CDO - ABX (Simulator and full paper to follow)

 

In this section we briefly outline how one of the vexed issues of clean up operations which is to determine the value of downgrades on subprime RMBS on an ongoing basis can be dealt with using a multi-agent model drawing on the spatial and dynamic US state by state data base for US subprime mortgagees. The validity of the ABX index spreads of different tranches of a subprime CDO (02-2007 vintage) is therefore sought in this exercise using an agent based model

 

Multi-Agent Modelling of the pricing of ABX index using spatial data

 

To illustrate the power of multi-agent modelling to incorporate fine grained detail on the different sectors we will consider the class of agents representing  the US households that constitute the prime and subprime mortgagees.  They have spatial and economic characteristics which will characterize their default behaviour.  The two following graphs give the regional distribution of subprime mortgagees in the US and data on the growth in defaults from 2005-2006.  The ABM model is able to digitally map these in a spatial dimension and historically track the collateral characteristics, repayment flows and default behaviour of these mortgagees (see, Fabozzi et, al, (2005) and Frankel (2006)). There are large differences in the behaviour of subprime mortgagees, the default and house price dynamics across the different US states.  Retaining these disaggregative features is important to get good quantitative outputs for the ABM simulations for the systemic risk emanating from sub prime lending.  


Figure 1: Subprime as Percentage of Loans Dec 2006 Map
Subprime as Percentage of Loans Dec 2006 Map
Source:  First American Loan Performance; Census Bureau , and Wall Street Journal Online


Figure 2: Increase in Sub-prime Delinquency 2005 to 2006 Map
Increase in Sub-prime Delinquency 2005 to 2006 Map
Source:  First American Loan Performance; Census Bureau , and Wall Street Journal Online

 

The COMISEF project is concerned with developing a multi-agent based computational economics (ACE) framework that can articulate and demonstrate the interrelationships of the financial contagion with a view to aid policy analysis.  The provenance of ACE has been attributed to a new paradigm based on markets as complex adaptive systems (see, Markose (2002, 2005, 2006) and Markose et. al  (2007) which include three  recent Special Issues) which subscribes to the view of computational incompleteness, self-reflexive decision problems which lead to heterogeneity in strategies, ‘surprises’ or innovation based structure changing dynamics and network

 

Brief Multi- Agent Analysis of the Validity of the ABX index

 


We will give a brief expose of the vexed issue for the clean up process of the subprime crisis which involves the tracking of the impairment of bank and near bank balance sheets from defaults on subprime mortgages.  While it is a widespread practice for financial institutions to use the ABX index to write down subprime assets (see, Fender and Scheicher, 2008), it is viewed that the ABX index is excessively depressed and its valuations are called into question.  Here we assess how  valid the ABX index valuations by replicating the cash flows into the water fall ABX structure of a Collateralized Mortgage Obligation (CMO) based on a state by state level agent based model of subprime mortgage defaults.       
In this exercise we track the final 2007 vintage of a $500 bn subprime US mortgage pool over a 3 year maturity date.   The cash flow consisting of interest and principal repayments at the initial date of no defaults is about $4.4 bn (see Table 1).  A multi-agent model is used over both the in sample and out of sample behaviour of the defaults and cash flow impairments into the CMO tranches. 


Table 1: Replication of the ABX Tranches of  02-07 Vintage of $500bn Subprime

 

Cash flow

Tranches

Face Value  

Upper limit of a tranche

70%     

AAA

350bn

4,434,421,913

30%

AA

75bn

1,330,326,574

15%

A

25bn

665,163,287

10%

BBB

15bn

443,442,191

7%

BBB-

20bn

310,409,534

3%

equity

15 bn

133,032,657

The agent based approach can be contrasted with the extant econometric approaches of Blundell and Wignall (2008),  Hatzius (2008) and Greenlaw et. al (2008). Blundell-Wignall (2008) estimates an equation that explains the subprime delinquency rate by GDP, house prices, and unemployment using data from 1998 to 2007. The study then uses the resulting equation along with assumptions about the relationship between delinquencies, defaults, and losses and the evolution of the explanatory variables to forecast credit losses. The problem with this approach is that the underlying data set is confined to 40 aggregate observations during which there was no housing downturn (except at the very end).  Hatzius (2008) and Greenlaw et. al (2008) attempt to over come some of these problems.  However, they fail to give an integrated model that can be dynamically rolled forward and have to rely on ad hoc back of the envelope calculations.

 

It is typical that applied mortgage credit analysts use detailed vintage-by-vintage data to estimate credit losses by “walking forward” historical delinquency, default, and loss curves.  The draw back of this framework is that defaults are not related to macro-economic conditions driving house prices and defaults. To remedy this it is important to incorporate the non-linear feedback relations between house prices, interest rates, the growth of mortgage supply and the failure of subprime lenders themselves.   Within an agent based model of the US state by state level data of US subprime loans in terms of mortgagee characteristics, it is relatively easy to track the nonlinear feedback loop at state level of defaults and house prices.  


What is very interesting is that the ABX prices for the 07 vintage is very similar to the prices we get.  This is given below in Figures 1.6a and 16b.  Tim Geithner, the US Treasury Secretary is known to be struggling to present a coherent framework for sequestering the toxic subprime assets from the balance sheets of banks. One of the core problems is to determine what price to pay for these assets.   Note in Figures 1.6 a,b, as months pass mark to market losses mount to 95% of 30% of $2tn and 70% loss on the super senior tranche which is 70% of $2 tn.   This totals $1.6 tn .  This is about the same size as capital in US commercial banks.  If the toxic assets are to be bought using the ABX prices it will cost the following : 1st quarter 09 pay 5 cents on tranches up to 30%.  The latter is $600 bn of the $2tn subprime and hence this costs  about 30bn.  Then 30 cents is paid on  Super Senior which is $420 bn (ie. 70% of $2tn).  The total cost to remove subprime assets off bank balance sheets is .5 Tn.   This will also give good upside for the tax payer.  Removing the toxic assets off the balance sheets of banks is a matter of urgency as the mark to market losses of these assets imply massive recapitilization to the tune of  $1.6 tn.

 

 

                                                   
Figure 3: ABX Prices Simulated from Agent Based Contagion Pricing Model of CMO 02_07 Vintage $500 bn Face Value of Subprime Mortgages

 

ABX Prices Simulated from Agent Based Contagion Pricing Model of CMO 07 Vintage $500 bn Face Value of Subprime Mortgages

 

Figure 4: ABX 02_07 quotes (from Markit)

ABX Prices Simulated from Agent Based Contagion Pricing Model of CMO 07 Vintage $500 bn Face Value of Subprime Mortgages