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Execution and Block Trade Pricing with Optimal Constant Rate of Participation

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DOI: 10.4236/jmf.2014.44023    3,116 Downloads   3,688 Views   Citations
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ABSTRACT

When executing their orders, different strategies are proposed to investors by brokers and investment banks. Most orders are executed using VWAP algorithms. Other basic execution strategies include POV (also called PVol)—for percentage of volume, IS—Implementation Shortfall, or Target Close. In this article dedicated to POV strategies, we develop a liquidation model in which a trader is constrained to liquidate a portfolio with a constant participation rate to the market. Considering the functional forms commonly used by practitioners for market impact functions, we obtain a closed-form expression for the optimal participation rate. Also, we develop a micro-founded risk-liquidity premium that allows better assessing the costs and risks of execution processes and giving a price to a large block of shares. We also provide a thorough comparison between IS strategies and POV strategies in terms of risk-liquidity premium.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Guéant, O. (2014) Execution and Block Trade Pricing with Optimal Constant Rate of Participation. Journal of Mathematical Finance, 4, 255-264. doi: 10.4236/jmf.2014.44023.

References

[1] Almgren, R. and Chriss, N. (1999) Value Under Liquidation. Risk, 12, 61-63.
[2] Almgren, R. and Chriss, N. (2001) Optimal Execution of Portfolio Transactions. Journal of Risk, 3, 5-40.
[3] Almgren, R.F. (2003) Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk. Applied Mathematical Finance, 10, 1-18.
http://dx.doi.org/10.1080/135048602100056
[4] Almgren, R. (2011) Optimal Trading with Stochastic Liquidity and Volatility. SIAM Journal of Financial Mathematics, 3, 163-181.
[5] Almgren, R. and Lorenz, J. (2007) Adaptive Arrival Price. Journal of Trading, 2007, 59-66.
[6] Forsyth, P.A., Kennedy, J.S., Tse, S.T. and Windcliff, H. (2009) Optimal Trade execution: A Mean Quadratic Variation Approach. Quantitative Finance,.
[7] Lorenz, J. and Almgren, R. (2011) Mean-Variance Optimal Adaptive Execution. Applied Mathematical Finance, To Appear.
[8] Tse, S.T., Forsyth, P.A., Kennedy, J.S. and Windcliff, H. (2011) Comparison between the Mean Variance Optimal and the Mean Quadratic Variation Optimal Trading Strategies. Applied Mathematical Finance, 20, 415-449.
[9] Schied, A., Schoneborn, T. and Tehranchi, M. (2010) Optimal Basket Liquidation for Cara Investors Is Deterministic. Applied Mathematical Finance, 17, 471-489.
http://dx.doi.org/10.1080/13504860903565050
[10] Guéant, O. (2012) Optimal Execution and Block Trade Pricing: The General Case. Working Paper.
[11] Schied, A. and Schoneborn, T. (2009) Risk Aversion and the Dynamics of Optimal Liquidation Strategies in Illiquid Markets. Finance and Stochastics, 13, 181-204.
http://dx.doi.org/10.1007/s00780-008-0082-8
[12] Obizhaeva, A. and Wang, J. (2005) Optimal Trading Strategy and Supply/Demand Dynamics. Technical Report, National Bureau of Economic Research, Cambridge.
http://dx.doi.org/10.3386/w11444
[13] Kratz, P. and Schoneborn, T. (2013) Optimal Liquidation in Dark Pools. EFA 2009 Bergen Meetings Paper.
[14] Kratz, P. and Schoneborn, T. (2012) Portfolio Liquidation in Dark Pools in Continuous Time. Mathematical Finance, Early View.
[15] Laruelle, S., Lehalle, C.A. and Pages, G. (2011) Optimal Split of Orders across Liquidity Pools: A Stochastic Algorithm Approach. SIAM Journal on Financial Mathematics, 2, 1042-1076.
http://dx.doi.org/10.1137/090780596
[16] Bayraktar, E. and Ludkovski, M. (2012) Liquidation in Limit Order Books with Controlled Intensity. Mathematical Finance, Early View.
http://dx.doi.org/10.1111/j.1467-9965.2012.00529.x
[17] Guéant, O. and Lehalle, C.A. (2012) General Intensity Shapes in Optimal Liquidation. Working Paper.
[18] Guéant, O., Lehalle, C.A. and Fernandez-Tapia, J. (2012) Optimal Portfolio Liquidation with Limit Orders. SIAM Journal on Financial Mathematics, 3, 740-764.
http://dx.doi.org/10.1137/110850475
[19] Gatheral, J. (2010) No-Dynamic-Arbitrage and Market Impact. Quantitative Finance, 10, 749-759.
http://dx.doi.org/10.1080/14697680903373692

  
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