Long-memory volatility in derivative hedging

被引:2
作者
Tan, Abby [1 ]
机构
[1] Univ Manchester, Sch Math, Manchester M60 1QD, Lancs, England
关键词
long memory; stochastic volatility; derivative hedging;
D O I
10.1016/j.physa.2006.02.041
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The aim of this work is to take into account the effects of long memory in volatility on derivative hedging. This idea is an extension of the work by Fedotov and Tan [Stochastic long memory process in option pricing, Int. J. Theor. Appl. Finance 8 (2005) 381-392] where they incorporate long-memory stochastic volatility in option pricing and derive pricing bands for option values. The starting point is the stochastic Black-Scholes hedging strategy which involves volatility with a long-range dependence. The stochastic hedging strategy is the sum of its deterministic term that is classical Black-Scholes hedging strategy with a constant volatility and a random deviation term which describes the risk arising from the random volatility. Using the fact that stock price and volatility fluctuate on different time scales, we derive an asymptotic equation for this deviation in terms of the Green's function and the fractional Brownian motion. The solution to this equation allows us to find hedging confidence intervals. (c) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码:689 / 696
页数:8
相关论文
共 31 条
[11]   Long memory continuous time models [J].
Comte, F ;
Renault, E .
JOURNAL OF ECONOMETRICS, 1996, 73 (01) :101-149
[12]  
COMTE F, 2001, AFFINE FRACTIONAL ST
[13]  
Courant R., 1989, METHODS MATH PHYS, VII
[14]   A GEOGRAPHICAL MODEL FOR THE DAILY AND WEEKLY SEASONAL VOLATILITY IN THE FOREIGN-EXCHANGE MARKET [J].
DACOROGNA, MM ;
MULLER, UA ;
NAGLER, RJ ;
OLSEN, RB ;
PICTET, OV .
JOURNAL OF INTERNATIONAL MONEY AND FINANCE, 1993, 12 (04) :413-438
[15]  
Ding Z., 1993, J EMPIR FINANC, V1, P83, DOI [DOI 10.1016/0927-5398(93)90006-D, 10.1016/0927-5398(93)90006-D]
[16]   Hedging options in market models modulated by the fractional Brownian motion [J].
Djehiche, B ;
Eddahbi, M .
STOCHASTIC ANALYSIS AND APPLICATIONS, 2001, 19 (05) :753-770
[17]   Stochastic calculus for fractional Brownian motion - I. Theory [J].
Duncan, TE ;
Hu, YZ ;
Pasik-Duncan, B .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (02) :582-612
[18]   LONG MEMORY STOCHASTIC VOLATILITY IN OPTION PRICING [J].
Fedotov, Sergei ;
Tan, Abby .
INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, 2005, 8 (03) :381-392
[19]   Rescaled variance and related tests for long memory in volatility and levels [J].
Giraitis, L ;
Kokoszka, P ;
Leipus, R ;
Teyssière, G .
JOURNAL OF ECONOMETRICS, 2003, 112 (02) :265-294