Stock Returns and Market Making with Inventory

Park, Seyoung; Jang, Bong‐Gyu

doi:10.7737/msfe.2012.18.2.001

Management Science and Financial Engineering

2012

DOI: 10.7737/msfe.2012.18.2.001

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Stock Returns and Market Making with Inventory

Seyoung Park¹,

Bong‐Gyu Jang²

Abstract: We study optimal trading strategy of a market maker with stock inventory. Following Avellaneda and Stoikov (2008), we assume the stock price follows a normal distribution. However, we take a constant expected rate of the stock return and assume that the stock volatility is an inverse function of the stock price level. We show that the optimal bid-ask spread of the market maker is wider for a higher expected rate of stock returns.

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Cited by 5 publications

References 11 publications

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An Approximation of the Cumulant Generating Functions of Diffusion Models and the Pseudo-likelihood Estimation Method

Lee¹,

Lee²

2013

Journal of the Korean Operations Research and Management Scienc

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Di ffusi on i s a basi c mathemati cal tool for modern fi nanci al engi neeri ng. The theory of the esti mati on methods for di ffusi on model s i s an i mportant topi c of the fi nanci al engi neeri ng. Many researches have been tri ed to appl y the l i kel i hood esti mati on method for esti mati ng di ffusi on model s. However, the l i kel i hood esti mati on method for di ffusi on i s compl i cated and needs much amount of computi ng.In thi s paper we devel op the esti mati on methods whi ch are si mpl e enough to be compared to the Eul er approxi mati on method, and effi ci ent enough stati sti cal l y to be compared to the l i kel i hood esti mati on method. We devi se pseudo-l i kel i hood and propose the maxi mum pseudo-l i kel i hood esti mati on methods. The pseudo-l i kel i hoods are obtai ned by approxi mati ng the transi ti on densi ty wi th normal di stri buti ons. The means and the vari ances of the di stri buti ons are obtai ned from the del ta expansi on suggested by Lee, Song and Lee (2012).We compare the newl y suggested esti mators wi th other exi sti ng esti mators by si mul ati on study. From the si mul ati on study we fi nd the maxi mum pseudo-l i kel i hood esti mator has very si mi l ar properti es wi th the maxi mum l i kel i hood esti mator. Al so the maxi mum pseudo-l i kel i hood esti mator i s easy to appl y to general di ffusi on model s, and can be obtai ned by si mpl e numeri cal steps.Keyword：Di ffusi on Model s, Transi ti on Densi ty, Del ta Expansi on, The Maxi mum Li kel i hood Esti mator 한국경영과학회지 제38권 제1호

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An Approximation of the Cumulant Generating Functions of Diffusion Models and the Pseudo-likelihood Estimation Method

Lee¹,

Lee²

2013

Journal of the Korean Operations Research and Management Scienc

View full text Add to dashboard Cite

show abstract

The Challenge of Managing Customer Networks under Change : Proving the Complexity of the Inverse Dominating Set Problem

Chung¹,

Park²,

Chung³

2014

Journal of the Korean Operations Research and Management Scienc

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Customer networks go through constant changes. They may expand or shrink once they are formed. In dynamic environments, it is a critical corporate challenge to identify and manage influential customer groups in a cost effective way. In this context, we apply inverse optimization theory to suggest an efficient method to manage customer networks.In this paper, we assume that there exists a subset of nodes that might have a large effect on the network and that the network can be modified via some strategic actions. Rather than making efforts to find influential nodes whenever the network changes, we focus on a subset of selective nodes and perturb as little as possible the interaction between nodes in order to make the selected nodes influential in the given network. We define the following problem based on the inverse optimization. Given a graph and a prescribed node subset, the objective is to modify the structure of the given graph so that the fixed subset of nodes becomes a minimum dominating set in the modified graph and the cost for modification is minimum under a fixed norm. We call this problem the inverse dominating set problem and investigate its computational complexity.

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A Genetic Algorithm for Minimizing Completion Time with Non-identical Parallel Machines

Choi¹,

Song²,

Lee

2013

Korean Management Science Review

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Stock Returns and Market Making with Inventory

Cited by 5 publications

References 11 publications

An Approximation of the Cumulant Generating Functions of Diffusion Models and the Pseudo-likelihood Estimation Method

An Approximation of the Cumulant Generating Functions of Diffusion Models and the Pseudo-likelihood Estimation Method

The Challenge of Managing Customer Networks under Change : Proving the Complexity of the Inverse Dominating Set Problem

A Genetic Algorithm for Minimizing Completion Time with Non-identical Parallel Machines

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