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| Title: | 單曲線LMM模型與OIS折現下多曲線LMM模型之價格與未來潛在曝險比較—以可贖回CMS利率交換為例
Comparison of Price and Potential Future Exposure of Callable CMS Swap Under Single Curve LMM Model and OIS Discount Multi-Curve LMM Model |
| Authors: | 黃詩淳
Huang, Shih-Chun |
| Contributors: | 廖四郎
Liao, Szu-Lang
黃詩淳
Huang, Shih-Chun |
| Keywords: | OIS折現
多曲線
LMM模型
未來潛在曝險
OIS Discount
Multi-Curve
LMM
Potential Future Exposure |
| Date: | 2019 |
| Issue Date: | 2019-08-07 16:10:49 (UTC+8) |
| Abstract: | 隨著現今LIBOR不再被視為無風險利率，因而在財務工程的定價領域裡的折現率，將不再是過去所慣用的LIBOR利率，取而代之，目前在金融商品定價中， OIS折現率是公認最受歡迎作為折現之無風險利率。由於折現率的改變將會對傳統的利率模型造成影響，因此本論文著重在比較在單曲線LMM模型、多曲線LMM模型（固定利差）、以及多曲線LMM模型（非固定利差）下，評價以CMS為標的之可贖回利率交換之價格差異。同時，亦分別透過三種模型，計算以CMS為標的之可贖回利率交換之未來潛在曝險，且利用過去歷史資料進行回測，以檢視此三種模型預估未來潛在曝險之能力。
Before the financial crisis in 2008, people have used to take LIBOR and LIBOR swap rates as proxies for risk-free rate when pricing derivatives. However, after the financial crisis burst out, many banks now consider the overnight indexed swap (OIS) should be the more appropriate risk-free rate when valuing derivatives. Substituting discount curve will not only have impact when pricing derivatives under specified interest rate model, it will meanwhile affect the potential future exposure result from counterparty.
Hence, this paper demonstrated how should we construct LMM model under multi-curves. We then compared the pricing results of callable CMS swap under single curve LMM model, multi-curve LMM model (deterministic LIBOR-OIS spread), and multi-curve LMM model (non-deterministic LIBOR-OIS spread). Besides, according to the construction of these three models, we calculated the potential future exposure within the life cycle of callable CMS swap, then had back-testing under these three models.
The result shows that no signification difference of price between single curve LMM model and multi-curve LMM model, however, the non-deterministic LIBOR-OIS spread LMM model tends to significantly reduce potential future exposure of contract. This may increase the efficiency of capital application when pricing under non-deterministic LIBOR-OIS spread LMM model. |
| Reference: | 1. Christian Crispoldi, Gerald Wigger, Peter Larkin, (2015). SABR and SABR LIBOR market models in practice, Palgrave.
2.Da miano Brigo, Fabio Mercurio, (2006). Interest rate models-theory and practice, Springer.
3. Damiano Brigo, Massimo Morini, Andrea Pallavicini, (2013). Counterparty credit risk, collateral and funding with pricing cases for all asset classes, Wiley.
4. Fabio Mercurio, (2010). Modern LIBOR Market Models: Using Different Curves for
Projecting Rates and for Discounting, International Journal of Theoretical and Applied Finance Vol. 13, No. 1, 113-137.
5. Fabio Mercurio, (2010). LIBOR Market Models with Stochastic Basis, Bloomberg Education & Quantitative Research Paper, No. 2010-05-frontiers.
6. Fabio Mercurio, (2018). SOFR So Far: Modeling the LIBOR Replacement, Swissquote Conference.
7. Francis A. Longstaff, Eduardo S. Schwartz, (2001). Valuing American Option by Simulation: A Simple Least-Squares Approach, The Review of Financial Studies Spring 2001 Vol. 14, No. 1, 113-147.
8. Marc Henrard, (2014). Interest rate modelling in the multi-curve framework, Palgrave.
9. Steven E. Shreve, (2004). Stochastic calculus for finance II continuous-time models, Springer. |
| Description: | 碩士
國立政治大學
金融學系
106352018 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0106352018 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU201900176 |
| Appears in Collections: | [金融學系] 學位論文
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