Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Optimal Liquidation with Conditions on Minimum Price
Download
iam_thesis.pdf
Date
2022-9-1
Author
Mervan, Aksu
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
278
views
74
downloads
Cite This
The classical optimal trading problem is the closure of an initial position q_0 in a financial asset over a time interval [0 T]; the trader tries to maximize an expected utility under the constraint q_T = 0, which is the liquidation constraint. Given that the trading takes place in a stochastic environment, the constraint q_T=0 may be too restrictive; the trader may want to relax this constraint or slow down/stop trading depending on price behavior. The goal of this thesis is the formulation and a study of these types of modified liquidation orders. We introduce two new parameters to the stochastic optimal control formulation of this problem: a process I taking values in \{0,1\} and a measurable set { S}. The set { S} prescribes when full liquidation is required and I prescribes when trading takes place. We give four examples for { S} and I which are all based on a lower bound specified for the price process. We show that the minimal supersolution of a related backward stochastic differential equation (BSDE) with a singular terminal value and with a convex driver term gives both the value function and the optimal control of the modified stochastic optimal control problem. The novelties of the BSDE arising from the modified control problem are as follows: the relaxation of the constraint q_T = 0 implies that the terminal value of the BSDE can take negative values; this and the convexity of the driver imply that the driver is no longer monotone and results from the currently available literature giving the minimal supersolution of this type of BSDE are not directly applicable. The same aspects of the problem imply that the BSDE can explode to -infty backward in time. To tackle these we introduce an assumption that balances the market volume process and the permanent price impact in the model over the trading horizon. The BSDEs reduce to PDE for Markovian price processes; we also present an analysis of these PDE for a Markovian price process involving stochastic volatility. We quantify the financial performance of our models by the percantage difference between the initial stock price and the average price at which the position is (partially) closed in the time interval [0,T]. We note that this difference can be divided into three pieces: one corresponding to permanent price impact (A_1), one corresponding to random fluctuations in the price (A_2) and one corresponding to transaction/bid-ask spread costs (A_3). A_1 turns out to be a linear function of 1-q_T/q_0, the portion of the portfolio that is closed; therefore, its distribution is fully determined by that of q_T/q_0. We provide a numerical study of the distribution of q_T/q_0 and the conditional distributions of A_2 and A_3 given q_T/q_0 under the assumption that the price process is Brownian for a range of choices of I and { S}.
Subject Keywords
Optimal Liquidation, BSDE, Minimum Price
URI
https://hdl.handle.net/11511/98803
Collections
Graduate School of Applied Mathematics, Thesis
Suggestions
OpenMETU
Core
Application of a rapid methodology for preliminary appraisal of kaolinite deposits
Cetin, Mahir Can; Altun, Naci Emre (EDP Sciences; 2016-09-28)
An approach that facilitates the mineralogical-compositional analysis and beneficiation-classification procedure was used for fast assessment of the evaluation possibility of kaolin deposits. The approach was applied on two different kaolin deposits from the Aegean region in Turkey. The kaolin samples were characterized using XRD and XRF analyses to determine the key mineralogical characteristics and major components such as Al2O3. The samples were then subjected to the attrition-scrubbing-hydrocycloning pr...
Uniqueness of the reserve price with asymmetric bidders
Günay, Hikmet; Meng, Xin; Nagelberg, Mark (Orta Doğu Teknik Üniversitesi (Ankara, Turkey), 2016-8)
We analyze the optimal reserve price in a second price auction when there are 𝑁 types of bidders whose valuations are drawn from different distribution functions. The seller cannot determine the specific “distribution type” of each bidder. In this paper, we give sufficient conditions for the uniqueness of the optimal reserve price. Then, we give sufficient conditions that ensure the seller will not use a reserve price; hence, the auction will be efficient.
BAYESIAN UNIT-ROOT TESTING IN STOCHASTIC VOLATILITY MODELS WITH CORRELATED ERRORS
Kalaylıoğlu Akyıldız, Zeynep Işıl; Ghosh, Sujit K. (2013-12-01)
A series of returns are often modeled using stochastic volatility models. Many observed financial series exhibit unit-root non-stationary behavior in the latent AR(1) volatility process and tests for a unit-root become necessary, especially when the error process of the returns is correlated with the error terms of the AR(1) process. In this paper, we develop a class of priors that assigns positive prior probability on the non-stationary region, employ credible interval for the test, and show that Markov Ch...
Solution of the Almgren-Chriss model with quadratic market volume via special functions
Ertürk, Eren; Sezer, Ali Devin; Department of Financial Mathematics (2020-9)
One of the current topics of research in mathematical finance is the scheduling of buy or sell orders to liquidate a position. A well-known framework for this problem is the one proposed by Almgren and Chriss that poses the problem as the maximization of the expected utility of the final terminal wealth. In the simplest formulation of the problem the market trading volume is taken as a constant. Under this and other assumptions an optimal trading curve can be computed in terms of the sinh function. This stu...
Monotonicity of Liquidity sensitive Option Prices with respect to Market Liquidity Parameters
Kuş, Selin Özlem; Sezer, Ali Devin; Department of Financial Mathematics (2022-2-18)
Classical option pricing models assume that market prices of traded securities are given and independent of the actions of the traders. Recently, a number of option pricing models emerged where the impact of hedging transactions on prices of the traded securities is also taken into account in the pricing of the option. In this term project we study one of these models proposed by Gueant and Pu that is based on the optimal liquidation framework of Almgren and Chriss. The model includes the price impact of th...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
A. Mervan, “Optimal Liquidation with Conditions on Minimum Price,” Ph.D. - Doctoral Program, Middle East Technical University, 2022.