Derivatives Pricing with Market Impact and Limit Order Book (Forthcoming in Automatica.)(Revised version of F-385)

Taiga Saito and Akihiko Takahashi
Additional contact information
Taiga Saito: Graduate School of Economics, The University of Tokyo
Akihiko Takahashi: Graduate School of Economics, The University of Tokyo

No CARF-F-417, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: This paper investigates derivatives pricing under existence of liquidity costs and market impact for the underlying asset in continuous time. Firstly, we formulate the charge for the liquidity costs and the market impact on the derivatives prices through a stochastic control problem that aims to maximize the mark-to-market value of the portfolio less the quadratic variation multiplied by a risk aversion parameter during the hedging period and the liquidation cost at maturity. Then, we obtain the derivatives price by reduction of this charge from the premium in the Bachelier model. Secondly, we consider a second order semilinear partial differential equation (PDE) of parabolic type associated with the control problem, which is analytically solved or approximated by an asymptotic expansion around a solution to an explicitly solvable nonlinear PDE. Finally, we present numerical examples of the pricing for a variance option and a European call option, and show comparative static analyses.

Pages: 16 pages
Date: 2017-08
New Economics Papers: this item is included in nep-mst
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/F417.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf417

Access Statistics for this paper

More papers in CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by ().