The most reliable approach to measure Value at Risk adjusted for market liquidity

Inhaltsverzeichnis (Table of Contents)

• 1 Introduction
• 2 Market liquidity and liquidity risk
  • 2.1 Concept of liquidity
  • 2.2 Liquidity costs
    • 2.2.1 Indirect liquidity cost measures
    • 2.2.2 Direct liquidity cost measures
  • 2.3 Liquidity risk
• 3 Theory of existing liquidity adjusted Value at Risk (IVaR) approaches
  • 3.1 Conventional market risk measurement with Value at Risk (VaR)
  • 3.2 Models based on indirect liquidity cost measures
    • 3.2.1 Trading volume approach by Cosandey (2001) .
    • 3.2.2 Stochastic supply curve approach by Jarrow & Protter (2005)
    • 3.2.3 Adjusted market price approach by Berkowitz (2000).
    • 3.2.4 Approach with stochastic execution lag and quantity discount by Jarrow & Subramanian (1997,2001) .
    • 3.2.5 Approach with permanent and temporary liquidity impact by Alm-gren & Chriss (2000) .
  • 3.3 Models based on direct liquidity cost measures
    • 3.3.1 Add-on approach with bid-ask spread by Bangia et al. (1999)
    • 3.3.2 Limit order approach by François-Heude & v. Wynendaele (2001)
    • 3.3.3 Net return approach with weighted spread by Stange & Kaserer (2008) and Giot & Gramming (2005)
  • 3.4 Synopsis
• 4 Liquidity adjusted Value at Risk accounting for non-normality
  • 4.1 The Cornish-Fisher expansion .
  • 4.2 Modified VaR approaches
    • 4.2.1 Modified add-on approach with bid-ask spread
    • 4.2.2 Modified add-on approach with weighted spread.
    • 4.2.3 Modified net return approach with bid-ask spread
    • 4.2.4 Modified net return approach with weighted spread
    • 4.2.5 Evaluation of the modified 1VaR approaches
• 5 Empirical Analysis
  • 5.1 Data
  • 5.2 General implementation specifications
    • 5.2.1 Situational assumptions
    • 5.2.2 Choice of confidence level and liquidation horizon
    • 5.2.3 Determination of liquidity impact. .
    • 5.2.4 Forecasting return volatility with an exponentially weighted moving average model (EWMA).
  • 5.3 Backtesting framework . .
  • 5.4 Analysis of IVaR approaches based on indirect liquidity cost measures
    • 5.4.1 Cosandey (2001)
    • 5.4.2 Berkowitz (2000)
  • 5.5 Analysis of IVaR approaches based on direct liquidity cost measures
    • 5.5.1 Bangia (1999).
    • 5.5.2 François-Heude & Wynendaele (2001)
    • 5.5.3 Stange & Kaserer (2008)
    • 5.5.4 Giot & Gramming (2005)
  • 5.6 Analysis of modified VaR approaches
    • 5.6.1 Modified add-on approach with bid-ask spread
    • 5.6.2 Modified add-on approach with weighted spread.
    • 5.6.3 Modified net return approach with bid-ask spread
    • 5.6.4 Modified net return approach with weighted spread
  • 5.7 Comparison of the implemented VaR approaches
    • 5.7.1 Overall ranking
    • 5.7.2 Model performance differentiated by order size
    • 5.7.3 Rate of over- and underestimations by order size
    • 5.7.4 Model performance differentiated by indices
    • 5.7.5
• 6 Conclusion and outlook

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This Master's thesis investigates the most reliable approach to measure Value at Risk (VaR) adjusted for market liquidity. It aims to explore and evaluate various methodologies for incorporating liquidity risk into VaR calculations, focusing on both indirect and direct liquidity cost measures.

• Understanding the concept of market liquidity and liquidity risk.
• Analyzing existing liquidity adjusted VaR (IVaR) approaches based on indirect and direct liquidity cost measures.
• Developing and evaluating modified VaR approaches that account for non-normality in liquidity cost distributions.
• Conducting an empirical analysis to compare the performance of different IVaR approaches.
• Identifying the most reliable approach to measure VaR adjusted for market liquidity.

Zusammenfassung der Kapitel (Chapter Summaries)

The thesis begins with an introduction to the concept of market liquidity and liquidity risk. It then delves into the theory of existing liquidity adjusted VaR approaches, categorizing them based on their use of indirect or direct liquidity cost measures. The chapter explores various models, including the trading volume approach by Cosandey (2001), the stochastic supply curve approach by Jarrow & Protter (2005), the adjusted market price approach by Berkowitz (2000), and the approach with stochastic execution lag and quantity discount by Jarrow & Subramanian (1997,2001). It also examines models based on direct liquidity cost measures, such as the add-on approach with bid-ask spread by Bangia et al. (1999) and the limit order approach by François-Heude & v. Wynendaele (2001).

Chapter 4 focuses on the Cornish-Fisher expansion and its application to address non-normality in liquidity cost distributions. It explores various modified VaR approaches that incorporate bid-ask spreads and weighted spreads. Chapter 5 presents an empirical analysis, outlining data selection, implementation specifications, and a backtesting framework. It analyzes the performance of different IVaR approaches, examining both indirect and direct liquidity cost measures. The chapter provides a comprehensive comparison of the implemented VaR approaches, considering factors like overall ranking, performance differentiated by order size, and model performance differentiated by indices.

Schlüsselwörter (Keywords)

The key themes and concepts explored in this thesis include: market liquidity, liquidity risk, Value at Risk (VaR), liquidity adjusted VaR (IVaR), indirect liquidity cost measures, direct liquidity cost measures, non-normality, Cornish-Fisher expansion, empirical analysis, backtesting framework, model performance, order size, and indices. This thesis provides a comprehensive exploration of the most reliable approach to measure VaR adjusted for market liquidity, offering valuable insights into risk management practices in financial markets.