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

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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 … continued below

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ix, 118 pages : illustrations (some color)

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Zhou, Jie December 2021.

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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.

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ix, 118 pages : illustrations (some color)

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  • December 2021

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  • Jan. 8, 2022, 3:30 p.m.

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Zhou, Jie. A New Class of Stochastic Volatility Models for Pricing Options Based on Observables as Volatility Proxies, dissertation, December 2021; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc1873733/: accessed May 27, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .

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