On the Pricing Formula for the Perpetual American Volatility Option Under the Mean-reverting Processes

This paper studies the properties of the parabolic free-boundary problem arising from pricing of American volatility options in mean-reverting volatility processes. When the volatility index follows the mean-reverting square root process (MRSRP), we derive a closed-form pricing formula for the perpe...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 25; no. 2; pp. 365 - 379
Main Authors Liu, Hsuan-Ku, Lin, Tse-Yu, Tsai, Yen-Lung
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.04.2021
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Summary:This paper studies the properties of the parabolic free-boundary problem arising from pricing of American volatility options in mean-reverting volatility processes. When the volatility index follows the mean-reverting square root process (MRSRP), we derive a closed-form pricing formula for the perpetual American power volatility option. Moreover, an artificial neural network (ANN) approach is extended to find an approximate solution of the free boundary problem arising from pricing the perpetual American option. The comparison results demonstrates that the ANN provides an accurate approach to approximate solution for the free boundary problem.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm/200803