Final Report Summary - POLYTE (Polynomial term structure models)
The quantification and management of financial risks relies on dynamic stochastic models. In this project, we developed a large class of new financial models based on polynomial jump-diffusions.
By definition, the generator of a polynomial jump-diffusion maps polynomials to polynomials of the same or lower degree. As a consequence, polynomial jump-diffusions admit closed form conditional moments, which renders them highly tractable for applications in finance. Exploiting this feature, we developed a generic polynomial modeling framework for the term structures of financial risks arising from various sources, including interest rates, volatility and credit risks, dividends, and electricity prices. We also developed an efficient methodology for derivatives pricing based on polynomial expansion.
The class of polynomial jump-diffusions strictly includes affine jump-diffusions, whose generators map exponential functions to linear polynomial-exponential functions. Affine models had traditionally been the preferred framework for modeling the term structures of financial risks, but they come along with some severe specification limitations, which can now be overcome by polynomial models. The systematic use of polynomial models in finance represents a major step above the use of affine models, both in terms of tractability and flexibility.
The main achievements of this project consist of three parts: first, a fundamental study of polynomial processes; second, the development of novel polynomial models in finance; and third, the numerical implementation and empirical estimation of these models using real market data.
With a core team of six researchers plus the Principal Investigator and the collaboration of another half a dozen external researchers (PhD students, postdocs, and professors), we produced about thirty scientific papers within five years. We organized special sessions on polynomial models in finance at three international conferences and held special courses at various schools.
By definition, the generator of a polynomial jump-diffusion maps polynomials to polynomials of the same or lower degree. As a consequence, polynomial jump-diffusions admit closed form conditional moments, which renders them highly tractable for applications in finance. Exploiting this feature, we developed a generic polynomial modeling framework for the term structures of financial risks arising from various sources, including interest rates, volatility and credit risks, dividends, and electricity prices. We also developed an efficient methodology for derivatives pricing based on polynomial expansion.
The class of polynomial jump-diffusions strictly includes affine jump-diffusions, whose generators map exponential functions to linear polynomial-exponential functions. Affine models had traditionally been the preferred framework for modeling the term structures of financial risks, but they come along with some severe specification limitations, which can now be overcome by polynomial models. The systematic use of polynomial models in finance represents a major step above the use of affine models, both in terms of tractability and flexibility.
The main achievements of this project consist of three parts: first, a fundamental study of polynomial processes; second, the development of novel polynomial models in finance; and third, the numerical implementation and empirical estimation of these models using real market data.
With a core team of six researchers plus the Principal Investigator and the collaboration of another half a dozen external researchers (PhD students, postdocs, and professors), we produced about thirty scientific papers within five years. We organized special sessions on polynomial models in finance at three international conferences and held special courses at various schools.