以往文獻主要是保證公司為一般公司提供貸款保證之模型, 本研究提出被保證公司為銀行的貸款保證模型。根據Chen et al. (2006) ,銀行主要資產投資組合為多個貸放款,分別貸放給多個彼此相關的借款公司, 因此銀行資產損益呈現截尾結構, 且銀行資產波動性主要來自於借款公司資產的波動性, 且銀行主要債務為存款額。本研究假設存
在多個貸款保證公司聯合保證多家銀行的主要債務之履行, 當銀行資產小於負債以致其淨值為負時, 貸款保證公司在給予銀行貸款保證時有界限限制, 並無法提供完全賠償, 而且基於貸款保證公司的立場, 貸款保證公司須隨時瞭解銀行資產的價值變化。因此本研究將貸款保證公司的界限限制賠償政策, 和隨時檢測銀行資產狀況需求納入銀
行貸款保證模型, 運用美式界限選擇權做為銀行貸款保證的定價模式, 探討各銀行需承擔的銀行貸款保證的價值, 並與傳統歐式與美式選擇權定價模式比較, 並且利用最小平方蒙地卡羅模擬法探討借款公司、銀行與貸款保證公司資本結構之關鍵變數對各銀行需承擔的銀行貸款保證價值與違約機率的影響, 和對貸款保證公司違約機率的影
響。

Our study focuses on a general framework for valuing the loan guarantee of banks.Based on Chen et al. (2006), the bank’s asset portfolio consists of several loans and the banks lend several correlated corporate firms the loans. So that the bank’s asset value is the truncated structure. The corporate firm’s asset volatility is the primitive risk in the bank’s asset portfolio. Our model is analyzed under a multiplecorporate firm , multiple-bank , and multiple-guarantor framework. The guarantors has the duty to guarantee the banks’ debt value. After considering the barrierm compensated policy and immediate examining system, we estimate the value of loan guarantee using the American barrier option approach. We compare the value of loan guarantee using American barrier option approach to that using Europe option and American option approach. We carry out simulations to investigate how the important parameters of corporate firms, banks, and guarantors affect the values
and default probability of loan guarantee.

1 Introduction 1
2 Model 4
2.1 The corporate firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 The banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 The guarantors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Numerical Methods 9
4 Numerical Results 11
4.1 Results under three type of option-pricing framework . . . . . . . . . 13
4.2 Results for the changes in critical parameters . . . . . . . . . . . . . . 14
5 Conclusion 19
Appendix 19
A Spectrum Decomposition 20
B Least Square Monte Carlo Simulations 20
Reference 22

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