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Stochastic Volatility Option Pricing

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Author Info
Ball, Clifford A.
Roma, Antonio
Abstract

This paper examines alternative methods for pricing options when the underlying security volatility is stochastic. We show that when there is no correlation between innovations in security price and volatility, the characteristic function of the average variance of the price process plays a pivotal role. It may be used to simplify Fourier option pricing techniques and to implement simple power series methods. We compare these methods for the alternative mean-reverting stochastic volatility models introduced by Stein and Stein (1991) and Heston (1993). We also examine the biases in the Black-Scholes model that are eliminated by allowing for stochastic volatility, and we correct some errors in the Stein and Stein (1991) analysis of this issue.

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Publisher Info
Article provided by Cambridge University Press in its journal Journal of Financial and Quantitative Analysis.

Volume (Year): 29 (1994)
Issue (Month): 04 (December)
Pages: 589-607
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:jfinqa:v:29:y:1994:i:04:p:589-607_00

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  1. Patrick Gagliardini & C. Gourieroux & E. Renault, 2005. "Efficient Derivative Pricing by Extended Method of Moments," University of St. Gallen Department of Economics working paper series 2005 2005-05, Department of Economics, University of St. Gallen. [Downloadable!]
  2. Robert F. Engle & Joshua V. Rosenberg, 1995. "GARCH Gamma," NBER Working Papers 5128, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Sam Howison & David lamper, 2000. "Trading Volume in Models of Financial Derivatives," OFRC Working Papers Series 2000mf03, Oxford Financial Research Centre. [Downloadable!]
  4. Björn Hansson & Peter Hördahl, 2005. "Forecasting variance using stochastic volatility and GARCH," European Journal of Finance, Taylor and Francis Journals, vol. 11(1), pages 33-57, February. [Downloadable!] (restricted)
  5. Kazuhiko NISHINA & Tatsuro Nabil MAGHREBI & Moo-Sung KIM, 2006. "Stock Market Volatility And The Forecasting Accuracy Of Implied Volatility Indices," Discussion Papers in Economics and Business 06-09, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP). [Downloadable!]
  6. Alvaro Cartea & Sam Howison, 2002. "Distinguished Limits of Levy-Stable Processes, and Applications to Option Pricing," OFRC Working Papers Series 2002mf04, Oxford Financial Research Centre. [Downloadable!]
  7. Elisa Alòs, 2004. "A Generalization of Hull and White Formula and Applications to Option Pricing Approximation," Economics Working Papers 740, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  8. Elisa Alòs & Jorge León & Josep Vives, 2007. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Finance and Stochastics, Springer, vol. 11(4), pages 571-589, October. [Downloadable!] (restricted)
  9. Nigel Clarke, Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(3), pages 177-195, September. [Downloadable!] (restricted)
  10. Jondeau, E. & Rockinger, M., 1998. "Reading the Smile: The Message Conveyed by Methods Which Infer Risk Neutral," Documents de Travail 47, Banque de France. [Downloadable!]
  11. Gabriele Fiorentini & Angel León & Gonzalo Rubio, . "Short-term options with stochastic volatility: Estimation and empirical performance," Studies on the Spanish Economy 02, FEDEA. [Downloadable!]
    Other versions:
  12. Jun Ma, 2009. "A Stochastic Correlation Model with Mean Reversion for Pricing Multi-Asset Options," Asia-Pacific Financial Markets, Springer, vol. 16(2), pages 97-109, June. [Downloadable!] (restricted)
  13. Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor and Francis Journals, vol. 6(4), pages 337-347, August. [Downloadable!] (restricted)
  14. Giovanni Barone-Adesi & Claudia Ravanelli & Henrik Rasmussen, 2003. "An Option Pricing Formula for the GARCH diffusion model," OFRC Working Papers Series 2003mf07, Oxford Financial Research Centre. [Downloadable!]
  15. Fabio Antonelli & Sergio Scarlatti, 2009. "Pricing options under stochastic volatility: a power series approach," Finance and Stochastics, Springer, vol. 13(2), pages 269-303, April. [Downloadable!] (restricted)
  16. Paul Söderlind, 2006. "C-CAPM without Ex Post Data," University of St. Gallen Department of Economics working paper series 2006 2006-22, Department of Economics, University of St. Gallen. [Downloadable!]
    Other versions:
  17. Vicky Henderson & David Hobson, 2001. "Passport options with stochastic volatility," Applied Mathematical Finance, Taylor and Francis Journals, vol. 8(2), pages 97-118, May. [Downloadable!] (restricted)
  18. P.A. Forsyth, K.R. Vetzal, R. Zvan, 1999. "A finite element approach to the pricing of discrete lookbacks with stochastic volatility," Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(2), pages 87-106, June. [Downloadable!] (restricted)
  19. Elisa Alòs & Jorge A. León & Josep Vives, 2006. "On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility," Economics Working Papers 968, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  20. Sam Howison & David Lamper, 2001. "Trading volume in models of financial derivatives," Applied Mathematical Finance, Taylor and Francis Journals, vol. 8(2), pages 119-135, May. [Downloadable!] (restricted)
  21. K. Ronnie Sircar, George C. Papanicolaou, 1999. "Stochastic volatility, smile & asymptotics," Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(2), pages 107-145, June. [Downloadable!] (restricted)
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