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Replication Scheme For The Pricing Of European Options

Author

Listed:
  • HIDEHARU FUNAHASHI

    (Faculty of Economics, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama-shi, Kanagawa 221-8686, Japan)

Abstract

This paper proposes an efficient method for calculating European option prices under local, stochastic, and fractional volatility models. Instead of directly calculating the density function of a target underlying asset, we replicate it from a simpler diffusion process with a known analytical solution for the European option. For this purpose, we derive six functions that characterize the density function of a diffusion process, for both the original and simpler processes and match these functions so that the latter mimics the former. Using the analytical formula, we then approximate the option price of the target asset. By comparison with previous works and numerical experiments, we show that the accuracy of our approximation is high, and the calculation is fast enough for practical purposes; hence, it is suitable for calibration purposes.

Suggested Citation

  • Hideharu Funahashi, 2021. "Replication Scheme For The Pricing Of European Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 1-37, May.
    • Handle: RePEc:wsi:ijtafx:v:24:y:2021:i:03:n:s021902492150014x
    DOI: 10.1142/S021902492150014X
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