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A Fourier-Cosine Method for Pricing Discretely Monitored Barrier Options under Stochastic Volatility and Double Exponential Jump

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  • Shoude Huang
  • Xunxiang Guo

Abstract

In this paper, the valuation of the discrete barrier options on the condition that the underlying asset price process follows the GARCH volatility and double exponential jump is studied. We derived an analytical approximation of the characteristic function for the underlying log-asset price. Then, a quasianalytical approximate formula of the price of the discrete barrier option is obtained based the on Fourier-cosine method. Numerical examples show that the Fourier-cosine method is fast and efficient for pricing discrete barrier options compared with the Monte Carlo simulation method. Finally, the influences of some important parameters on the prices of discrete barrier options are studied to further illustrate the rationality of the model.

Suggested Citation

  • Shoude Huang & Xunxiang Guo, 2020. "A Fourier-Cosine Method for Pricing Discretely Monitored Barrier Options under Stochastic Volatility and Double Exponential Jump," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, October.
    • Handle: RePEc:hin:jnlmpe:4613536
    DOI: 10.1155/2020/4613536
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    Cited by:

    1. Huang, Chun-Sung & O'Hara, John G. & 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, Elsevier, vol. 414(C).

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