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Optimal Portfolio Liquidation with a Markov Chain Approach

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Jingnan Chen

on 8 October 2013

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Transcript of Optimal Portfolio Liquidation with a Markov Chain Approach

Optimal Portfolio Liquidation with a Markov Chain Approach
LiteRature ReView
ProBlem ForMulation
Objective
Ph.D. Candidate
University of Illinois at Urbana-Champaign

How to liquidate large blocks of assets in a short time period?
Price Impact
Trading Cost
Market Volatility
VS
Limited Market Liquidity
PortFolio LiquiDation is CompliCated
R.Almgren and N.Chriss.
"Optimal Execution of Portfolio Transactions"
trading cost

trading risk
Price Dynamics:
Unaffected Price:
Executed Price:
Holding Dynamics:
Trading Cost:
Trading Risk:
QV:
VaR:
ContriButions
Propose efficient numerical method:
Markov chain approximation

Obtain analytical properties:
effect of price impact, risk-averse parameters and risk measures
Numerical Method
Bellman Equation:
Convergence Rate:
clear-cut O(1/n)!
Properties
Proposition:
With zero drift rate, the optimal initial selling rate is
decreasing
w.r.t.
price impact
, but
increasing
w.r.t.
risk aversion parameter.
Effect of Price Impact
Effect of Risk Aversion
Conclusion
Highly efficient DP algorithm
Analytical properties of optimal strategy
Thank You!
Jingnan Chen
Binomial Approach:
Multiple assets: BEG multi-variate binomial model
Single asset: CRR binomial model
MCA: build locally consistent discret Markov chain to approximate original continuous process
Trading Risk
Question?
Numerical Example
Risk Measure: VaR
Optimal Solution=-75 share/sec
Our Work
1.
Asset price dynamics:
general geometric Brownian motion
3.
Comparison of risk measures:
quadratic variation, value-at-risk
2.
New numerical scheme:
Markov chain approximation
4.
Analytical properties:
effects of influential factors
Proposition:
When
quadratic variation
is the risk measure, the optimal trading strategy is a pure
selling
program under zero drift rate.
Simulation Result
Price Dynamics: GBM
1. Mannual order
2. Automated execution algorithm
1. Simulate asset dynamics
2. Visualize trading trajectories
Forsyth et al.

"Optimal Trade Execution: a mean-quadratic

-variation approach"
+
Joint work with Liming Feng and Jiming Peng
strictly convex
Computational Time:
0.087 sec
Full transcript