Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
  • G06Q40/02—Banking, e.g. interest calculation or account maintenance

Definitions

• Structured finance is a financing technique whereby specific assets are placed in a trust, thereby isolating them from the bankruptcy risk of the entity that originated them. Structured finance is known to be a market in which all parties rely to a great extent on the ratings and rating announcements to understand the credit risks and sources of protection in structured securities (of which there are many types, asset-backed commercial paper (ABCP) , asset-backed securities (ABS) , mortgage-backed securities (MBS) , collateralized bond obligation (CBO) , collateralized loan obligation (CLO) , collateralized debt obligation (CDO) , structured investment vehicles (SIV) , and derivatives products company (DPC) , synthetic CLOs, CBOs of ABS, collectively "structured finance.”) Structured financings are typically the result of the sale of receivables to a special purpose vehicle created solely for this purpose. Securities backed by the receivables in the pool
• asset pool (“asset pool”) are then issued. These are normally separated into one or more “tranches” or “classes”, each with its own characteristics and payment priorities. Having different payment priorities, the tranches accordingly have different risk profiles and payment expectations as a function of the potential delinquencies and defaults of the various receivables and other assets in the pool. The senior tranche usually has the lowest risk.
• structured finance is a zero-sum game in its purest form.
• it means that, in a world where multiple securities are issued out of one asset pool, it is by definition impossible to make one security holder better off without making another worse off because both share in a single set of cash flows.
• the only way to make both security holders better off simultaneously is to assume that the aggregate cash flow to be expected from the pool of assets is somehow better than previously thought. Accordingly, bankers, analysts and investors desire to solve the problem of structuring deals already rated or the "inverse problem.”
• a major stumbling block of optimization within structured finance is the fact that the rating of a structured finance security is given by the average reduction of yield that security would experience over the universe of possibilities to be expected from asset performance. If it is also assumed that the "ergodic" hypothesis holds, i.e. that temporal averages are equal to ensemble averages, then the same reduction of yield would be experienced by an investor holding a well diversified portfolio of similarly rated securities.
• This non-linearity causes local optima to be globally sub-optimal in a multi-dimensional space. The result is that we cannot optimize one variable at a time and that we require a more sophisticated technique. If the entire multi-dimensional space of many variables is explored, the analysis of the number of possible values will quickly exhaust the capabilities of even the fastest computer. It is therefore desirable to provide a method for solving the inverse problem in a fast and efficient manner by minimizing the necessary computational resources.
• a method of solving the inverse problem through an iterative process whereby each iterative effectively solves one forward problem without having to sample the entire non-linear space.
• This method is a selective and iterative process for optimizing many variables that substantially achieves a global optimum solution. More particularly, one such process comprises a neo-Darwinism method. Under this method, the sample space is iteratively analyzed via "mutations" to the value of the variable involved. Starting from a basic structure, assumed sub-optimal, small variations or mutations, are applied to each variable in turn, and those that are determined to improve the outcome value are kept.
• a better outcome value is determined to exist when a set of ratings is within a predetermined range of an average rating. Because the average rating is an invariant, the variable space is operated on throughout the process of looking for the combination of factors that will lead to the better outcome value.
• Fig. 1 illustrates a process for determining the inverse solution problem according to an embodiment of the present invention
• Fig. 2 illustrates a flow chart of a process for solving the inverse solution problem according to another embodiment of the present invention
• Fig. 3 illustrates a computer system for performing the processes according to the embodiments of the present invention.
• the method of solving the inverse problem according to the embodiments of the present invention utilizes an iterative process. Each iterative effectively solves one forward problem without having to sample the entire non-linear space. As a result, the method according to the present invention substantially achieves a global optimum solution by optimizing the many variables.
• the first step in solving the inverse problem is to determine the average rating of the securities in the transaction, or the "feasible range.” This step is performed as a consequence of the average rating of asset-backed securities being approximately constant for a given set of cash flow histories from the pool.
• the average rating is approximately constant because non-linearity in the yield curve will still introduce arbitrage possibilities of a second order as compared to the zero-sum game condition.
