately than models with .[1]
Later empirical studies by Bliss and Smith have shown the reverse: sometimes lower values (like 0.5) in the CKLS model can capture volatility dependence more accurately compared to higher values. Moreover, by redefining the regime period, Bliss and Smith have shown that there is evidence for regime shift in the
Federal Reserve between 1979 and 1982. They have found evidence supporting the square root Cox-Ingersoll-Ross model (CIR SR), a special case of the CKLS model with .[15]
The period of 1979-1982 marked a change in
monetary policy of the
Federal Reserve, and this regime change has often been studied in the context of CKLS models.[6]