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 the polynomial property is preserved under polynomial transformations and L\'evy 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 L\'evy based on polynomial jump-diffusions.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Hermite Polynomial-based Valuation of American Options with General Jump-Diffusion Processes
We present a new approximation scheme for the price and exercise policy of American options. The scheme is based on Hermite polynomial expansions of the transition density of the underlying asset dynamics and the early e…
Pricing Asian Options with Correlators
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 for a polynomial jump-…
Joint calibration to SPX and VIX options with signature-based models
We consider a stochastic volatility model where the dynamics of the volatility are described by a linear function of the (time extended) signature of a primary process which is supposed to be a polynomial diffusion. We o…
Betting on Moments: Legendre Jumper Martingales for Online Exchangeability Testing
A fundamental assumption in statistics and machine learning is that ``the future looks like the past,'' formalized as exchangeability: the joint data distribution is order-invariant. In practice, this assumption is often…
Reinforcement Learning for Jump-Diffusions, with Financial Applications
We study continuous-time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump-diffusion processes. We formulate an entropy-regularized exploratory control problem with stochast…
Q-Learningreinforcement-learningReinforcement LearningReinforcement Learning (RL)