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Option Pricing in ARCH‐type Models

Option Pricing in ARCH‐type Models 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Finance Wiley

Option Pricing in ARCH‐type Models

Mathematical Finance , Volume 8 (1) – Jan 1, 1998

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References (23)

Publisher
Wiley
Copyright
Blackwell Publishers 1998
ISSN
0960-1627
eISSN
1467-9965
DOI
10.1111/1467-9965.00042
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Mathematical FinanceWiley

Published: Jan 1, 1998

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