本金增長型可贖回利率交換評價: Hull-White下最小平方蒙地卡羅法與三元樹比較

Valuation of Callable Accreting Interest Rate Swaps: Comparison between the Least-Squares Monte-Carlo Method and Trinomial Tree under Hull-White Interest Rate Model

鄭文杰(Cheng Wen-Chieh)

指導教授 ： 林士貴 ； 莊明哲

國立政治大學/商學院/金融學系/碩士(2019年)

https://doi.org/10.6814/NCCU201900195

摘要

本文利用Hull and White 利率模型架構下試圖回答以下兩項問題。第一，本金增長型可贖回利率交換之評價如何進行? 第二，近年來公司經常使用零息可贖回債券作為熱門債券籌資工具之一，並且以本金增長型可贖回利率交換作為對應之風險管理工具，此種風險管理方式是否合適?
首先，本金增長型可贖回利率交換可以拆解為本金增長型支付者利率交換加上百慕達式本金增長型收取者利率交換選擇權。拆解後的商品，前者可由推導之封閉解求得評價價值，而後者具有提前履約的特性因此無封閉解。為解決提前履約商品無封閉解之評價，本文採用Longstaff and Schwartz (2001) 提出之最小平方蒙地卡羅法與 Hull and White (1994) 提出之三元樹兩種數值方法。最後，由於本金增長型可贖回利率交換之條款設計與零息可贖回債券配合，將造成兩者最佳贖回策略相同但因期初風險管理金額在考慮時間價值下相異，因此前項商品雖可對後者之發行商給予風險管理建議，但前者並非最適風險管理商品。

關鍵字

可贖回利率交換 ； 百慕達交換選擇權 ； 最小平方蒙地卡羅法 ； 三元樹 ； Hull and White 短利模型

並列摘要

This paper discusses two problems based on Hull-White term structure model as follow: (i) How to conduct a valuation of callable accreting interest rate swap(CAIRS) ? (ii) CAIRS is a type of widely used risk management instruments for zero callable bonds (ZCB) . Is it suitable enough to hedge risks of zero callable bond? First, CAIRS can be decomposed into accreting payer interest rate swaps and Bermudan swaptions. Considering financial valuation of both components, the former can be directly valued by the pricing formula, while the latter has no close form due to its early exercise characteristics. In order to solve the problem, the approaches here include LSM method in Longstaff and Schwartz (2001) and trinomial tree in Hull and White (1994) . We find out that the two options embedded in ZCB and CAIRS have same exercise strategy since the terms of the swaps will consist with the bonds in practice. However, the cash flow of risk management in swaps and bonds can be different when considering the discount of time value. Hence, CAIRS are not the best financial instrument for managing risks of zero callable bonds under current design.

並列關鍵字

Callable interest rate swaps ； Bermudan swaptions ； Least Square Monte Carlo ； Trinomial tree ； Hull and White model

參考文獻

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