Option Pricing Under Rough Heston Model With Jumps
Date
2022-09
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Abstract
The rough Heston model with jumps is proposed and studied in the thesis which is inspired by some well-known models, including the Heston model, rough Heston model, and Kou's jump model. Our new model considers adding a Poisson jump process to the rough Heston model, which not only keeps the roughness of the volatility process, and also adds an extra noise to improve the model performance. To have better comparisons across models and to understand well how the jumps and roughness improve the model performance, we involve another interesting model called the Heston model with jumps where we used the similar jump process as in Kou's model. The concerned topics are reviewed in the front part of the thesis including option pricing methods, Fourier-inversion techniques, Black-Scholes implied volatilities, and the introduction of related models such as model dynamics and their characteristic functions/moment-generating-functions. In the empirical analysis section, two option pricing methods were compared in the dimension of accuracy and efficiency by the results from Monte Carlo's simulation and their CPU computational time. The calibration based on implied volatilities were processed by four discussed models we mentioned above: the Heston model, rough Heston model, Heston model with jumps, and rough Heston model with jumps. We have the in- and out-of-sample tests to monitor the performances of the models by using the 2014-2019 S&P 500 options, where the former test focuses on the calibrated implied volatilities and the latter conducts a time-series forecast based on the in-sample test results. Significant improvements are shown in the rough Heston model with jumps in both tests which lead us to the conclusion that the combination of the volatility roughness and the add-on Poisson jump process can help the model to reach a better performance.
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Keywords
Heston model, rough Heston model, volatility process, jump-diffusion process, affine process, affine Volterra process, Poisson process, implied volatility, calibration, option pricing, Fourier transform, characteristic function/moment-generating-function
Citation
Jin, Y. (2022). Option pricing under rough Heston model with jumps (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.