Tighter Robust Upper Bounds for Options via No-Regret Learning

Shan Xue, Ye Du, Liang Xu

Abstract: Classic option pricing models, such as the Black-Scholes formula, often depend on some rigid assumptions on the dynamics of the underlying asset prices. These assumptions are violated essentially in practice and thus inevitably induce the model risk. To reduce the model risk, robust option pricing that only requires the no-arbitrage principle has attracted a great deal of attention among researchers. In this paper, we give new robust upper bounds for option prices based on a novel η -momentum trading strategy. Our bounds for European options are tighter for most common moneyness, volatility and expiration date setups than those presented in (DeMarzo, Kremer, and Mansour 2016). Our bounds for Asian options are the first closed-form robust upper bounds for those options. Numerical simulations demonstrate that our bounds significantly outperform the benchmarks for both European options and Asian options.