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Non-parametric Liquidity Adjusted VaR Model:

A Stochastic Programming Approach

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Technical Report ERGO-10-001

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E. Fragniere,
J. Gondzio,
N. S. Tuchschmid and
Qun Zhang
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Abstract
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This paper proposes a Stochastic Programming (SP) approach
for the calculation of the Liquidity adjusted Value at Risk (LVaR).
The model presented in this paper offers an alternative to Almgren
and Chriss’s mean-variance approach (1999 and 2000). In this research,
a two-stage stochastic programming model is developed with the intention
of deriving the optimal trading strategies that respond dynamically
to a given market situation. The sample paths approach is adopted
for scenario generation. The scenarios are thus represented
by a collection of simulated sample paths rather than the “tree
structure” usually employed in stochastic programming. Consequently,
the SP LVaR presented in this paper can be considered as a non-parametric
approach, which is in contrast to Almgren and Chriss’s parametric
solution. Initially, a set of numerical experiments indicates that
the LVaR figures are quite similar for both approaches when all
the underlying financial assumptions are identical. Following this
sanity check, a second set of numerical experiments shows how
the randomness of the different types (e.g., Bid and Ask spread)
can be easily incorporated into the problem due to the stochastic
programming formulation and how optimal and adaptive trading
strategies can be derived through a two-stage structure (i.e.,
a “recourse” problem). Hence, the results presented in this paper
allow the introduction of new dimensionalities into the computation
of LVaR by incorporating different market conditions.

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Key words:
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Liquidity adjusted Value at Risk (LVaR); Liquidation Cost; Stochastic programming;

Optimal trading strategy; Non-parametric approach; Sample paths.

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Text
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PDF ERGO-10-001.pdf.

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History:
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Written: February 3, 2010.

Published:
**Journal of Financial Transformation** 28 (2010) pp 111-118.
Final PDF.