The Market for OTC Credit Derivatives

Transcription

1 The Market for OTC Credit Derivatives Andrew G. Atkeson Andrea L. Eisfeldt Pierre-Olivier Weill UCLA Economics UCLA Anderson UCLA Economics July 23, 213

2 over-the-counter (OTC) derivatives Credit default swaps, interest rate swaps, forex large volume: over $2 trillions outstanding in the U.S. banks buy and sell simultaneously intricate liabilities structure linking banks Volume is highly concentrated in large banks worldwide, about 8% of contracts held by 14 large banks Concentration arises from specific patterns of entry and participation large banks participate a lot as intermediaries middle-sized banks participate less, as customers small-sized banks do not participate much some data

3 what we do in this paper A model of entry, trade, and price formation in an OTC market Positive question: OTC frictions ) observed market structure? bilateral trade patterns: linkages btw banks and price dispersion entry patterns: why do large banks become intermediaries? why do middle-sized banks become customers? Normative question: can planner or policy maker do better? ine ciencies arise at the entry stage the market is too concentrated in large banks

4 some related literature Models of OTC markets Du e Gârleanu Pedersen (5), Afonso Lagos (12) Babus and Kondor (13), Malamud and Rostek (13) Formation and stability of financial networks Rochet Tirole (96), Allen and Gale (), Babus (9) and many papers on the program of this conference! CDS markets Bolton and Oehmke (12,13)

5 the economic environment

6 preference and endowment Unit continuum of identical CARA agents called traders Traders are organized in large coalitions called banks Banks di er in size size: measure of traders in the coalition the distribution of bank sizes: S f (S), R 1 Sf (S) ds =1 Banks di er in endowment of risky trees! 2 [, 1] trees per trader,! S for the bank! U [,1] in banks cross-section, independent from S each tree has the same random payo 1 D = aggregate default risk factor D

7 timing Entry each bank receives its endowment! 2 [, 1] per trader chooses whether to pay a fixed cost to enter the OTC market OTC market trading traders from all participating banks are matched sign derivative contracts (CDS) subject to trade size limit Consolidation and payo each bank consolidates the contracts signed by all its traders loan portfolios and contracts payo

8 timing Entry each bank receives its endowment! 2 [, 1] per trader chooses whether to pay a fixed cost to enter the OTC market OTC market trading traders from all participating banks are matched sign derivative contracts (CDS) subject to trade size limit Consolidation and payo each bank consolidates the contracts signed by all its traders loan portfolios and contracts payo

9 OTC market trading, after entry

10 period one: OTCmarketopens All traders match, and all matches are equally likely traders from large banks have no exogenous advantage When bank-! trader matches with a bank-! trader, they bargain Trader! sells (!,!) contracts to trader! each contract promises the state-contingent payment D in exchange for fixed payment R(!,!) = the price Position limit: (!,!) 2 [ k, k] common risk management practices

11 period one: OTCmarketopens All traders match, and all matches are equally likely traders from large banks have no exogenous advantage When bank-! trader matches with a bank-! trader, they bargain Trader! sells (!,!) contracts to trader! each contract promises the state-contingent payment D in exchange for fixed payment R(!,!) = the price Position limit: (!,!) 2 [ k, k] common risk management practices this is the main trading friction (6= search) in our model

12 period two: consolidationandpayo All traders from bank! consolidate their positions. Payo per cap.:!(1 D)+ R 1 (!,!) R(!,!) D n(!) d!

13 period two: consolidationandpayo All traders from bank! consolidate their positions. Payo per cap.:!(1 D)+ R 1 (!,!) R(!,!) D n(!) d! CARA certainty equivalent payo! + R 1 (!,!)R(!,!)n(!)d! [g(!)] where g(!) =! + Z 1 (!,!)n(!) d! = per cap. post trade exposure [g] 1 log E e gd = certainty equivalent cost of g The function [g] is increasing and convex

14 Nash Bargaining A!-trader is small and does not coordinate with others in her bank sell CDS =) cost of risk bearing increases by [g(!)]

