Arbitrage hedging strategy and one more explanation of the volatility smile

TL;DR

This paper introduces an explicit arbitrage hedging strategy that demonstrates market arbitrage opportunities and explains the volatility smile by analyzing the skewness in implied volatility derived from observed option prices.

Contribution

It provides a novel explicit hedging approach that proves arbitrage in markets with assets driven by the same stochastic factor and offers a new explanation for the volatility smile.

Findings

Market arbitrage can be demonstrated with the proposed hedging strategy.

The implied volatility exhibits skewness consistent with observed market data.

The strategy links the shape of the implied volatility graph to market skewness.

Abstract

We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of the graph of the option price, related to our strategy, demonstrates the "skewness" inherent to the observational data.