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| Title: | 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 |
| Authors: | 鄭文杰
Cheng, Wen-Chieh |
| Contributors: | 林士貴
莊明哲
Lin, Shih-Kuei
Chuang, Ming-Che
鄭文杰
Cheng, Wen-Chieh |
| Keywords: | 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
Callable interest rate swaps
Bermudan swaptions
Least Square Monte Carlo
Trinomial tree
Hull and White model |
| Date: | 2019 |
| Issue Date: | 2019-08-07 16:10:24 (UTC+8) |
| Abstract: | 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。
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. |
| Reference: | [1] 林妍如(2018)。零息可贖回債券商品定價:三元樹與最小平方蒙地卡羅方法之比較。碩士論文，國立政治大學，金融學系研究所，台灣台北市。
[2] 黃一峰2018）。在Hull-White Model之下分析交換銀行贖回策略對(零息)含息可贖回債券影響。碩士論文，國立交通大學，財務金融研究所，台灣新竹市。
[3] Andersen, L. (1999). A simple approach to the pricing of Bermudan swaptions in the multifactor LIBOR market model. Journal of Computational Finance, 3(2), 5-32.
[4] Brennan, M. J. and Schwartz, E. S. (1977). Convertible bonds: valuation and optimal strategies for call and conversion. The Journal of Finance, 32(5), 1699-1715.
[5] Feng, Q., Jain, S., Karlsson, P., Kandhai, D., and Oosterlee, C. (2016). Efficient computation of exposure profiles on real-world and risk-neutral scenarios for Bermudan swaptions. Journal of Computational Finance, 20(1), 139–172.
[6] Hull, J. and White, A. (1990). Pricing Interest-Rate Derivatives Securities. Review of Financial Studies, 3, 573-592.
[7] Hull, J. and White, A. (1994). Numerical Procedures for Implementing Term Structure Models I：Single-Factor Models. Journal of Derivatives, 2, 7-15.
[8] Hull, J. (2003). Option, futures and other derivatives, New Jersey: Pearson Education.
[9] Hippler, S. (2008). Pricing Bermudan Swaptions in the LIBOR Market Model, master dissertation, University of Oxford.
[10] Jain, S. and Oosterlee, C. (2015). The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks. Applied Mathematics and Computation 269, 412–431
[11] Longstaff, F.A. and Schwartz, E.S. (2001). Valuing American Options by Simulation: A Simple Least-Squares Approach. Review of Financial Studies, 14, 113-147.
[12] Rappe, M. and Friberg, K. (2010). Pricing cancellable swaps using tree models calibrated to swaptions, master dissertation, Linköping Institute of Technology |
| Description: | 碩士
國立政治大學
金融學系
106352016 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0106352016 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU201900195 |
| Appears in Collections: | [金融學系] 學位論文
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