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Notes for Modeling the Accrual Portfolio


Following the idea of Net Interest Margin Optimization (NIMo) and Dynamic Programming (dyNIM0?) we survey the literature on quantitative models for accrual portfolio products: deposits, credit cards, loans, short term and long term debt. Assuming the quantitative cashflow modeling field for some of these products is relatively new we also track down and list the historical sources of data for these products for eventual model testing, error measurement, and estimation. There is about 100mm to 200mm USD per annum per basis point recovered in the optimization/dynamic programming. The money, the technology, the math, and the data are all ready to go, it is just a simple matter of programming.

The general idea in Net Interest Margin optimization is to realize that, in 2016, the implementation of any bank’s Capital Allocation plan is typically manual and not optimized at the security level. The reality is now, following the regulatory response to the Credit Crisis,  all banks are centrally reporting their accrual portfolios of tens or hundreds of millions of securities, contracts, and accounts. We can directly stochastically simulate bank accrual portfolios and aggregations of bank books security-by-security against standard econometic variable time series, market rates, and term structures. One major issue for the security-by-security modeling is that  the cashflows and drawdowns for any given deposit, credit card, or loan is, by itself, idiosyncratic and unlikely to be directly tied to either contractual terms or econometric variable levels/market prices. Part of the challenge in modeling the cash flow characteristics of these products is to aggregate them into collections where we can forecast cash movement more accurately and smooth out the idiosyncratic component. This security aggregation  has the two-fold benefit of reducing the number of entities requiring simulation and reducing the error of the expected payment or receipt of cashflows. Of the two benefits, the error control is much more important. If we could control the approximation error and simulate security-by -security we would do that, the economics work out trivially.  In fact the error control in the expected time of the cashflow arrival is probably why this NIMo idea is more applicable initially to Financial Services Firm’s balance sheets than Industrial or non-Financial Corp. balance sheets. We will look at the data but I would expect that the Deposit, Credit Card, and Loan models will behave (with respect to forecast econometric time series) in large part like  prepayment models applied to collateralized mortgages. The reason that has not happened up to now is timing. Mortgages moved into secondary two-way  market trading in the 1980’s. Cards and Loans came into the securitized secondary trading market in early 2000s  as technology  performance improved. Deposits (50% of the Liabilities more or less) stayed on the banking book and really were not centrally reported until Dodd-Frank happened in 2010. Now all this portfolio data is centrally gathered and reported for the CCAR program, the timing looks good.

The process of banking automation has reached the Accrual Portfolio and entire markets for that matter. The computational resources, the mathematical modeling, and the raw data are available to make this happen. Net Interest Margin Optimization can and will play out, if not at the large banks, then at the smaller banks and the FinTech lending startups. It is just a matter of time before this technology hits central banks for market level supervision.

Accrual Portfolio Products

What is the need for quantitative modeling of contracts in the accrual portfolio? One interesting thing to note is that we do not want quantitative pricing models for these securities. The accrual portfolio is not a trading book where inventory is sold to other banks or investors. The accrual portfolio is referred to as the banking book where securities are typically, but not always, held to security maturity or contract termination or dissolution.

What we are looking for is quantitative modeling for how much cash is produced or consumed by individual securities or collections of securities. It does not really matter to us how to NPV these cashflows to any particular value date. We don’t typically plan to sell out of our positions in these securities (remember they are in the banking book), so we do not need a no-arbitrage price.

Quantitative modeling history and context goes back to the early 60s. The quantitative pricing market typically starts from Black Scholes and moves through various interest rate, credit, and mortgages pricing models.


The mortgage cashflow models are the most interesting to us for their similarity to what we are looking for in Banking book security modeling. These are models used for pricing two-way markets and stochastically predicting the timing and size of aggregated cashflow commercial and residential mortgage payments according to a standard set of publically available econometric variable levels and term structures. These models have been in use globally for upwards of 40 years since Lewis Raineri was hired in the Solly mailroom, back in the day.

Capital Adequacy models for Regulatory reporting typically are very rudimentary and are not well tested in the market for their stochastic precision. But they cover the securities in the accrual portfolio so the banks can report CCAR to the Fed.

The issue is to get a predictive expected cash flow model based on econometric variables like the CMBS models but applied to the accrual portfolio securities like the Capital Adequacy models.

What are the prospects of developing a standard Central Bank or Federal Reserve accrual product model for capital adequacy supervision and global market modeling.

From the Finding NIMo paper we know the main components of the optimization problem underlying Net Interest Margin Optimization. At the individual Bank Accrual Portfolio level we need to optimize the implementation of the capital allocation plan with respect to the efficiency of the business units charged with implementing portions of the plan and the cash flow characterization of the securities producing and consuming cash.


This survey will look at the global econometric variables that will drive the cash flow models. Then we look at the literature on Capital Plan effectiveness. Our survey continues examining each of the major banking book securities: deposits, cards, and loans. Then we look at the literature for Treasury funding sources short term and long term debt. We will conclude with an annotated set of references.

Econometric Variables

Variables can be classified as Economic Data, Rates, and Fx, Rates

  • Unemployment
  • GDP_level
  • GDP_level_real
  • M2 money supply
  • Equity Index
  • Vehicle Sales
  • Disposable Income
  • Trade Balance
  • Mortgage Rates
  • Export goods
  • 30Y mort – 10 Y Swap
  • CPI
  • Import Goods
  • HPI
  • Sov Curves
  • FX Rates









Capital Plan Implementation Effectiveness Data and Models









Assets                                     Liabilities

Loan Assets                            Deposits

Cash                                        Purchased Funds

Deposits                                 Long Term Debt

Fed Funds




Consumer Loans, Corporate Loans, Consumer Deposits, Corporate Deposits


The main modeling problem is the deposits, cards, and loan typically do not have a contractual maturity date. Moreover, the notional amount in the contract/account/security can amortize or pay down at the counterparty’s option.











Deposits Data and Models


In normal circumstances Deposits are the Banks cheapest source of funds. In this low interest rate environment of 2016 short term borrowing may sometimes be cheaper than pulling in Deposits.


Typically running at 50 to 60 percent of the Firm Liabilities.


Demand Deposits vs Savings Time Deposits.


Term Sheets


https://www.law.cornell.edu/cfr/text/31/344.7 – what are Demand Deposit securities?


https://www.jpmorgan.com/jpmpdf/1320700456990.pdf – JMP APAC Time Deposit Agreement


https://www.bankofamerica.com/deposits/resources/deposit-agreements.go BAS deposit agreement


https://www.chase.com/content/dam/chasecom/en/checking/documents/deposit_account_agreement.pdf Chase deposit agreement









http://finance.wharton.upenn.edu/~itayg/Files/bankruns-published.pdf Demand Deposit contracts and the probability of Bank Runs.


https://minneapolisfed.org/research/qr/qr2412.pdf Diamond and Dybvig















https://research.stlouisfed.org/fred2/series/WDDNS – Total Demand deposits






Cards Data and Models






Term Sheet











Credit cards accounts have been used as collateral for ABS so there are models.

Credit card securitization






















Loans Data and Models


Term Sheet








Short Term Debt Data and Models


Term Sheet








Long Term Debt Data and Models


Term Sheet











Term Sheet









Future of Demand Deposits – http://www.equifax.com/assets/USCIS/retail_banking_alternative_data_wp.pdf


What are demand deposit securities https://www.law.cornell.edu/cfr/text/31/344.7



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