15 Nash Bargaining A!-trader is small and does not coordinate with others in her bank sell CDS =) cost of risk bearing increases by [g(!)] ) Low post-trade exposure sells CDS to high post-trade exposure 8 >< k if g(!) < g(!) (!,!) = [ k, k] if g(!) =g(!) >: k if g(!) > g(!) ) CDS prices split the gains from trade in half R(!,!) = 1 [g(!)] + [g(!)] 2

16 the equilibrium fixed point problem Contracts (!,!) are optimal given post-trade exposures 8 >< (!,!) = >: k if g(!) > g(!) [ k, k] if g(!) =g(!) k if g(!) < g(!) Post-trade exposures are consistent with the signed contracts Z 1 g(!) =! + (!,!)n(!) d!

17 basic properties Conditional on entry patterns, n(!): equilibrium socially optimal minimize R 1 [g(!)] n(!) d! s.t. to matching and trading capacity constraints Unique g(!) andr(!,!) Post-trade exposures, g(!), are non-decreasing and closer together than pre-trade exposures!! =) apple g(!) g(!) apple!! a manifestation of partial risk sharing!

18 aspecialcaseofinterest n(!) pre-trade exposures,! n(!) depends on the size distribution of banks entering around! we endogenize it later when we study entry

19 post-trade exposure, g(!) 1 post-trade exposure, g(!).5.5 1!! pre-trade exposure,! g(!) is flat in regions where the density of traders, n(!), is large ) traders in these region match a lot and have closeby exposure so they can share risk easily despite trading limit

20 contracts signed per capita gross notional per capita ! Middle-! banks trade more than extreme-! banks

21 contracts signed per capita CDS sold per capita CDS bought per capita !.5 1! Middle-! banks trade more than extreme-! banks Low-! banks sell much more than they buy High-! banks buy much more than they sell

22 contracts signed per capita CDS sold per capita CDS bought per capita !.5 1! Middle-! banks trade more than extreme-! banks Low-! banks sell much more than they buy High-! banks buy much more than they sell All banks provide some intermediation: they buy and sell CDS

23 intermediation per capita ! Volume of fully o setting CDS contracts min{cds sold, CDS purchased} Middle-! banks are the biggest intermediaries net exposures ' use all their trading capacity

24 entry in the OTC market

25 entry incentives Utility of entering per capita, before cost: Z 1 (!) = [!] [g(!)] + (!,!)R(!,!)n(!) d! Two entry incentives sharing aggregate risk with others by changing exposure earning trading profits from price dispersion and intermediation

26 the entry decision Enter if and only if: (!) c S () S > (!) c (!)

27 the entry decision Enter if and only if: (!) c S () S > (!) c (!) Implies a fixed point equation for n(!) n(!) = [ (!)] R 1 [ (!)] d!,where (S) # traders in banks S Schauder ) an equilibrium with positive entry exists

28 quadratic cost of risk bearing, [g] Entry incentives, (!), are U-shaped and symmetric

29 quadratic cost of risk bearing, [g] Entry incentives, (!), are U-shaped and symmetric 1 utility of entering: (!) 5 entry threshold: (!).5.5 1!.5 1!

30 quadratic cost of risk bearing, [g] Entry incentives, (!), are U-shaped and symmetric 1 utility of entering: (!) 5 entry threshold: (!).5.5 1!.5 1! only large-sized banks enter in the middle, as intermediaries middle-sized banks only enter at the extremes, as customers small-sized banks do not enter

31 positive results gross notional per capita absolute net notional per capita intermediation volume per capita.1 1 price dispersion size percentile 5 1 size percentile

32 linkages per capita size percentile size percentile.2 everyone trades more with largest banks large banks endogenously emerge as central counterparties even though trading technology is the same for all!

33 is equilibrium entry socially optimal? Add a small measure " of!-banks at the entry threshold (!)

