No arbitrage assumption implies the differentiability of derivative pricing function

2025/06/27 by Nam, Kihun, Xu, Yunxi
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.22213

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.

Citations

• Flows for Singular Stochastic Differential Equations with Unbounded\n Drifts
• Some Norm Estimates for Semimartingales
• Stochastic Calculus for a Time-Changed Semimartingale and the Associated Stochastic Differential Equations

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• No-arbitrage conditions and absolutely continuous changes of measure
• Modeling financial assets without semimartingales
• Criteria for the absence of arbitrage in general diffusion markets
• Arbitrage-Free Pricing Before and Beyond Probabilities