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Highly Efficient Shannon Wavelet-based Pricing of Power Options under the Double Exponential Jump Framework with Stochastic Jump Intensity and Volatility

Huang, Chun-Sung and O'Hara, John G and Mataramvura, Sure (2022) 'Highly Efficient Shannon Wavelet-based Pricing of Power Options under the Double Exponential Jump Framework with Stochastic Jump Intensity and Volatility.' Applied Mathematics and Computation, 414. p. 126669. ISSN 0096-3003

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Abstract

We propose a highly efficient and accurate valuation method for exotic-style options based on the novel Shannon wavelet inverse Fourier technique (SWIFT). Specifically, we derive an efficient pricing methods for power options under a more realistic double exponential jump model with stochastic volatility and jump intensity. Inclusion of such innovations may accommodate for the various stylised facts observed in the prices of financial assets, and admits a more realistic pricing framework as a result. Following the derivation of our SWIFT pricing method for power options, we perform extensive numerical experiments to analyse both the method's accuracy and efficiency. In addition, we investigate the sensitivities in the resulting prices, as well as the inherent errors, to changes in the underlying market conditions. Our numerical results demonstrate that the SWIFT method is not only more efficient when benchmarked to its close competitors, such as the Fourier- cosine (COS) and the widely-acclaimed fast-Fourier transform (FFT) methods, but it is also robust across a range of different market conditions exhibiting exponential error convergence.

Item Type: Article
Uncontrolled Keywords: Shannon wavelets; Fourier transform inversion; power options; double exponential jumps; stochastic volatility; stochastic jump intensity
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 21 Sep 2021 13:39
Last Modified: 18 Aug 2022 12:32
URI: http://repository.essex.ac.uk/id/eprint/31144

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