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1、Securitization of Financial assets Asset-Backed Securitization (ABS) is a financial tool which allows financial institutions (usually commercial banks) to move unmarketable assets (e.g.lease assets mortgage assets or commercial papers) from their balance sheets in exchange for a long term loan which
2、 can be ploughed back into more profitable investments. More precisely ,the financial assets are converted into bonds (so called notes ) and the proceeds of their market issuance become a long term loan for the assets owner (the originator ).We will look at the ABS operation mainly from the point of
3、 view of this financial institution. Our analysis will concentrate on the critical phase of the ABS operation avoiding to describe in detail the role of some of the participating operators, such as banks and insurance companies, which provide the credit protection (risk hedging) of the operation .It
4、 should be noted that the issue of credit protection is an interesting research topic in itself .However ,the corresponding features such as credit guarantees and cash flow riskiness are beyond the scope of this paper . In an ABS, the assets are sold by the originator to a special purpose vehicle (S
5、PV), an institution created solely for that purpose .The SPV funds the purchase through issuing debt securities-the notes-which are collateralized by the assets. Note that the assets transfer is a true sale. Thus , if the originator becomes insolvent or is involved in bankruptcy the transferred fina
6、ncial assets will not be part of the bankruptcy the transferred financial assets will not be part of the bankruptcy assets. This makes the notes an interesting investment opportunity .In apass through payment scheme the final investors who buy these notes receive periodic inflows (interests on their
7、 investments). These are directly related to the periodic installments paid by the holders of the assets (e.g. lessees or mortgage holders) to the originator (e.g. the lessor ). Using the ABS structure the originator bypasses the problem of an impossible outright sale of its assets and thus reduces
8、its overall exposure to them. For instance ,lease or mortgage contracts which tie up the capital of leasing companies can be moved into notes. This replacement of illiquid assets improves the return on equity (ROE). From the point of view of the originator, an ABS allows the achievement of three mai
9、n Financial objectives:1. Replacement of the assets in the balance sheet, thereby improving ROE and allowing ( if the originator is a bank) a more flexible keeping of the asset/liability composition constraints imposed by the control authorities (i.e. the Central Bank).2. Diversification of fund sou
10、rces. Althrough the originator may be low rated, its notes usually get a higher rating (e.g. AAA) due to the presence of banks and insurance companies which guarantee the whole operation .This implies that such notes can be dealt on the main financial markets allowing the originator to reach markets
11、 which would otherwise be unaccessible for him since attended only by more established companies.3. Higher rated notes are more reliable investments and thus are allowed to pay lower interest rates to holders. If the cost to get a higher rating is lower than the saving obtained by issuing notes whic
12、h higher rating, then the global cost to acquire funds decreases. Let us assume that an institution with a BB rating can get money at a rate such as Libor (London interbank offering rate) plus 150 basis points. Such an institution, as originator, may decide pay an additional 100 basis points to get
13、credit warranties 1 and be able to issue notes with rating AAA at the cost of Libor plus 10 basis points. In this case an ABS will produce a saving on interest rates of 40 basis points. This situation applies in practice, since there is no efficient market for the underlying assets. The interest in
14、this financial operation drastically increased in the last years all over Europe. In Italy, one of the most recent and relevant ABS has been performed by the pulic institution in charge of the management of the social security system, i.e. the Istituto Nazionale della Previdenza Sociale (INPS).This
15、operation has allowed INPS to move delinquent contributions from its balance sheet. Other transactions of this type took place in the area of public housing agencies. The interest in this financial operation drastically increased in the last years all over Europe. In Italy, one of the most recent an
16、d relevant ABS has been performed by the public institution in charge of the management of the social security system, i.e. the Istituto Nazionale della Previdenza Sociale (INPS). This operation has allowed INPS to move delinquent con-tributions from its balance sheet. Other transactions of this typ
17、e took place in the area of public housing agencies. Many papers dealing with ABS from a modeling point of view have appeared in the last few years. Since an extensive review is beyond the scope of this paper we will only mention the papers by Kang and Zenios 6,7 and by Mansini and Speranza 12,13 an
18、d refer to the references given therein. For a better insight in the complex problem of securitization we suggest the textbooks 3,5,15. In particular, motivated by the analysis of a real-world case, Mansini in 11 and then Mansini and Speranza in 12 have studied the problem of optimally selecting the
19、 assets to refund the loan. In other case only lease assets are considered, although many other types of assets have the same basic characteristics. In their paper the outstanding principal of the assets is computed based on constant general installments (the so called French amortization). The resu
20、lting problem of selecting assets at unique date can be modeled as a d-dimensional knapsack problem, which is hardly tractable by exact algorithms but is typically solved by constructive heuristics (see e.g.1,16) or metaheuristics (see e.g.2,4. The authors also show that in the special case where al
21、l lease assets share the same financial characteristics (amortization rule, internal interest rate and term ) all but one constraint turn out to be redundant and hence the model reduces to a classical 0-1 knapsack problem (KP), which is relatively easy to handle (cf.8,9,14). See 10 for a general int
22、roduction to knapsack problems. Their work does not take into account the occurrence of a different rule for the asset amortization. In many practical applications (both for lease and mortgage contracts) the customers receiving the assets choose to pay back their debt by constant periodic principal
