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Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility

  • Gatfaoui Hayette

    (University Paris I - Panthéon-Sorbonne)

  • Chauveau Thierry

    (University Paris I - Panthéon-Sorbonne)

Starting from the European option valuation framework of Chauveau & Gatfaoui (2002), we establish the link with stochastic volatility models. And, we propose both a new vision and a general framework for valuing European options in the light of systematic and idiosyncratic risks affecting risky assets in the financial market. Therefore, we account for the well-known volatility smile in the light of the literature addressing the determinants of the smile effect among which stochastic volatility and market risk. We further discuss briefly the hedging of European options along with the local risk minimization principle. Specifically, we attempt to find a strategy, which dominates the usual partial hedging technique often imposed by market’s incompleteness.

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File URL: http://128.118.178.162/eps/fin/papers/0404/0404002.pdf
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Paper provided by EconWPA in its series Finance with number 0404002.

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Length: 26 pages
Date of creation: 07 Apr 2004
Date of revision:
Handle: RePEc:wpa:wuwpfi:0404002
Note: Type of Document - pdf; pages: 26
Contact details of provider: Web page: http://128.118.178.162

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  1. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
  2. Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116.
  3. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  5. Vicky Henderson, 2002. "Analytical Comparisons of Option prices in Stochastic Volatility Models," OFRC Working Papers Series 2002mf03, Oxford Financial Research Centre.
  6. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
  7. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  8. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
  9. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52.
  10. Chauveau, Thierry & Gatfaoui, Hayette, 2002. "Systematic risk and idiosyncratic risk: a useful distinction for valuing European options," Journal of Multinational Financial Management, Elsevier, vol. 12(4-5), pages 305-321.
  11. Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March.
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