Candidate point selection using a self-attention mechanism for generating a smooth volatility surface under the SABR model

摘要

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 selfattention 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.