Valuation of power options under Heston's stochastic volatility model

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

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume36
Issue number11
DOIs
Publication statusPublished - 2012 Nov

Keywords

  • 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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