Abstract
We develop a comprehensive mathematical framework for polynomial jump diffusions in a semimartingale context, which nest affine jump diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and Lévy time change. We present a generic method for option pricing based on moment expansions. As an application, we introduce a large class of novel financial asset pricing models with excess log returns that are conditional Lévy based on polynomial jump diffusions.
Highlights
Polynomial jump diffusions have broad applications in finance
We introduce a large class of novel financial asset pricing models with excess log returns that are conditional Lévy based on polynomial jump diffusions
We introduce a large class of novel financial asset pricing models that are based on polynomial jump diffusions and that are beyond the affine class
Summary
Polynomial jump diffusions have broad applications in finance. A jump diffusion is polynomial if its extended generator maps any polynomial to a polynomial of equal or lower degree. We introduce a large class of novel financial asset pricing models that are based on polynomial jump diffusions and that are beyond the affine class In these models, the excess log return processes are conditional Lévy in the sense of Çinlar (2003). Focusing on the affine case, one finds an even richer history in the finance literature, in which affine jump diffusions have long been used to address a large number of problems in asset pricing, optimal investment, equilibrium analysis, and so on In addition to their usefulness in applications, polynomial jump diffusions are of theoretical interest because of their rich mathematical structure. Appendix A, B, C, and D contain additional results and all proofs
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
