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A New Class of Stochastic Volatility Models for Pricing Options Based on Observables as Volatility Proxies

One basic assumption of the celebrated Black-Scholes-Merton PDE model for pricing derivatives is that the volatility is a constant. However, the implied volatility plot based on real data is not constant, but curved exhibiting patterns of volatility skews or smiles. Since the volatility is not observable, various stochastic volatility models have been proposed to overcome the problem of non-constant volatility. Although these methods are fairly successful in modeling volatilities, they still rely on the implied volatility approach for model implementation. To avoid such circular reasoning, we propose a new class of stochastic volatility models based on directly observable volatility proxies and derive the corresponding option pricing formulas. In addition, we propose a new GARCH (1,1) model, and show that this discrete-time stochastic volatility process converges weakly to Heston's continuous-time stochastic volatility model. Some Monte Carlo simulations and real data analysis are also conducted to demonstrate the performance of our methods.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc1873733
Date12 1900
CreatorsZhou, Jie
ContributorsSong, Kai-Sheng, Liu, Jianguo, Iaia, Joseph A.
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatix, 118 pages : illustrations (some color), Text
RightsPublic, Zhou, Jie, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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