Arbitrage Opportunity Identification Model Based on Stochastic Modelling of Implied Volatility Surfaces

Abstract

The paper considers insufficient fit accuracies, fragmented modelling and identification, and high misjudgement rate with fixed thresholds in implied volatility surface modelling and arbitrage opportunity identification. It proposes an in-depth algorithm based on stochastic coefficient Vol Transformer-adaptive arbitrage threshold (SC-VT-AT), which integrates the stochastically coefficient mechanism of Vol Transformer. The algorithm employs stoically coefficients to describe the technically dynamic features of implied volatility surface, and uses Vol Transformed to efficiently extract the two-dimensional features of the currency size and time to expiration. In parallel, it develops an adaptive threshold module to dynamically update the arbitrage decision criteria based on real-time market volatility factors and simultaneously perform surface modelling & arbitrage opportunities identification. The results on daily CSI 300 ETF options from 2019 to 2023 show the RMSE, MAE, and QLIKE losses of the proposed algorithm are smaller than the ones of traditional comparison methods such as SABR, ordinary Vol Transformer, and GAN. arbitrage identification accuracy reaches 86.7%, data processing time per trading day is 0.87 seconds, annualized return of the simulated arbitrage scheme is 12.3%, and maximum drawdown is only 4.1%. The proposed algorithm can efficiently improve the accuracy of surface modelling with minimizing misjudgement and missing judgment of arbitrage offers in real-times and trading practicality. It can also provide an efficient integrated decision tool to quantitatively track the options markets.