{getToc} $title={Table of Contents}
Summary
The Financial Harry Dym equation is derived from the Black-Scholes framework, and its traveling wave solutions are explored. The equation is a variant of the Harry Dym equation, and its solutions have a remarkable qualitative similarity to reconstructed volatility surfaces.
Highlights
- The Financial Harry Dym equation is derived from the Black-Scholes framework.
- The equation is a variant of the Harry Dym equation.
- Traveling wave solutions of the equation are explored.
- The solutions have a remarkable qualitative similarity to reconstructed volatility surfaces.
- The equation is derived using a zero-curvature condition deformation of the operator L.
- The solutions are obtained using a pseudopotential function.
- The equation has potential applications in financial markets.
Key Insights
- The Financial Harry Dym equation is a nonlinear evolution equation that is derived from the Black-Scholes framework, which is a fundamental model in finance. This equation has the potential to provide new insights into the behavior of financial markets.
- The traveling wave solutions of the Financial Harry Dym equation have a remarkable qualitative similarity to reconstructed volatility surfaces, which are important in finance. This suggests that the equation may be useful for modeling and understanding volatility in financial markets.
- The equation is derived using a zero-curvature condition deformation of the operator L, which is a common technique in soliton theory. This technique allows for the derivation of nonlinear evolution equations that have soliton solutions.
- The solutions of the Financial Harry Dym equation are obtained using a pseudopotential function, which is a common technique in soliton theory. This function allows for the construction of solutions that have a specific form.
- The Financial Harry Dym equation has potential applications in financial markets, particularly in the modeling and understanding of volatility. The equation may be useful for pricing options and other financial derivatives.
- The equation is a variant of the Harry Dym equation, which is a well-known equation in soliton theory. This suggests that the Financial Harry Dym equation may have similar properties and behavior to the Harry Dym equation.
- The solutions of the Financial Harry Dym equation have a specific form, which is determined by the pseudopotential function. This form may be useful for understanding the behavior of the solutions and for making predictions about the behavior of financial markets.
Mindmap
If MindMap doesn't load, go to the Homepage and visit blog again or Switch to Android App (Under Development).
Citation
Zubelli, J. P., Singh, K., Albani, V., & Kourakis, I. (2024). Travelling wave solutions of an equation of Harry Dym type arising in the Black-Scholes framework (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.19020