Valuation of power options under Heston's stochastic volatility model

Jerim Kim, Bara Kim, Kyoung Sook Moon, In Suk Wee

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We derive semi-analytic solutions for power option prices under the Heston model; specifically, the pricing formula is shown to be valid whenever the power of the underlying asset price has a finite moment. Unlike the majority of stochastic volatility models, there remains a significant problem to check the existence of moments of assets prices of order higher than one. Fortunately, the moment explosion property under the Heston model is examined systematically in Andersen and Piterbarg (2000). Incorporating with their results, we present explicit formulas for moment generating function of log price and for power option prices under the circumstances when the corresponding moments are finite. In case that the corresponding moment explodes, we provide two numerical methods to derive prices of power put and capped power call options. In spite of a simple idea, numerical examples show that the approximations are extremely accurate and efficient.

Original languageEnglish
Pages (from-to)1796-1813
Number of pages18
JournalJournal of Economic Dynamics and Control
Issue number11
Publication statusPublished - 2012 Nov

Bibliographical note

Funding Information:
B. Kim's research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0004133 ). K.-S. Moon's research was supported by the Gachon University Research Fund in 2012. I.-S. Wee's work was supported by Seoul R&BD Program ( 10551 ).


  • Change of numeraire
  • Fourier transform
  • Heston model
  • Power option
  • Stochastic volatility

ASJC Scopus subject areas

  • Economics and Econometrics
  • Control and Optimization
  • Applied Mathematics


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