考慮顧客提前還款行為之銀行最佳兩階段利率合約設計

Optimal Two-stage Interest Rate Contract Design for a Bank Facing Customer Prepayment Behavior

徐嘉琪(Chia-Chi Hsu)

指導教授 ： 孔令傑

國立臺灣大學/管理學院/資訊管理學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202002701

摘要

貸款一直都是銀行主要的收入來源之一，在人們來到銀行申請貸款的當下，一定是他們需要一筆龐大且自己無法負擔的金額，然而當顧客投資成功後，每期額外的利息費用容易使他們萌生提早還款的念頭，若利息費用又相對他行來的高，不想負擔的顧客亦會轉而到其他銀行申請代償方案;在銀行方面，為了吸引顧客，各家銀行時不時地推出第一期優惠利率的貸款方案，若顧客在銀行提供兩段式利率時提早還款，銀行將不僅因為優惠利率少收了前期的利息，又因顧客提早還款失去後期的利息，對銀行的利潤造成雙重打擊，所以銀行常常使用提前還款違約金來限制顧客，同時銀行也會失去一部份想要保有資金彈性和自由的顧客，但也有些銀行為了吸引顧客而提供有第一期優惠利率但免綁約的方案。有鑑於此，本研究在不限制顧客提前還款的前提下，探討銀行兩階段合約的可行性與合約設計策略。
在本篇論文中，我們討論一家銀行貸款給一個顧客且顧客可以自由提前還款的情境， 並建構考慮顧客提前還款能力的篩選模型，在完全資訊和不完全資訊的情況下探討銀行應 如何訂定利率，進而分析在各種情況下的獲利情形，我們發現在顧客提前還款能力未知的 時候，若市場上的顧客普遍提前還款能力高，銀行應該提供引導顧客正常還款的單一合 約;若普遍都低，應該提供引導顧客提前還款的單一合約;在市場上混雜不同能力但整體 提前還款傾向不高的顧客時，銀行應該提供複數個合約供顧客選擇，因為在這種情形裡偏 好提前還款的顧客通常最後沒有能力提前還款，透過賺取高估自己能力顧客的第二期利 息，銀行可以獲得比提供單一合約更大的收益。

關鍵字

提前還款 ； 兩段式利率 ； 銀行訂價策略 ； 顧客篩選

並列摘要

Issuing loans to customers is one of the main revenue streams for banks. When people apply for loans, they are in need of great amount of money they are unable to afford. However, if their investments are successful, they will want to prepay to get rid of paying the extra interest fee. Moreover, if the interest rate is relatively high compared to other banks, they might apply a loan at another bank in order to prepay. As for the banks, they promote two-period contracts with a lower first-period rate to attract customers from time to time. If a customer who applied this kind of loan from a bank ends up prepaying, the bank will not only lose part of the interest of the first period, but also all the interest after he prepays. This will cause a great damage to the bank’ s profit. As a result, banks often limit customers’ prepaying behavior by prepayment penalties, which at the same time make them lose some customers who want to keep their flexibilities. Nevertheless, to make the contract more attractive, some banks still provide discounted two-period contracts without prepayment penalties. Given this, we decide to study the two-period contract design problem where customers are allowed to prepay without any penalties and its feasibility.
In this thesis, we assume a situation that a customer applies a loan from a bank and build models to screen customer’s prepaying ability. Under complete information and information asymmetry, we derive optimal rates and analyze the expected profits for the bank. We find some useful insights when the customer’s ability to prepay is unknown. The bank should offer a single contract inducing the customer to repay regularly if most of the customers in the market are able to prepay. While the customers are prone to have low prepaying ability, a single contract that induces prepaying is more recommended. Interestingly, when customers in the market have different prepaying abilities and on the whole not too high, the bank should offer a menu of contracts. In this case, the customer with medium prepaying ability but still prefers to prepay would choose the contract that induces him to prepay. Thus, the bank will gain more profit because he overestimates his ability to prepay and is not able to prepay in the end.

並列關鍵字

Prepayment ； Two-period interest contract ； Bank loan pricing ； Screening

參考文獻

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