# Polynomial Jump-Diffusion Models

@article{Filipovic2017PolynomialJM, title={Polynomial Jump-Diffusion Models}, author={Damir Filipovi'c and Martin Larsson}, journal={ERN: Asset Pricing Models (Topic)}, year={2017} }

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 preserved under exponentiation and subordination. 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 that are based on polynomial jump-diffusions.

## 35 Citations

### Polynomial jump-diffusions on the unit simplex

- MathematicsThe Annals of Applied Probability
- 2018

Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization…

### Correlators of Polynomial Processes

- MathematicsSIAM Journal on Financial Mathematics
- 2021

In the setting of polynomial jump-diffusion dynamics, we provide a formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula…

### Option pricing with orthogonal polynomial expansions

- MathematicsMathematical Finance
- 2019

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein–Stein, and Hull–White models, for which we…

### Probability measure-valued polynomial diffusions

- MathematicsElectronic Journal of Probability
- 2019

We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional…

### J ul 2 01 8 Probability measure-valued polynomial diffusions

- Mathematics
- 2018

We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming–Viot process is a particular example. The defining property of finite dimensional…

### Pricing Asian Options with Correlators

- MathematicsInternational Journal of Theoretical and Applied Finance
- 2021

We derive a series expansion by Hermite polynomials for the price of an arithmetic Asian option. This series requires the computation of moments and correlators of the underlying price process, but…

### Existence of probability measure valued jump-diffusions in generalized Wasserstein spaces

- Mathematics
- 2019

We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other similar spaces of…

### Infinite-dimensional polynomial processes

- MathematicsFinance and Stochastics
- 2019

We introduce polynomial processes taking values in an arbitrary Banach space B ${B}$ via their infinitesimal generator L $L$ and the associated martingale problem. We obtain two representations of…

### Linear credit risk models

- EconomicsFinance and Stochastics
- 2019

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps…

### Linear credit risk models

- EconomicsFinance and Stochastics
- 2019

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps…

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Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization…

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We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert…

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We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein–Stein, and Hull–White models, for which we…

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We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional…

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