23、installments (the rule is known as Italian amortization). Up to now this common rule has been totally ignored in models formalization. The objective of this paper is twofold .First of all we innovate with respect to previous modeling approaches by introducing a general model to select financial asse
24、ts at multiple dates. The motivation derives from the practical need of finding alternative and possibly more effective formulations for the problem of asset selection in ABS to achieve a better utilization for the long term loan. Secondly, we analyze the frequently encountered practical case in whi
25、ch the assets (lease or mortgage contracts) are paid back by constant periodic principal installments ( Italian amortization rule). In this way the paper aim to provide analysis of an alternative amortization rule available in practices as well as the development of better tools for the institutions
26、 responsible for the planning and management of ABS. Before defining the new model we should give a more detailed sketch of the ABS process. To help the reader in visualizing and better understanding the structure of an ABS process. The SPV issues notes on the financial market receiving funds from i
27、nstitutional investors who purchase the notes and hold them until maturity subject to the availability of acceptable short-term financing. The proceeds obtained by the notes issuance are used by the SPV to make revolving purchases of the unrated assets from the originator. The latter receives a long
28、 term loan which is payable solely by assets. In particular, the originator has to select the assets to be handed over for the loan reimbursement. These assets are“converted into” the notes issued by the SPV.The assets which are included in an ABS process have to be selected in a way such that the s
29、um of their outstanding principals never exceeds the outstanding principal of the received loan (from now on simply the main outstanding principal) at any point in time. Now in order to maximize the financial gain of the operation the critical problem for the originator consists of minimizing the ga
30、p between the main outstanding principal and the outstanding principal of the selected assets over all points in time. This gap constitutes a loss of profit due to missing more profitable investments with higher yields.Actually the area of the main outstanding principal covered by the sum of outstan
31、ding principals of the handed-over assets yields a return for the originator ( e.g. the lessor) depending on the difference between the percent interest rate per year that the originator got from its customers (e.g. the lessees) and the lower percent interest rate paid to the note holders. If the su
32、m of the outstanding principals of the selected assets has a global reimbursement profile which decreases more rapidly than that of the main outstanding principal, then the originator gets funds from its customers in advance with respect to the deadline at which it should pay the capital installment
33、 to the SPV. Such funds have to be reinvested in some predefined type of investments indicated in the ABS agreement. These investments last for a brief period (from the date in which they are available to the following date of reimbursement for the main loan) and usually yield a very low interest ra
34、te. Given the rate B payed for the notes it frequently happens that B is close to zero and may also be negative involving a loss for the originator. This justifies the interest in minimizing the gap between the two profiles and stresses the importance of studying alternative shapes for the outstandi
35、ng principals.Another important aspect in an ABS process is the risk of assets prepayment (cf.Schwartz and Torous 18).A decline in interest rates may cause an earlier repayment of the outstanding principals of the assets and hence has a negative effect on the value of the objective function over tim
36、e since the gap towards the main outstanding principal increases.For some types of assets such as auto loans or credit card receivables this prepayment is unusual. However, leasing-like assets do face the risk of interest-rate based prepayment. Since prepayment events are non-predictable they cannot
37、 be taken explicitly into account in a deterministic off-line optimization model. Implicitly, it is assumed that all assets have the same probability of prepayment. In all cases where the risk of early paybacks is particularly high, a re-optimization of the whole ABS process at a later point in time
38、 is strongly recommended.Concerning the time line, in our case the assets are handed over by the originator and purchased by the SPV starting at a closing date (initial date for the loan) and on a Fixed basis thereafter during the so called revolving period. Each date at which a purchase takes place
39、 is called settlement date. The assets handed over by the originator at the closing date and thereafter at the settlement dates are collectively referred to as the initial and subsequent portfolios, respectively. Issued notes yield an interest payable on periodic bases (usually quarterly) and are re
40、deemed at different final maturity dates. For this reason, notes are divided into tranches characterized by different deadlines. The reimbursement to the holders of the principals of a tranche of notes corresponds to a reimbursement installment of the main outstanding principal. Hence, the outline o
41、f the outstanding principal of the loan has as many installments (steps)as the number of notes with different maturity issued on the market. The main source of payment of interest and principal on notes are recoveries arising out of the assets. In particular, the cash-flow deriving from assets is us
42、ed by the SPV to satisfy its obligations to the holders of notes. Naturally, the outstanding principal of an asset depends on the rule used for amortization. As mentioned above, two different rules mainly appear in practice, In the first rule, usually known as French amortization, the general period
43、ic installment (sum of periodic interests and principal installment) is constant over time. In this case the customers who hold assets (mortgage or lease contracts) have to pay the same geometrically over time .In this case the customers who hold assets (mortgage or lease contracts) have to pay the
44、same constant amount at each deadline. Since the principal installments increase geometrically over time (see figure 2(b) ), the outstanding principal can be approximated by a concave piece-wise linear function. Source: D. Bertsimas and R. Demir. Securitization of Financial Assets: Approximation in Theory and Practice. Computational Optimization and Applications, 2008(29), P147-171