• the inverse solution proceeds by exploring each factor in turn within its range of possible variations while introducing small disturbances in the remaining factors in search for a globally optimal solution. These small variations can be exploited through the neo-Darwinian solution method described in more detail hereinafter to achieve global optimality. Due to the non-linearity of the yield curve, it will generally be possible to achieve a slightly better result than a "feasible solution" found during the first step. Although there is no guarantee that a global optimum will actually be found, each new iterate will be analyzed to determine whether its result is better than the existing result.
• the solution procedure can then be halted at any time to retrieve the current optimal structure.
• Each factor in the list above is to be placed inside an iterative loop within which "mutated" levels are sampled.
• Each set of factors is then fed to the forward solution process for producing a set of results to be compared with the required set.
• the forward solution can be halted when a predetermined " figure of merit" is reached which can be stated in terms of a total cost of issuance, a total issued amount, maximum proceeds or some combination of these factors or others.
• step 110 a figure of merit for the transaction is defined in coordination with the issuer.
• the metric for determining this figure of merit is obtained by computing the average cost of issuance, the total proceeds or a weighted combination thereof.
• step 120 a determination is made at step 120 for the range of allowable variation for each factor and the range is normalized to embed it into a Binomial or another statistical distribution of discrete values. The mean of that distribution is determined so as to advantage the most likely a priori range for the factor.
• a trial structure is obtained based on the prior transaction or a similar transaction executed by a comparable issuer.
• the average tranche rating is computed. If the average tranche rating is below the required set, the issuance is reduced. If the average tranche rating is above the required set, the issuance is increased until the discrepancy between the required and actual average is within a prescribed tolerance.
• the figure of merit for each factor is determined at step 140 for two levels separated by a small distance, so that the gradient of the structure is established in that direction.
• the range from 0 to 1 is partitioned into a probability distribution function given by the relative gradient probability distribution for the factors.
• a factor with a large gradient will give rise to more frequent sampling of that factor, and vice versa.
• this procedure guarantees that the currently most sensitive factor is advantaged during the optimization without excluding the other factors completely.
• a non-linear space "loop structure" is entered.
• Each factor (listed generically as factor 1, factor 2, etc.) is mutated in turn with the requirement that the mutation is preserved if it leads to a higher figure of merit.
• Factor sampling uses the Binomial distribution defined above and the inverse cumulative distribution function method. The next iterate is defined as the previous iterate plus the Binomial factor increase. It is appreciated that Binomial factor may be negative which indicates a Binomial factor decrease.
• a mutation is determined to be successful at step 160, the relevant factor is retained at that value until its next mutation. If the mutation is determined not to be successful at step 160, the factor value before the mutation is retained and another factor is tried at step 162. Thereafter, the gradient is re-computed each time for the factor that was mutated if success was achieved and the gradient probability distribution is re- normalized for the factor selection at step 164. The factor value from the mutation is retained before proceeding to the next iterate at step 166. More generally, a standard optimization method such as the steepest descent or Newton-Raphson method may be used to accelerate the search for the global optimum.
• a standard optimization method such as the steepest descent or Newton-Raphson method may be used to accelerate the search for the global optimum.
• the solution procedure is halted periodically or after many cycles at step 170.
• the resulting structure is examined for robustness by mutating each factor in turn using a larger difference at step 172. Thereafter, a determination is made at step 174 as to whether the range of possible improvement using one factor at a time variations is smaller than a specified value. If the criterion is satisfied, the method is stopped at step 180. Otherwise, the method proceeds to the loop structure at step 150.
• there will be an initial figure of merit generated which will set the desired outcome for each issuer for the investment in pooled assets. For example, one set of situations may be for early cash returns while another may be for maximum overall returns.
• a desired or target rating and interest rate for each component or tranche of the investors can be set.
• Statistical analysis is then used to test the investment according to cash flow models of the financial institutions, typically insurance companies or retirement funds, making the investments and to determine how closely the investment can be tailored to fit those targets. Because the cash flow models cannot be solved for the desired output, information of the tranche rating, an iterative approach is undertaken as is known in the art by varying the output until convergence to the actual input factors is achieved.
• the factors or variables available for adjustment in the effort to reach the targets are various and may change for each deal.
• One set of typical and non-limiting factors is shown in Table I. It is to be clearly understood that other factors may be selected due to the ability to control them for different deals.
• the cash flow model is provided with starting values for each of the factors.
