Empirical Analysis of SPX Options Volatility Arbitrage Strategies: Relative Differences in Historical and Implied Volatility

Contemporarily, volatility arbitrage strategy is one of the common strategies in quantitative finance. This study evaluates the effectiveness of volatility arbitrage strategies within the SPX options market by analyzing the relative differences between daily historical volatility and daily implied volatility. Using the Black-Scholes-Merton (BSM) model and Newtons method, the research finds that the strategy performs particularly well during periods of heightened market volatility. Specifically, in the final 60 days of the study period, when implied volatility increased significantly, the strategy achieved a maximum single trade profit of $162.5, contributing to a total gain of $326.1. These findings highlight the strategy's potential for substantial profits and demonstrate its effectiveness in capitalizing on volatility discrepancies. The study enhances theoretical models by showing how increased volatility impacts arbitrage opportunities and fills a gap in the literature regarding the empirical application of these strategies, offering valuable insights for options traders and risk managers. However, limitations related to the BSM models assumptions and the omission of market shocks and macroeconomic factors suggest that future research should refine models, incorporate broader market factors, and use more comprehensive datasets to better capture real-world dynamics.