路徑獨立與相依的利率區間債券之評價與避險

The Valuation and Hedging of the Path-dependent and Path-independent Range Notes

林佳欽(Chia-Chin Lin)

指導教授 ： 李賢源

國立臺灣大學/管理學院/財務金融學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.10230

摘要

本文研究多因子Gaussian HJM利率模型架構下，利率區間債券(包含金字塔行債券及路徑相依債券)的評價原理與避險方法探討。本文推廣João Pedro Vidal Nunes (2003)多因子Gaussian HJM，在此一利率模型架構下，利用改變機率測度的方式，及運用零息債券價格之隨機過程推導遞延區間數位選擇權、遞延區間資產買權和界限數位選擇權，進而求出債券價格。再者，探討利率區間債券、金字塔行債券及路徑相依區間債券的應用與風險分析。金字塔型債券的債券利息收益並無固定型態，因此在定價與避險方面較為困難。但是，此一型式的債券一律可拆解成零息債券及一系列的遞延區間數位選擇權與遞延區間資產買權，然後針對此兩種選擇權進行定價與避險即可。至於評價路徑相依區間債券時，需要考慮其路徑關係，最後只能求得近似封閉解。而隱含於債券中的界限選擇權，亦可將其指標價格定義為公債到期報酬殖利率（即YTM），並且應用於債券市場，以利投資者進行避險，或是獲取更高的報酬。

關鍵字

利率區間債券 ； 路徑相依區間債券 ； 金字塔型債券

並列摘要

The main purposes of this paper are to value and to hedge the Path-dependent and Path-independent range notes. The first is to derive exact analytical valuation formulas for target redemption notes and range notes with double barrier of knock-out digital options in the context of a multi-factor Gaussian Heath, Jarrow, and Morton (1992) term structure model. The last is to find the best tools which exists in the derivatives markets and then we can use it to hedge or unwind the products (for example: target redemption notes and range notes with double barrier of knock-out digital options).
A target redemption note pays a floating, inverse floating, or fixed coupon rate at the end of each coupon period, based on the value of some reference interest rate (e.g. 6-month US Libor) in the beginning of each coupon period. However, a range note with double barrier of knock-out digital options, which belongs to a Path-dependent range note, pays a fixed coupon rate at the end of each compounding period, based on the value of the reference interest rate in the compounding period. And unlike a standard range note, the coupon also depends on the number of days that the reference interest rate all lies inside a corridor during each compounding period.
Next sections are organized as follows. Section 2 describes the most relevant probabilistic features of the multi-factor Gaussian HJM model that will be used hereafter. Section 3 introduces the Path-dependent and Path-independent range notes. Section 4 provides closed-form solutions for the exotic options that will be used to price non-standard range notes. Section 5 prices non-standard range notes and generalizes, under a multi-factor formulation. Then, section 6 discusses how to hedge these kinds of products. Finally, section 7 concludes.

並列關鍵字

Target Redemption Note ； Range Note

參考文獻

1.Turnbull, S. (1995): Interest Rate Digital Options and Range Notes, Journal of Derivatives, Fall, 92—101.

2.CHO H. HUI (1996)： One-touch double barrier binary option Values,

Applied Financial Economics, 343Ð 346

3.Navatte, P., and F. Quittard-Pinon (1999): The Valuation of Interest Rate Digital Options and Range Notes Revisited, European Financial Management 5, 425—440.

4.João Pedro Vidal Nunes (2003): Multi-factor Valuation of Floating Range Notes, Forthcoming Mathematical Finance.