No arbitrage assumption implies the differentiability of derivative pricing function

Kihun Nam; Yunxi Xu

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arXiv · 2506.22213

No arbitrage assumption implies the differentiability of derivative pricing function

Kihun Nam·Yunxi Xu

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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.

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Kihun Nam, Yunxi Xu. 2025-06-27. No arbitrage assumption implies the differentiability of derivative pricing function. https://arxiv.org/abs/2506.22213

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