The market model of interest rate dynamics

被引：335
作者：
Brace, A
Gatarek, D
Musiela, M
机构：
[1] UNIV NEW S WALES,SCH MATH,DEPT STAT,SYDNEY,NSW 2052,AUSTRALIA
[2] CITIBANK NA,TREASURY,SYDNEY,NSW,AUSTRALIA
来源：
MATHEMATICAL FINANCE | 1997年 / 7卷 / 02期
关键词：
term structure models; HJM framework; lognormality of rates; stochastic partial differential equations; caps; swaptions;
D O I：
10.1111/1467-9965.00028
中图分类号：
F8 [财政、金融];
学科分类号：
0202 ;
摘要：
A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.
引用
收藏
页码：127 / 155
页数：29
相关论文
共 13 条
[1]  
[Anonymous], 1993, JOURNEES INT FINANCE
[2]  
BRACE A, 1994, MATH FINANC, V2, P259
[3]  
BRACE A, 1994, SWAP DERIVATIVES GAU
[4]  
CINLAR E, 1981, SEMINAR STOCHASTIC P, P159
[5]  
Da Prato G, 1992, STOCHASTIC EQUATIONS
[6]  
GOLDYS B, 1994, LOGNORMALITY RATES T
[7]   BOND PRICING AND THE TERM STRUCTURE OF INTEREST-RATES - A NEW METHODOLOGY FOR CONTINGENT CLAIMS VALUATION [J].
HEATH, D ;
JARROW, R ;
MORTON, A .
ECONOMETRICA, 1992, 60 (01) :77-105
[8]  
MILTERSEN K, 1994, CLOSED FORM TERM STR
[9]  
MILTERSEN K, 1995, CLOSED FORM SOLUTION
[10]   GENERAL FRAMEWORK FOR PRICING DERIVATIVE SECURITIES [J].
MUSIELA, M .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1995, 55 (02) :227-251
12