信用額度之選擇權價值及
其對利差之解釋能力

房貸產品中的理財型房貸，額外給予客戶的信用額度（銀行給予貸款者在特定期間、以高於房貸部分的利率、向銀行借特定金額的權利）可視為銀行給予貸款者的一個選擇權。由於此類貸款具有相同的貸款期間、抵押品價值、以及借款人信用風險，理財型房貸和一般房貸的利率差異（以下簡稱利差）應可充分反映其選擇權價值。因此本文認為，相較於過去的文獻，利用此類貸款資料所估計的選擇權價值將更為「純化」。本研究蒐集國內二家銀行所推出的理財型房貸資料共48筆，首先利用最小平方蒙地卡羅模擬法計算其選擇權理論價值。在模擬短期利率方面，研究模型為均衡模型中的CIR模型。敏感性分析的結果顯示，當利率變動率越大，模擬的選擇權價值會越高。若未來利率呈現上升趨勢，利率調整速度越快，選擇權的價值會越高，然而若未來利率呈現下跌趨勢，利率調整速度越快，選擇權的價值會越低。本文進一步驗證估計的選擇權理論價值對於利差的橫斷面解釋能力。結果顯示，信用額度所提供的選擇權理論價值與利差呈顯著正相關，顯示實務上銀行在訂定理財型房貸利差時的確有反應其選擇權價值。在控制變數方面，同業平均利率水準與利差呈顯著負相關，雖與預期不符，但可從市場供給與需求來獲得解釋。此外，銀行流動比率對於利差則無顯著影響。本研究結果可作為銀行訂定理財型房貸利率之參考，並供貸款者瞭解銀行所制定的利率是否合理。

關鍵字

最小平方蒙地卡羅模擬法；利率期限結構；信用額度

並列摘要

Revolving mortgage (bank commits to the borrower an extra line of credit with a higher borrowing rate in a certain period) can be considered as a “borrowing option” provided by the bank to borrower. Because the original mortgage and the line of credit share the same timing, mortgage, and credit risk, the interest spread between them will precisely reflect the option value. Thus, we believe that, compared with previous studies, the revolving mortgage data provides an excellent sample to estimate the “pure” option value. We first collect 48 observations involving revolving mortgage from two Taiwanese banks, and use least squares Monte Carlo simulation to price the option value. Moreover, we use Cox, Ingersoll, and Ross’s (1985) model to simulate the dynamic behavior of interest rate. The sensitivity analysis shows that the higher the interest rate volatility is, the higher the option value. If the future interest rate is high, the higher the mean-reverting parameter emerges, the higher the option value. If the future interest rate is low, the higher the mean-reverting parameter emerges, the lower the option value. We then examine the relationship between interest spread and the simulated option value. The result shows that interest spread is significantly and positively related to the simulated option value, suggesting that bank managers do take account of option value when pricing revolving mortgage. Inconsistent with our expectation, however, the industry’s average interest rate is negatively correlated with the interest spread, which may be rationalized by the market demand and supply. Finally, liquidity ratio of the bank plays no role in explaining interest spread. The results help bank managers to effectively price the interest spread, and help borrowers to evaluate the rationality of bank’s offers

並列關鍵字

least squares Monte Carlo simulation ； term structure of interest rates ； line of credit

參考文獻

陳家彬，1999，台灣地區銀行基本放款利率之訂價：模型與實證，台大管理論叢，第69~63頁

Black F., and Scholes M., 1973, “The pricing of options and corporate liabilities,” Journal of political economy, 81, 637-654.

Boyle P., 1977, “Options: a montecarlo approach,” Journal of financial economics, 4, 323-338

Brennan M. J., and Schwartz E. S., 1978, “Finite difference methods and jump processes arising in the pricing of contingent claims: a synthesis”, Journal of Financial and Quantitative Analysis, 13, 461-474.

Campbell T. S., 1978, “A model of the market for lines of credit,” Journal of Finance, 33, 231-244.

國際替代計量

信用額度之選擇權價值及其對利差之解釋能力

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