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Analytical formulas for option prices under time-changed CARMA process

Author

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  • Zhigang Tong

    (Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, K1N 6N5, Canada)

Abstract

We consider the option pricing problem when the underlying asset price is driven by a continuous time autoregressive moving average (CARMA) process, time changed a Lévy subordinator or/and an absolutely continuous time change process. We derive the analytical formulas for the option prices by employing the orthogonal polynomial expansion method. Our method is based on the observation that the CARMA process belongs to the class of polynomial diffusion and the time variable and underlying state variables enter the polynomial expansion separately. We demonstrate the accuracy of the method through a number of numerical experiments. We also investigate the price sensitivities with respect to the key parameters that govern the dynamics of the underlying state and time change variables.

Suggested Citation

  • Zhigang Tong, 2023. "Analytical formulas for option prices under time-changed CARMA process," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(03), pages 1-24, September.
    • Handle: RePEc:wsi:ijfexx:v:10:y:2023:i:03:n:s242478632350024x
    DOI: 10.1142/S242478632350024X
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