On the regularity of the free boundary in the parabolic obstacle problem. Application to American options

被引:19
作者
Blanchet, Adrien [1 ]
机构
[1] Univ Paris 09, CEREMADE, F-75775 Paris 16, France
关键词
parabolic obstacle problem; American option; free boundary; exercise region; exercise boundary;
D O I
10.1016/j.na.2005.10.009
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper is devoted to local regularity results on the free boundary of the one-dimensional parabolic obstacle problem with variable coefficients. We give an energy criterion and a density criterion for characterising the subsets of the free boundary which are Holder continuous in time with exponent 1/2. Our results apply in the theory of American options. As an illustration, we apply these results to the generalised Black-Scholes model of a complete market which rules out arbitrage if the volatility and the interest rate do not depend on time. In this case we prove that the exercise boundary of the American put and call options are Holder continuous with exponent 1/2 in time for every time. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1362 / 1378
页数:17
相关论文
共 23 条
[1]   An inverse problem for a parabolic variational inequality arising in volatility calibration with American options [J].
Achdou, Y .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2005, 43 (05) :1583-1615
[2]  
[Anonymous], METHODES MATH INFORM
[3]  
BARLES G, 1993, CR ACAD SCI I-MATH, V316, P171
[4]  
BENSOUSSAN A, 1984, ACTA APPL MATH, V2, P139
[5]  
Berestycki H., 2002, Quantitative Finance, V2, P61, DOI 10.1088/1469-7688/2/1/305
[6]  
BJORK T, 1997, LECT NOTES MATH, V1656, P53
[7]  
BLANCHET A, 2005, 4421 HAL
[8]   Regularity of a free boundary in parabolic potential theory [J].
Caffarelli, L ;
Petrosyan, A ;
Shahgholian, H .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 17 (04) :827-869
[9]   REGULARITY OF FREE BOUNDARIES IN HIGHER DIMENSIONS [J].
CAFFARELLI, LA .
ACTA MATHEMATICA, 1977, 139 (3-4) :155-184
[10]   Critical price near maturity for an American option on a dividend-paying stock in a local volatility model [J].
Chevalier, E .
MATHEMATICAL FINANCE, 2005, 15 (03) :439-463