金融资产证券化外文文献(2)

[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 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 resulting 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 all 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 introduction 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 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 assets 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 which 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 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 institutional 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 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 sum 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 gap 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 outstanding 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 sum 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 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 rate. 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 outstanding 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 time since the gap towards the main outstanding principal increases.

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