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.
Definition.
The CKLS process formula_1 is defined by the following stochastic differential equation:
formula_2
where formula_3 denotes the Wiener process. The CKLS process has the following equivalent definition:
formula_4
Special cases.
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. In all cases, formula_8 is assumed to be positive.
Financial applications.
The CKLS process is often used to model interest rate dynamics and pricing of bonds, bond options, currency exchange rates, securities, and other options, derivatives, and contingent claims. It has also been used in the pricing of fixed income and credit risk and has been combined with other time series methods such as GARCH-class models.
One question studied in the literature is how to set the model parameters, in particular the elasticity parameter formula_6. Robust statistics and nonparametric estimation techniques have been used to measure CKLS model parameters.
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 formula_10 can model short-term interest rates more accurately than models with formula_11.
Later empirical studies by Bliss and Smith have shown the reverse: sometimes lower formula_6 values (like 0.5) in the CKLS model can capture volatility dependence more accurately compared to higher formula_6 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 formula_14.
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.
References.
 ;templatestyles src="Reflist/styles.css" / ;