34 is equilibrium entry socially optimal? Add a small measure " of!-banks at the entry threshold (!) Net utility of entrants is zero, because of free entry condition!

35 is equilibrium entry socially optimal? Add a small measure " of!-banks at the entry threshold (!) Net utility of entrants is zero, because of free entry condition! Net utility of incumbents has two terms " new matches with type-! entrants are created: gain = " k 2 Z 1 [g(!)] [g(!)] n(!) d! = " 2 F (!). " 2 old matches with other incumbents are destroyed: loss = " 2 Z 1 F (!)n(!) d!

36 is equilibrium entry socially optimal? The entry of a type-! bank increase welfare i F (!) > Z 1 F (!)n(!) d! - extreme-! banks (small at the margin) enter too little - middle-! banks (large at the margin) enter too much

37 is equilibrium entry socially optimal? The entry of a type-! bank increase welfare i F (!) > Z 1 F (!)n(!) d! - extreme-! banks (small at the margin) enter too little - middle-! banks (large at the margin) enter too much Note: this reasoning only works at the margin of the equilibrium because only then we can ignore the net utility of entrants!

38 conclusion AnewframeworkforOTCcreditderivatives Networks of cross-exposures arises endogenously incentives to share risk and intermediate economies of scale when entering in OTC markets Rationalizes observed patterns of participation Identifies an ine ciency large banks enter too much middle sized banks enter too little

39 large banks trade disproportionately more 25 2 Total CDS Notional/Trading Assets by Trading Asset Size Top 25 HC in Deriviatives TD BANK US HOLDING COMPANY ALLY FINANCIAL INC. CAPITAL ONE FINANCIAL CORPORATION UNIONBANCAL CORPORATION BB&T CORPORATION CITIZENS FINANCIAL GROUP, INC. KEYCORP FIFTH THIRD BANCORP REGIONS FINANCIAL CORPORATION U.S. BANCORP NORTHERN TRUST CORPORATION PNC FINANCIAL SERVICES GROUP, INC., THE SUNTRUST BANKS, INC. STATE STREET CORPORATION RBC USA HOLDCO CORPORATION METLIFE, INC. BANK OF NEW YORK MELLON CORPORATION, THE HSBC NORTH AMERICA HOLDINGS INC. WELLS FARGO & COMPANY TAUNUS CORPORATION BANK OF AMERICA CORPORATION MORGAN STANLEY CITIGROUP INC. GOLDMAN SACHS GROUP, INC., THE JPMORGAN CHASE & CO.

40 large banks intermediate for large banks, net positions are much smaller than gross positions Net Notional/Gross Notional (CDS Bought-CDS Sold)/(CDS Sold+CDS Bought) TD BANK US HOLDING COMPANY ALLY FINANCIAL INC. CAPITAL ONE FINANCIAL CORPORATION UNIONBANCAL CORPORATION BB&T CORPORATION CITIZENS FINANCIAL GROUP, INC. KEYCORP FIFTH THIRD BANCORP REGIONS FINANCIAL CORPORATION U.S. BANCORP NORTHERN TRUST CORPORATION PNC FINANCIAL SERVICES GROUP, INC., THE SUNTRUST BANKS, INC. STATE STREET CORPORATION RBC USA HOLDCO CORPORATION METLIFE, INC. BANK OF NEW YORK MELLON CORPORATION, THE HSBC NORTH AMERICA HOLDINGS INC. WELLS FARGO & COMPANY TAUNUS CORPORATION BANK OF AMERICA CORPORATION MORGAN STANLEY CITIGROUP INC. GOLDMAN SACHS GROUP, INC., THE JPMORGAN CHASE & CO

41 middle-sized banks hedge Q2 29 to Q4 211, % notional that count as hedge ( guarantee ) i.e., that the bank can use to reduce regulatory capital requirement 1% 9% 8% 7% 6% 5% 4% 3% 2% 1% % Top 12 Bottom 13 Purchased CDs NOT eligible as guarantee Purchased CDs eligible as guarantee back to main slide