Option pricing under autoregressive random variance models

Tak Kuen Siu

Research output: Contribution to journalArticle

Abstract

The autoregressive random variance (ARV) model introduced by Taylor (1980, 1982, 1986) is a popular version of stochastic volatility (SV) models and a discrete-time simplification of the continuous-time diffusion SV models. This paper introduces a valuation model for options under a discrete-time ARV model with general stock and volatility innovations. It employs the discrete-time version of the Esscher transform to determine an equivalent martingale measure under an incomplete market. Various parametric cases of the ARV models, are considered, namely, the log-normal ARV models, the jump-type Poisson ARV models, and the gamma ARV models, and more explicit pricing formulas of a European call option under these parametric cases are provided. A Monte Carlo experiment for some parametric cases is also conducted.

Original languageEnglish
Pages (from-to)62-75
Number of pages14
JournalNorth American Actuarial Journal
Volume10
Issue number2
Publication statusPublished - Apr 2006

Fingerprint

Option pricing
Discrete-time
Stochastic volatility model
Continuous time
Jump
Call option
Esscher transform
Pricing
Innovation
Valuation model
Incomplete markets
Equivalent martingale measure
Monte Carlo experiment

Cite this

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Option pricing under autoregressive random variance models. / Siu, Tak Kuen.

In: North American Actuarial Journal, Vol. 10, No. 2, 04.2006, p. 62-75.

Research output: Contribution to journalArticle

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