Markov Cubature Rules for Polynomial Processes

  title={Markov Cubature Rules for Polynomial Processes},
  author={Damir Filipovi'c and Martin Larsson and Sergio Pulido},
  journal={ERN: Other Econometrics: Econometric \& Statistical Methods (Topic)},
We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study such rules using algebraic techniques. Markov cubature rules aid the tractability of path-dependent tasks such as American option pricing in models where the underlying factors are polynomial… 
Abstract polynomial processes.
We suggest a novel approach to polynomial processes solely based on a polynomial action operator. With this approach, we can analyse such processes on general state spaces, going far beyond Banach
Cubature Method for Stochastic Volterra Integral Equations
The cubature measure is introduced for Stochastic Volterra Integral Equations, and construct it explicitly in some special cases, including a long memory stochastic volatility model.
Polynomial Jump-Diffusion Models
A large class of novel financial asset pricing models that are based on polynomial jump-diffusions are introduced, including a generic method for option pricing based on moment expansions.
M F ] 2 1 Ju l 2 01 9 Polynomial Jump-Diffusion Models ∗
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
M F ] 2 1 N ov 2 01 7 Polynomial Jump-Diffusion Models ∗
We develop a comprehensive mathematical framework for polynomial jump-diffusions, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is
Quantization goes polynomial
Recursive marginal quantization has a high convergence rate in numerical approximation of stochastic volatility option pricing models and it is shown that this convergence rate is higher in classical quantization models than in the discrete-time models.


Polynomial processes and their applications to mathematical finance
We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains
Polynomial Processes for Power Prices
  • T. Ware
  • Mathematics
    Applied Mathematical Finance
  • 2019
ABSTRACT Polynomial processes have the property that expectations of polynomial functions (of degree n, say) of the future state of the process conditional on the current state are given by
Cubature on Wiener space in infinite dimension
  • C. Bayer, J. Teichmann
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2008
We prove a stochastic Taylor expansion for stochastic partial differential equations (SPDEs) and apply this result to obtain cubature methods, i.e. high-order weak approximation schemes for SPDEs, in
A generalized correlated random walk is a process of partial sums Xk = k P j=1 Y j such that (X;Y ) forms a Markov chain. For a sequence (X n ) of such processes where each Y n j takes only two
The Jacobi stochastic volatility model
A novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process is introduced and the Heston model is included as a limit case.
Polynomial diffusions and applications in finance
This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest
Numerical Methods for Stochastic Control Problems in Continuous Time
A powerful and usable class of methods for numerically approximating the solutions to optimal stochastic control problems for diffusion, reflected diffusion, or jump-diffusion models is discussed.
Cubature methods for stochastic (partial) differential equations in weighted spaces
The cubature on Wiener space method, a high-order weak approximation scheme, is established for SPDEs in the case of unbounded characteristics and unbounded test functions. We first describe a
Approximation and Weak Convergence Methods for Random Processes
Control and communications engineers, physicists, and probability theorists, among others, will find this book unique. It contains a detailed development of approximation and limit theorems and