We applied nine stochastic processes to WTI crude oil prices, following the CKLS model suggested by Chan et al.(1982). In particular, we divide study period into two so that we can analyze structural change in the price. We found that the crude oil price volatilities follow different stochastic processes in two sub-periods. Thus, we can conclude that the main characteristics of the crude oil price dynamics do change over time so that we need to consider multiple stochastic processes for long-term analyses of crude oil price series. We also calculate the option values for comparing the effects of contingent claims depends on periods.