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R. Engle, C. Mustafa (1992)
Implied ARCH models from options pricesJournal of Econometrics, 52
J. Kallsen, M. Taqqu (1995)
Option Pricing in ARCH-type Models: with Detailed Proofs, 8
R. Merton (1976)
Option pricing when underlying stock returns are discontinuousJournal of Financial Economics, 3
(1995)
The Incremental Volatility
S. Heston (1993)
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency OptionsReview of Financial Studies, 6
E. Stein, J. Stein (1991)
Stock Price Distributions with Stochastic Volatility: An Analytic ApproachReview of Financial Studies, 4
M. Rubinstein. (1983)
Displaced Diffusion Option PricingJournal of Finance, 38
J. Harrison, S. Pliska (1981)
Martingales and stochastic integrals in the theory of continuous tradingStochastic Processes and their Applications, 11
(1994)
On Strong Solutions, Birgit Operators, and Filtrations in Girsanov’s Theorem
T. Bollerslev, R. Chou, Kenneth Kroner (1992)
ARCH modeling in finance: A review of the theory and empirical evidenceJournal of Econometrics, 52
R. Geske (1979)
THE VALUATION OF COMPOUND OPTIONSJournal of Financial Economics, 7
H. Johnson, D. Shanno (1987)
Option Pricing when the Variance Is ChangingJournal of Financial and Quantitative Analysis, 22
James Wiggins (1987)
Option values under stochastic volatility: Theory and empirical estimatesJournal of Financial Economics, 19
David Hobson, L. Rogers (1998)
Complete Models with Stochastic VolatilityMathematical Finance, 8
Angelo Melino, S. Turnbull (1990)
Pricing foreign currency options with stochastic volatilityJournal of Econometrics, 45
M. Taqqu, W. Willinger (1987)
The analysis of finite security markets using martingalesAdvances in Applied Probability, 19
J. Duan (1995)
THE GARCH OPTION PRICING MODELMathematical Finance, 5
Bent Christensen, N. Prabhala (1994)
On the Dynamics and Information Content of Implied Volatility: A Bivariate Time Series PerspectiveMicroeconomic Theory eJournal
J. Hull, Alan White (1987)
The Pricing of Options on Assets with Stochastic VolatilitiesJournal of Finance, 42
J. Cox, S. Ross, M. Rubinstein. (1979)
Option pricing: A simplified approach☆Journal of Financial Economics, 7
J. Cox, S. Ross (1976)
The valuation of options for alternative stochastic processesJournal of Financial Economics, 3
Louis Scott (1987)
Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an ApplicationJournal of Financial and Quantitative Analysis, 22
F. Black, Myron Scholes (1973)
The Pricing of Options and Corporate LiabilitiesJournal of Political Economy, 81
ARCH models have become popular for modeling financial time series. They seem, at first, however, to be incompatible with the option pricing approach of Black, Scholes, Merton et al., because they are discrete‐time models and possess too much variability. We show that completeness of the market holds for a broad class of ARCH‐type models defined in a suitable continuous‐time fashion. As an example we focus on the GARCH(1,1)‐M model and obtain, through our method, the same pricing formula as Duan, who applied equilibrium‐type arguments.
Mathematical Finance – Wiley
Published: Jan 1, 1998
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