Complete models with stochastic volatility

被引:151
作者
Hobson, DG [1 ]
Rogers, LCG [1 ]
机构
[1] Univ Bath, Dept Math Sci, Sch Math Sci, Bath BA2 7AY, Avon, England
关键词
option pricing; stochastic volatility; complete markets; smiles;
D O I
10.1111/1467-9965.00043
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
The paper proposes an original class of models for the continuous-time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log-price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many Other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference-independent options prices. We find a partial differential equation for the price of a European call option. Smiles and skews are found in the resulting plots of implied volatility.
引用
收藏
页码:27 / 48
页数:22
相关论文
共 42 条
[1]  
[Anonymous], 1991, ANN APPL PROBAB, DOI DOI 10.1214/AOAP/1177005873
[2]   THE CONSTANT ELASTICITY OF VARIANCE MODEL AND ITS IMPLICATIONS FOR OPTION PRICING [J].
BECKERS, S .
JOURNAL OF FINANCE, 1980, 35 (03) :661-673
[3]  
Bensoussan A, 1994, PHILOS T ROY SOC A, V347, P449
[4]   PRICING OF OPTIONS AND CORPORATE LIABILITIES [J].
BLACK, F ;
SCHOLES, M .
JOURNAL OF POLITICAL ECONOMY, 1973, 81 (03) :637-654
[5]   COMPARISON OF STABLE AND STUDENT DISTRIBUTIONS AS STATISTICAL MODELS FOR STOCK PRICES [J].
BLATTBERG, RC ;
GONEDES, NJ .
JOURNAL OF BUSINESS, 1974, 47 (02) :244-280
[6]   GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY [J].
BOLLERSLEV, T .
JOURNAL OF ECONOMETRICS, 1986, 31 (03) :307-327
[7]   PRICING EUROPEAN CURRENCY OPTIONS - A COMPARISON OF THE MODIFIED BLACK-SCHOLES MODEL AND A RANDOM VARIANCE MODEL [J].
CHESNEY, M ;
SCOTT, L .
JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS, 1989, 24 (03) :267-284
[8]   VALUATION OF OPTIONS FOR ALTERNATIVE STOCHASTIC-PROCESSES [J].
COX, JC ;
ROSS, SA .
JOURNAL OF FINANCIAL ECONOMICS, 1976, 3 (1-2) :145-166
[9]   AN INTERTEMPORAL GENERAL EQUILIBRIUM-MODEL OF ASSET PRICES [J].
COX, JC ;
INGERSOLL, JE ;
ROSS, SA .
ECONOMETRICA, 1985, 53 (02) :363-384
[10]   TEMPORAL AGGREGATION OF GARCH PROCESSES [J].
DROST, FC ;
NIJMAN, TE .
ECONOMETRICA, 1993, 61 (04) :909-927