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| Title: | 可贖回CMS價差區間計息型商品之評價分析：基於LFM與最小平方蒙地卡羅法之模擬加速實證
Pricing of Callable Range Accrual Linked to CMS Spread: Empirical Analysis with Multiprocessing Based on Lognormal Forward LIBOR Model and Least-Squares Monte Carlo Simulation |
| Authors: | 王韋之
Wang, Wei-Chih |
| Contributors: | 林士貴
岳夢蘭
Lin, Shih-Kuei
Yueh, Meng-Lan
王韋之
Wang, Wei-Chih |
| Keywords: | 利率衍生性商品
對數常態遠期利率市場模型
固定期限交換利率
最小平方蒙地卡羅法
平行運算
Interest Rate Derivative
Lognormal Forward LIBOR Model
Constant Maturity Swap
Least-Squares Monte Carlo Simulation
Multiprocessing |
| Date: | 2020 |
| Issue Date: | 2020-07-01 13:41:12 (UTC+8) |
| Abstract: | 本研究使用對數常態遠期利率市場模型與最小平方蒙地卡羅法，對沒有封閉解之可贖回固定期限交換利率價差區間計息商品進行評價。透過市場資料建構殖利率曲線與遠期利率曲線，而後基於對數常態遠期利率市場模型之動態過程，將其離散化後進行遠期利率模擬並計算遠期交換利率，最後使用最小平方蒙地卡羅法求解商品價值。本研究利用市場資料估計校準參數，基於兩種波動度結構與兩種實務上常用之相關係數假設進行模擬。此外，在結合Python平行運算的基礎上，整體的評價計算與模擬速度得到較大提升。
In this paper, we apply Lognormal Forward LIBOR Model (LFM) and Least-Squares Monte Carlo simulation (LSMC) to price the Constant Maturity Swap (CMS) Spread Range Accruals, which have no closed form solution. We build the yield curve and forward rate curve with market data. Based on the dynamic process under LFM, we discretize the formula to calculate forward rate and forward swap rate. And the derivatives are evaluated by using Least-Squares Monte Carlo method. The parameters are estimated with two types of volatility assumptions and two types of correlation assumptions based on the practical experience. Besides, combined with multiprocessing, the speed of valuation and simulation has been greatly increased. |
| Reference: | 中文部分
陳松男 (2006)。利率金融工程學-理論模型及實務應用。台北：新陸書局。
陳威光 (2010)。衍生性商品：選擇權、期貨、交換與風險管理。台北：智勝文化
馮冠群 (2018)。可贖回CMS區間計息型商品之評價與實證分析：LIBOR與GARCH市場模型之比較。國立政治大學統計研究所碩士論文，未出版。
英文部分
Andersen, L. B. (1999). A simple approach to the pricing of Bermudan swaptions in the multi-factor Libor market model.
Andersen, L. B., & Brotherton-Ratcliffe, R. (2001). Extended LIBOR market models with stochastic volatility.
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Brigo, D., Capitani, C., & Mercurio, F. (2001). On the joint calibration of the Libor market model to caps and swaptions market volatilities.
Brigo, D., & Liinev, J. (2002). On the distributional distance between the Libor and the Swap market models. Preprint.
Brigo, D., & Mercurio, F. (2007). Interest rate models-theory and practice: with smile, inflation and credit. Springer Science & Business Media.
Gatarek, D. (2003). Calibration of the LIBOR market model: three prescriptions.
Goschen, W. S. (2005). Incompatibility of lognormal forward-Libor and Swap market models. University of Cape Town,
Hull, J., & White, A. (1988). The use of the control variate technique in option pricing. Journal of Financial and Quantitative analysis, 23(3), 237-251.
Hull, J. C., & White, A. D. (2000). Forward rate volatilities, swap rate volatilities, and implementation of the LIBOR market model. The Journal of Fixed Income, 10(2), 46-62.
Jamshidian, F. (1997). LIBOR and swap market models and measures. Finance and Stochastics, 1(4), 293-330.
Joshi, M. S., & Kwon, O. K. (2010). Monte Carlo market Greeks in the displaced diffusion LIBOR market model.
13. Longstaff, F.A., & Schwartz, E.S. (2001). Valuing American options by simulation: a simple least-squares approach. The review of financial studies, 14(1), 113-147.
Mercurio, F. (2010). LIBOR market models with stochastic basis. Bloomberg education and quantitative research paper(2010-05).
Moreno, M., & Navas, J. F. (2003). On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Review of Derivatives Research, 6(2), 107-128.
Pietersz, R. (2003). The LIBOR market model. Universität Leiden.
Piterbarg, V. (2003). Computing deltas of callable LIBOR exotics in forward LIBOR models.
Piterbarg, V. V. (2003). A practitioner’s guide to pricing and hedging callable LIBOR exotics in forward LIBOR models. Preprint. |
| Description: | 碩士
國立政治大學
金融學系
107352012 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0107352012 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202000618 |
| Appears in Collections: | [金融學系] 學位論文
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