전이확률을 이용한 단일요인 확산과정의 검증

To investigate whether the underlying asset price follows one-dimensional diffusion process is important because all models in the one-dimensional diffusion class share three basic properties of the monotonicity property, the perfect correlation property and the option redundancy property. But, the previous studies which have focused directly on the above model predictions could not completely exclude the impact of time decay in option premium on empirical results. Therefore, this study examines Aït-sahalia(2002)’s approach which relies on identifying a necessary and sufficient restriction on the transition densities of diffusions. If options trade on the underlying asset, the test is very convenient since we can obtain the transition density function directly from the cross-section of option prices at any fixed time horizon. So, there is no necessity to decompose an option price change in a given period into a time-decay and a non-time-decay. In fact, Aït-sahalia(2002) relied on the transition density to determine whether the discontinuities observed are the result of the discreteness of sampling, or rather evidence of genuine jump dynamics for the underlying continuous-time process. However, since the test is constructed under the one-factor Markovian setting, his diffusion criterion could also be violated if the index follows a continuous sample path, but is not Markovian in itself. For this reason, Aït-sahalia(2002)’s approach is more suited to test whether the underlying asset price follows one-dimensional diffusion process. Our analysis of KOSPI 200 index options indicates that the hypothesis which the discrete observations came from a diffusion is rejected. Therefore options are not redundant securities, nor monotonically increasing(decreasing) in the underlying asset price.