利率變動下美元計價可贖回債券之實證分析

Abstract

國際債券市場中，以美元計價的可贖回債券占最多數，美國於2020年時連續降息，造成159檔國際債券遭提前贖回，顯現出壽險公司面臨的可贖回風險。因此本文參照宣葳與張士傑(2019)的方法，使用美國政府公債的利率資料以建立利率期限結構，並使用歐式利率交換選擇權來估計Hull-White短期利率模型的參數，最後以三元樹法來評價國際債券，衡量國際債券隱含可贖回權的價值。本研究將分別探討可贖回債券的隱含年利率、可贖回頻率、不可贖回期間對可贖回債券期初價值與可贖回權價值的影響。\n研究結果顯示，(1) 給定三十年期可贖回債券可贖回頻率為5年，不可贖回期間為7年，當隱含年利率從3.5%上升至5.5%時，該債券期初價值由30下降至22.1隱含選擇權價值由9.8上升至17.2。 (2) 給定三十年期可贖回債券不可贖回期間為10年，隱含年利率為4.5%當可贖回頻率由5年增加至1年時，該債券期初價值由27.5下降至27隱含選擇權價值由12上升至12.8。 (3) 給定三十年期可贖回債券可贖回頻率為5年，隱含年利率為 5.5%，當不可贖回期間由1年增加至10年時，該債券期初價值由20增加至24隱含選擇權價值由19.5降低至15.9。

In 2020, the United States has successively cut interest rates, resulting in the redemption of 159 international bonds, showing the call risk faced by the life insurance industry. In this study, based on the Hull-White short rate model, we detail how we use the US Treasury Constant Maturity Rate to construct the interest rate term structure, together with the implied volatility on the European swaption to calibrate the parameters of the Hull-White short rate model. Then we use the trinomial tree method to compute the fair value of the dollar-denominated callable bonds, and compute the value of implied option.\nWe find that: (1) given a 30-year callable bond which has a call frequency of 5 years and a non-call period of 7 years, when the implied annual interest rate rose from 3.5% to 5.5%, the initial value of the bond decreased from 30 to 22.1, and the value of implied option increased from 9.8 to 17.2; (2) given a 30-year callable bond with a non-call period of 10 years and an implied annual interest rate of 4.5%, when the call frequency increased from 5 years to 1 year, the initial value of the bond decreased from 27.5 to 27, and the value of implied option increased from 12 to 12.8; (3) given a 30-year callable bond with a calla frequency of 5 years and an implied annual interest rate of 5.5%, when the non-call period increased from 1 year to 10 years, the initial value of the bond increased from 20 to 24, and the value of implied option decreased from 19.5 to 15.9.