This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black–Scholes model is a simpler case that has a velocity dependent Lagrangian.

Over the past two decades, the US stock market has undergone significant changes in its structure, with small firms disappearing and large firms gaining market share. This study investigates whether the dominance of large firms in the market creates positive spillover for or shifts resources...