No arbitrage assumption implies the differentiability of derivative pricing function
Probability
2025-12-22 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2506.22213,
title = {No arbitrage assumption implies the differentiability of derivative pricing function},
author = {Kihun Nam and Yunxi Xu},
journal= {arXiv preprint arXiv:2506.22213},
year = {2025}
}