In the past, several research studies have highlighted the idea that spectral data produces better tone-accurate images. Inspired by these studies, this paper introduces the spectral image color appearance model titled SiCAM, designed for tone mapping an HDR hyperspectral radiance cube to a three-channel LDR image. It is to be noted that SiCAM is inspired by the iCAM06 image color appearance model, where we adapted the iCAM06 for hyperspectral input by embedding a spectral adaptation transformation, extending the existing chromatic adaptation transform (CAT) method. Additionally, we conducted a psychophysical experiment to evaluate the proposed model and the effectiveness of having spectral data instead of traditional three-channel HDR input, for HDR image rendering. The proposed model is also assessed in comparison to the performance of iCAM06 and the gamma tone mapping approaches. The subjective evaluation indicates that SiCAM either outperformed these methods in terms of both accurate color appearance and pleasantness or atleast generated comparable results. This also hints that the spectral information might be able to improve not only the acquisition capabilities but also display rendering. Due to the lack of openly available HDR hyperspectral datasets, we captured the HDR hyperspectral radiance images of four HDR scenes, which will be made publicly accessible.