Candidate point selection using a self-attention mechanism for generating a smooth volatility surface under the SABR model. (1st July 2021) - Kim, Hyeonuk; Park, Kyunghyun; Jeon, Junkee; Song, Changhoon; Bae, Jungwoo; Kim, Yongsik; Kang, Myungjoo
Highlights: We propose two models to generate a smooth volatility surface under the SABR. We utilize a transformer as a backbone network of the two models. The combined two models perform practitioner's candidate point selection task. We test the models on the S&P500 and KOSPI200 market data. The combined models can be applied in other stochastic volatility models. Abstract: In real markets, generating a smooth implied volatility surface requires an interpolation of the calibrated parameters by using smooth parametric functions. For this interpolation, practitioners do not use all the discrete parameter points but manually select candidate parameter points through time-consuming adjustments (e.g., removing outliers, comparing with the surface from the previous day, and considering daily market indexes) to generate a smooth and robust surface. In this paper, we propose neural network models that assist practitioners in generating a smooth implied volatility surface under the SABR (Hagan et al., 2002) model. Utilizing the self-attention mechanism of a transformer network (Vaswani et al., 2017) as a backbone network, we design two models: one that orders the parameter points by their likelihood to be selected as candidate parameter points and one that determines the candidate point set among the combinations of high-priority points. Experimental results from a 3-year period of real market S&P500 and KOSPI200 data show that the combination of two models can assist practitioners in the point selection task.