Quantile LASSO in arbitrage-free option markets

Abstract

The option price function and the implied volatility surface are both key tools for the derivative pricing strategies and the financial market analysis. Modern and sophisticated methods are used but their credibility suffered due to the financial crisis in 2007–2010. Instead, a method based on a standard semiparametric smoothing is proposed and the overall complexity and robustness (with respect to various anomalies, such as bid-ask spreads, discrete ticks in price, non-synchronous trading, or even heavy tailed error distributions) is achieved by using the conditional quantile estimation. The overestimation and the sparsity principle are adopted to introduce additional flexibility and the LASSO-type penalty and the set of well-defined linear constraints are employed to produce the final estimate which complies with the arbitrage-free criteria dictated by the financial theory. The theoretical results of the model are discussed, finite sample properties are investigated via a simulation study and a practical application of the proposed method is illustrated for the Apple Inc. (AAPL) call options.