The Application of Symbolic Regression on Identifying Implied Volatility Surface

One important parameter in the Black-Scholes option pricing model is the implied volatility. Implied volatility surface (IVS) is an important concept in finance that describes the variation of implied volatility across option strike price and time to maturity. Over the last few decades, economists and financialists have long tried to exploit the predictability in the IVS using various parametric models, which require deep understanding of financial practices in the area. In this paper, we explore how a data-driven machine learning method, symbolic regression, performs in identifying the implied volatility surface even without deep financial knowledge. Two different approaches of symbolic regression are explored through a simulation study and an empirical study using a large panel of option data in the United States options market.