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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/11438

Title: Theories on the Relationship between Price Process and Stochastic Volatility Matrix with Compensated Poisson Jump Using Fourier Transforms
Authors: Andam, Perpetual Saah
Ackora-Prah, Joseph
Mataramvura, Sure
Keywords: Stochastic Differential Equation
Fourier Transform
Compensated Poisson Jump
Issue Date: 2017
Publisher: Journal of Mathematical Finance
Citation: Journal of Mathematical Finance, 2017, 7, 633-656; http://www.scirp.org/journal/jmf
Abstract: Investors find it difficult to determine the movement of prices of stock due to volatility. Empirical evidence has shown that volatility is stochastic which contradicts the Black-Scholes framework of assuming it to be constant. In this paper, stochastic volatility is estimated theoretically in a model-free way without assuming its functional form. We show proof of an identity establishing an exact expression for the volatility in terms of the price process. This theoretical presentation for estimating stochastic volatility with the presence of a compensated Poisson jump is achieved by using Fourier Transform with Bohr’s convolution and quadratic variation. Our method establishes the addition of a compensated Poisson jump to a stochastic differential equation using Fourier Transforms around a small time window from the observation of a single market evolution.
Description: An article published in Journal of Mathematical Finance, 2017, 7, 633-656; http://www.scirp.org/journal/jmf; https://doi.org/10.4236/jmf.2017.73033
URI: http://hdl.handle.net/123456789/11438
Appears in Collections:College of Science

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