Duration and Convexity Gaps: Definition and Hedging

持續時間與凸性缺口：定義與避險

郭震坤(Cheng-Kun Kuo)

《臺大管理論叢》 6卷2期 (1995/08) Pp. 159-174

https://doi.org/10.6226/NTURM1995.6.2.159

摘要

本文延伸Bierwag and Kaufman (1992)持續期間缺口的討論，考慮在預期較大利率變動下，銀行經營的利率風險。應用Dunetz and Mohoney (1998)債券凸性的定義，定出凸性缺口的型式，以補充Bierwag and Kaufman持續期間缺口的不足。
Bierwag and Kaufman將資産負債表外的期貨交易納入缺口分析中以測度金融機構經營的早率敏感性。方法是用現金賬來反映期貨交易的每日結算，導出持續期間缺口。持續期間是用簡單的Macauley定義。
但持續期間缺口基本能測度微小利率變動（例如5或10基點）對一系列現金流量現值的影響。當預期較大利率變動時，因爲利率與價值的關系非爲直線，有必要考慮曲度的影響，即所謂的凸性。另方面，因到期日、市場利率與息券利率等因素影響凸性，而銀行的缺口分析小及資産與負債，兩值得常有不同的到期日，資産之平均到期日常大於負債，因此，缺口分析若不考慮凸性，其準確性將大受影響。
本文導出銀行淨值與經濟收入的持續期間與凸性缺口，俾能較爲精確地測度銀行利率風險。並提議一種簡單避險模式以供避險操作。

關鍵字

持續期間 ； 缺口 ； 凸性 ； 淨值 ； 經濟收入

並列摘要

In this paper, we extend some of the recently expanded duration gaps by Bierwag and Kaufman (1992) to take into account the price effects of convexity. The expanded duration gaps incorporate futures contracts and swap agreements into the assets/liabilities combinations of depository institutions. Therefore, they are better indicators of the sensitivity of the market value of net worth and economic income to interest rate fluctuations. However, duration measures the percentage change in the market value of a stream of cash flow for a given small change in interest rate. When larger changes are expected, It is necessary to consider convexity to accurately measure the impacts. This is particularly true for depository institutions attempting to create an asset/liability match.
After duration and convexity gaps are well-defined, these gaps can be established as targets. And managers can utilize financial futures contracts to affect the target value. In this regards, this paper also propose a simple hedging approach that allows managers to control the interest rate risk implied by the gaps.

並列關鍵字

Duration ； Gap ； Convexity ； Net Worth ； Economic Income