• one such factor to be the size of each tranche in a two-tranche deal. Because the level of risk and possible level of gain is different for each tranche, typically one of little risk and one of high risk but great potential, there will be a greater size for the lower risk tranche and a smaller size for the riskier one for a number of reasons not the least of which is the availability of accurate information on the probability of a high return. For exemplary purposes only a starting point for the tranche size factor could then be 90/10 for lower/higher risk respectively.
• Initial values for the other factors will also be selected. The analysis begins by first running a statistical analysis of the cash flow model for the initial factor value selections. Then one factor is varied.
• the tranche size Assuming it is the tranche size, it could typically be varied by 0.5, to say 90.5/9.5.
• the statistical iterative analysis is run again and the result is normally a different set of ratings for each tranche.
• the first factor is then returned to its prior value and another factor varied and the statistical iteration is converged again. This is repeated for all the factors and at that point a gradient is established as the slope of the curve represented by the cash flow model at those initial factor values.
• Fig. 2 shows the invention diagramatically in the form of a flow chart. While most of the steps are computer executed, several like the initializing step 12 and final determination steps are done by human means.
• the initializing step 12 accomplishes the formulation of the figure of merit and target ratings for the deal along with the number and approximate risk, starting values for the factors, and participation rules for the tranches.
• Computer execution begins in step 14 using the applicable cash flow model (s) and comprises an iterative determination of the effect on the ratings as defined in the cash flow model from a one step move (out and back) in a first (or next) one of the several factors. Once that is done, a decision step 16 determines whether all of the factors has experienced the one step evaluation of step 14.
• a subsequent step 18 indexes or advances to the next factor in the list and returns processing' to step 14. As can be seen this accomplishes a one-step move in all the factors and provides the change in the rating information for each.
• a subsequent step 20 establishes the gradient in the rating information for the various changes in factor value for each move. This is in effect a partial differential over each of the factors.
• Subsequent step 22 is a decision for whether the process to this point has reached a suitable conclusion. Normally the process will loop through this decision many times with a no determination, returning to the step 14 for another round of factor steps.
• the step size and direction is a function of the gradient so the iterative analysis moves each factor toward a higher or preferred rating outcome as determined in a step 24. If the gradient is steep, the process may increase the step size.
• decision 22 may decide that the process had progressed far enough and progress to step 26 where a determination is further made as to whether it is time to quit the process and live with the results obtained or go further by mutating the factors. If the step 26 determines the process is finished, it proceeds to a deal evaluation step in step 28 that is largely human powered. But if the process is not yet done, a step 30 mutates one or more factors by stepping them a large distance compared to the small steps that had been taken previously in the changes of factor value. The step size is large enough to give a high probability of moving out of the region of slope of a local maximum about which the cash flow model was used to reach to or nearly to the local maximum.
• the step is of a size that it is likely, though not certain to reach the region of a separate local maximum that may be higher or lower.
• the mutation may by one, several or all factors at a time. After the mutation, the entire process is repeated leading to finding the local maximum for the ratings by iterative analysis of the cash flow model (s) .
• This process of mutation will also be made many times in the process of deal evaluation leading to several maxima and thus allowing selection of the highest or one of the highest thereof. As can be seem there is an enormous amount of calculation going forth in this process given the iterative nature of the models involved and the need to repeat the entire procedure a great many time for each maximum to be found. Only high capability computation equipment can be used for this to be done efficiently.
• the invention is typically performed in a powerful computer environment given the number of iterations that are performed.
• one or more CPUs or terminals 310 are provided as an I/O device for a network 312 including distributed CPUs, sources and internet connections appropriate to receive the data from sources 314 used in these calculations as illustrated in Fig. 3 in an embodiment of the present invention.

Applications Claiming Priority (3)

Publications (2)

Family

ID=22886877

Family Applications (1)

Country Status (5)

Citations (4)

Family Cites Families (2)

• 2001
  • 2001-09-26 WO PCT/US2001/030074 patent/WO2002027996A2/en not_active Application Discontinuation
  • 2001-09-26 AU AU2001291251A patent/AU2001291251A1/en not_active Abandoned
  • 2001-09-26 JP JP2002531662A patent/JP2004511036A/ja active Pending
  • 2001-09-26 EP EP01971355A patent/EP1232462A4/de not_active Withdrawn
• 2003
  • 2003-02-18 HK HK03101223.4A patent/HK1049384A1/zh unknown

Patent Citations (4)

Non-Patent Citations (3)

Also Published As

Similar Documents

Legal Events