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Saddlepoint approximations to option price in a general equilibrium model


  • Xiong, Jian
  • Wong, Augustine
  • Salopek, Donna


In the recent literature on option valuation, Fourier analysis has been successfully applied to determine numerically the prices of options. However, most of these numerical methods can both be slow and inaccurate. Rogers and Zane (Ann. Appl. Probab. 9 (1999) 493-503) first propose the application of the saddlepoint approximation method to compute European-type options. In this paper, we extend their approach to price a variety of European options, and in particular, when the return process of a general equilibrium model has stochastic volatility and stochastic interest rates. The model is calibrated on the S&P 500 index, and we also discuss the pros and cons of saddlepoint approximations.

Suggested Citation

  • Xiong, Jian & Wong, Augustine & Salopek, Donna, 2005. "Saddlepoint approximations to option price in a general equilibrium model," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 361-369, March.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:361-369

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    References listed on IDEAS

    1. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-636.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    5. Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, vol. 55(2), pages 205-238, February.
    6. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
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    Cited by:

    1. Kristensen, Dennis & Mele, Antonio, 2011. "Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models," Journal of Financial Economics, Elsevier, vol. 102(2), pages 390-415.
    2. Takashi Kato & Jun Sekine & Kenichi Yoshikawa, 2013. "Order Estimates for the Exact Lugannani-Rice Expansion," Papers 1310.3347,, revised Jun 2014.
    3. Wendong Zheng & Yue Kuen Kwok, 2014. "Saddlepoint Approximation Methods for Pricing Derivatives on Discrete Realized Variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(1), pages 1-31, March.


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