No arbitrage assumption implies the differentiability of derivative pricing function
Kihun Nam, Yunxi Xu
TL;DR
This paper demonstrates that under no-arbitrage conditions, the asset pricing function is differentiable with respect to the underlying noise, provided the asset prices and noise are continuous Markov semimartingales.
Contribution
It establishes necessary and sufficient conditions for the transformation of continuous Markov semimartingales, linking no-arbitrage to differentiability of pricing functions.
Findings
No-arbitrage ensures differentiability of asset prices
Conditions for transforming Markov semimartingales are characterized
Asset prices are differentiable with respect to underlying noise
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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Taxonomy
TopicsStochastic processes and financial applications · Risk and Portfolio Optimization · Credit Risk and Financial Regulations