本文在连续远期利率期限结构Brace, Gatarek and Musiela（BGM）模型框架下研究了一类新的利率期权,即具有可变执行利率的利率上限、利率下限和利率双限的定价问题,并分别给出它们价格的解析解，进一步拓宽了Black-Scholes期权定价公式的应用.
Abstract
In this paper, under the framework of Brace, Gatarek and Musiela（BGM） model for term structure of continuous forward interest rate, the pricing problem of a new kind of interest rate options, namely caps, floors and collars with changeable exercise interest rates are discussed, and analytic solutions of their pricing are given. The results extend the application of Black-Scholes pricing formulas.
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Cox J C, Ingersoll J E. and Ross, S A. A Theory of the Term Structure of Interest Rates[J]. Econometrica,1985,53(2):385-407.
[2] Heath D, Jarrow R and Morton A. Bond Pricing and the Term Structure of Interest Rates: A New Methodology[J]. Econometrica ,1992,60: 77-105.
[3] 周荣喜,邱菀华. BDT模型的扩展及应用研究[J].数量经济技术经济研究, 2005,(2):87-94.
[4] Miltersen K, Sandmann K and Sondermann D. Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates[J].The Journal of Finance,1997,52: 409-430.
[5] Brace A, Gatarek D and Musiela M. The Market model of Interest Rate Dynamics[J]. Mathematical Finance, 1997,7(2):127-155.
[6] Tang Y and Lange J. A Non-exploding Bushy Tree Technique and Its Application to the Multifactor Interest Rate Market Model[J]. The Journal of Computational Finance, 2001,(4):5-31.
[7] Christiansen C and Charlotte S H. Implied Volatility of Interest Rate Options: An Empirical Investigation of the Market Model[J]. Review of Derivative Research 2002,(5):51-80.
[8] Glasserman, P and Nicholas M. Cap and Swaption Approximations in LIBOR Market Models with Jumps[J]. The Journal of Computational Finance,2003, (7):1-36.
[9] Shively, P A. Time-Varying Risk Components In the Single-Factor Market Model: An Exact Most Powerful Invariant Test[J]. Applied Financial Economics, 2004, 14(13):945-952.
[10] Shin J M, Mikkel S. Efficient Control Variates and Strategies for Bermudan Swaptions in a LIBOR Market Model[J]. Journal of Derivatives, 2005,12(4):20-33.
[11] 王新哲,周荣喜,邱菀华.具有可变执行利率的利率上限定价研究[J].哈尔滨工业大学学报, 2006,(1):116-118.
[12] 邵宇编著. 微观金融学及其数学基础[M]. 北京: 清华大学出版社, 2003,11:240-243.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(691 KB)
