High frequency market making problem under a jump diffusion process

2016 ◽  
Author(s):  
Zhiying Xu
Keyword(s):  
Diffusion Process ◽  
High Frequency ◽  
Jump Diffusion ◽  
Market Making ◽  
Jump Diffusion Process

scholarly journals Adaptive nonparametric drift estimation of an integrated jump diffusion process

2018 ◽  
Vol 22 ◽  
pp. 236-260 ◽  
Author(s):  
Benedikt Funke ◽  
Émeline Schmisser
Keyword(s):  
Diffusion Process ◽  
High Frequency ◽  
Jump Diffusion ◽  
High Frequency Data ◽  
Compact Set ◽  
Penalized Least Squares ◽  
Adaptive Estimator ◽  
Drift Estimation ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

In the present article, we investigate nonparametric estimation of the unknown drift function b in an integrated Lévy driven jump diffusion model. Our aim will be to estimate the drift on a compact set based on a high-frequency data sample. Instead of observing the jump diffusion process V itself, we observe a discrete and high-frequent sample of the integrated process Xt := ∫0t Vsds Based on the available observations of Xt, we will construct an adaptive penalized least-squares estimate in order to compute an adaptive estimator of the corresponding drift function b. Under appropriate assumptions, we will bound the L2-risk of our proposed estimator. Moreover, we study the behavior of the proposed estimator in various Monte Carlo simulation setups.

scholarly journals A switching self-exciting jump diffusion process for stock prices

2018 ◽  
Vol 15 (2) ◽  
pp. 267-306 ◽  
Author(s):  
Donatien Hainaut ◽  
Franck Moraux
Keyword(s):  
Diffusion Process ◽  
Stock Prices ◽  
Jump Diffusion ◽  
Jump Diffusion Process
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