Due to the need for more renewable energy, interest in floating wind turbines has greatly increased over the last years. These turbines have to withstand harsh environmental conditions, such as extreme waves called rogue waves. These rogue waves (or freak waves) are exceptionally large waves compared to the surrounding sea state and are defined by two different size criteria, one relating to the crest height and the other to the wave height. Research has shown that these rogue waves occur more frequently than expected, from which the question arose whether these rogue waves could be dangerous for floating wind turbines. This thesis aims to answer that question by evaluating the probability of such a wave interacting with a floating offshore wind turbine and the subsequent induced motion response. A location off shore California is evaluated for a spar-type floating wind turbine (SFWT). In this research, different time-extreme (TE) and space-time-extreme (STE) statistical wave crest and crest-to-trough models are used with historical wave data to estimate rogue wave occurrence probabilities. The STE models approximate the probability of a wave occurring within an area in time, as opposed to a point in time (TE), and are considered state-of-the-art. Wave data from 1998-2020 is used, which is a significant amount compared to the life of a typical offshore structure. A frequently chosen model for research into a SFWT is the OC3-Hywind concept, which consists of the National Renewable Energy Laboratory (NREL) 5MW reference turbine and a substructure based on the Hywind spar. The area size which leads to the STE models estimating a higher rogue wave occurrence probability than the TE models is investigated for the first time. This is done by comparing the TE and STE probability models to each other on the basis of their maximum estimated exceedance probability of the rogue threshold, for different area sizes. Only on rare occasions, with a very small area, did the most conservative TE wave crest model estimate a higher probability than the STE2 (wave crest STE) model. Therefore, the STE2 model appears most conservative when evaluating rogue crests for a SFWT. The Rayleigh model was the most conservative among TE crest-to-trough models that were considered, and estimated higher probabilities than the STE1QD (wave crest-to-trough STE) model in several sea states up until an area size of 12x12m2. The influence of the shape of the wave spectrum was investigated by two spectral bandwidth parameters. All four wave crest models showed an increase in rogue crest probability as the wave spectrum became narrower. Regarding the crest-to-trough models, no clear preference was observed. Long-term rogue wave probabilities were calculated for four sizes of rogue crests and waves, where the squared area of the STE models was based on the waterline diameter of the OC3-Hywind spar (6.5x6.5m2). Probabilities were averaged per sea state bin, and it was observed that for this area the STE1QD model was more conservative than the Rayleigh model. When single maximum exceedance probabilities are compared, the Rayleigh model can be more conservative in several sea states until an area of 12x12m2, but when overall occurrence probabilities are considered, this area appears to be roughly 6.5x6.5m2. Following the long-term rogue wave probability analysis, four rogue waves were each embedded in random wave series, based on their most likely wave spectrum, using a deterministic extreme wave model. With these wave time histories, simulations were run in OrcaFlex using a publicly available OC3-Hywind model. During the simulation the turbine was assumed to be in parked condition and only the wave loading was considered. Mostly the pitch angles and nacelle accelerations are limiting for safety, due to stability criteria and sensitive components in the nacelle. These limits are imposed by turbine manufacturers but are never shared publicly. Therefore, the results were compared with reference values from the literature. The dynamic response did not exceed these maximum reference values, but they can be considered quite serious as some did exceed lower thresholds. Based on the long return period of the considered rogue waves, together with their induced dynamic response which does not exceed maximum reference values, it appears that these rogue waves alone are not dangerous for the considered SFWT. However, ultimately this will depend on the sensitivity of the components inside the turbine, as well as the desired risk profile of the wind farm owner.