Coherent liquidity risk measures

Transcription

1 Coherent liquidity risk measures Erwan KOCH ISFA, Université Lyon 1 and CREST-ENSAE, Paris 6th Financial Risks INTERNATIONAL FORUM Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

2 Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

3 Outline Introduction 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

4 Introduction Introduction Management of liquidity risk is a very important issue. There are a lot of existing liquidity measures. Liquidity risk is latent and thus very difficult to assess. Always good to have new risk measures. Two types of liquidity: funding liquidity and market liquidity. Two papers proposing liquidity measures : Chen et al. (2013) "Valuing Financial Assets with Liquidity Discount: An ": Funding liquidity measure. Empirical work. Sgarra and Rosazza Gianin (2013) "Acceptability Indexes via g-expectations: an Application to Liquidity Risk". Market liquidity. Very theoretic. Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

5 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

6 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

7 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An Chen (2012) presents a liquidity discount model. Financial securities can be evaluated with substantial discounts when a liquidity squeeze occurs. Merton (1974), Geske (1977) describe the capital structure of a firm. Develop a link between equity and asset prices. Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

8 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

9 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An Chen et al (2013): The method Main contribution Combining Geske (1977) and Chen (2012) models, it provides empirical analysis of financial institutions asset values. It computes both liquid asset values and illiquid asset values. Market capitalization = equity price. The liquid asset price is obtained from the equity price using Geske model. The illiquid asset price is then derived from the Chen model (2012). Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

10 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An Chen et al (2013): Data Data Lehman Brothers and a set of the 23 largest banks in the US. Particular focus on the Lehman case. Period: January, December, 2009 Debt data: FactSet. Simplification of the debt structure to obtain first year and second year debts. Equity data: Yahoo.com Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

11 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

12 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An Liquidity and discontinuity: Liquidity means discontinuity. In a liquid or normal situation, the classical financial theory holds. Illiquidity represents a constraint (difficult to sell the asset) and thus the illiquid asset price must be higher than the liquid one. In an illiquid context there is no price anymore. Everybody wants to sell at any price. The discontinuity in this model is a good point. But not very clear where is the illiquidity. How is defined the fundamental economy W? Which is the relation between W and the illiquidity? Why two situations in case of liquidity? Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

13 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An (cont d) Link between the two parts in the Chen model (2012)? binomial tree model of Cox, Ross and Rubinstein (1979) for the liquid asset value. A T = max(w T K, 0) The illiquid value is: A t = 1 ( ) E[A T ] β $ (E[W T ] R(t, T )W t) R(t, T ) The model for liquidity could be a particular case of the model for illiquidity (when the illiquidity parameter tends towards 0). It is not the case. Funding liquidity or market liquidity? It would be interesting to take into account the correlation between the different institutions: a very important phenomenon in crisis period is the re-correlation. Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

14 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

15 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

16 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Acceptability Indices Cherny and Madan (2009): Introduces the concept of acceptability index (encompasses performance measures) Develops a complete static theory: particular cases and connections with coherent risk measures. Bielecki et al. (2012): Extension of the definition of acceptability indices (AI) to a dynamic setting. Develops a theory of coherent AI in a dynamic framework. Shows a duality between coherent risk measures and AI. Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

17 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Application of AI to liquidity Cherny and Madan (2010): illiquid markets are modeled via AI and bid and ask prices are described through a "Conic Finance" approach. Corcuera et al. (2012): il(liquidity) is measured by an implied liquidity parameter in a static case Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

18 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Models for the liquidity and its dynamics Acerbi and Scandolo (2008): studies the connection between coherent risk measures and liquidity risk. Criticism to frequently adopted assumptions like positive homogeneity. Jouini (1995), Jouini and Kallal (2000), Bion-Nadal (2009) introduce a dynamic approach to bid and ask prices. Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

19 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

20 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Definition of more general AIs. Extension to the quasi-concave case of the relationship between risk measures and AIs obtained by Cherny and Madan (2009) in the coherent case. Link between AI and risk measures based on the notion of g-expectation. Allows to apply AI to liquidity in a dynamic framework (fills the gap between Corcuera et al. (2012) and Bion-Nadal (2009)). Application to ATM European Call options data. Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

21 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Outline 1 Introduction 2 Chen et al. (2013): Valuing Financial Assets with Liquidity Discount: An 3 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22

22 Sgarra and Rosazza Gianin (2013): Acceptability Indexes via g-expectations: an Application to Liquidity Risk Very interesting paper from a theoretical point of view. It would be helpful to give tangible examples of such an Acceptability Index : simple example corresponding to the VaR in case of risk measures. How to estimate such index from real data? The implied liquidity parameter seems to be quite powerful. Shows the liquidity crisis as well as the sovereign debt crisis. But it would be nice to have a precise decription of the data you are using. Do you have data for bid and ask prices? What is your estimation method for the liquidity parameter γ? Erwan KOCH (ISFA and CREST) Coherent liquidity risk measures March 25, / 22