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

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  • Thierry Chauveau
  • Hayette Gatfaoui

Abstract

Starting from the European option valuation framework of Chauveau and 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.

Suggested Citation

  • Thierry Chauveau & Hayette Gatfaoui, 2004. "Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility," Research Paper Series 122, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:122
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    File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp122.pdf
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    References listed on IDEAS

    as
    1. RĂ¼diger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116.
    2. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
    3. 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.
    4. 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 727-752.
    5. 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 637-654, May-June.
    6. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    7. Vicky Henderson, 2002. "Analytical Comparisons of Option prices in Stochastic Volatility Models," OFRC Working Papers Series 2002mf03, Oxford Financial Research Centre.
    8. 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.
    9. Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March.
    10. 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.
    11. 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.
    12. repec:spr:portec:v:2:y:2003:i:3:d:10.1007_s10258-003-0024-5 is not listed on IDEAS
    13. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187.
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    More about this item

    Keywords

    call pricing; idiosyncratic risk; incomplete market; stochastic volatility; systematic risk;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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