  This paper employs a novel Lie symmetry-based framework to model the
intrinsic symmetries within financial market. Specifically, we introduce {\it
Lie symmetry net} (LSN), which characterises the Lie symmetry of the
differential equations (DE) estimating financial market dynamics, such as the
Black-Scholes equation and the Va\v{s}i\v{c}ek equation. To simulate these
differential equations in a symmetry-aware manner, LSN incorporates a Lie
symmetry risk derived from the conservation laws associated with the Lie
symmetry operators of the target differential equations. This risk measures how
well the Lie symmetry is realised and guides the training of LSN under the
structural risk minimisation framework. Extensive numerical experiments
demonstrate that LSN effectively realises the Lie symmetry and achieves an
error reduction of more than {\it one order of magnitude} compared to
state-of-the-art methods. The code is available at
\href{https://github.com/Jxl163/LSN_code}{https://github.com/Jxl163/LSN$\_$code}.
