No arbitrage assumption implies the differentiability of derivative pricing function

In this article, we show necessary and sufficient conditions for a function to transform a continuous Markov semimartingale to a semimartingale. As a result, the no-arbitrage principle guarantees the differentiability of asset prices with respect to the underlying noise, if the asset prices are continuous and the underlying noise is a continuous Markov semimartingale.

💡 Research Summary

The paper investigates the minimal regularity that a pricing functional must possess in order for the resulting price process to be a semimartingale under the no‑arbitrage (NFLVR) condition. Working on a filtered probability space generated by a Brownian motion, the authors consider a continuous Markov semimartingale (X) solving the stochastic differential equation
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