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Saddlepoint approximations to option price in a general equilibrium model

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

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 71 (2005)
    Issue (Month): 4 (March)
    Pages: 361-369

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    Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:361-369

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    Keywords: Option pricing Saddlepoint approximations Stochastic interest rates Stochastic volatility;

    References

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    1. 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 363-84, March.
    2. 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.
    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 327-43.
    4. 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 613-36.
    5. Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, vol. 55(2), pages 205-238, February.
    6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
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    Cited by:
    1. Takashi Kato & Jun Sekine & Kenichi Yoshikawa, 2013. "Order Estimates for the Exact Lugannani-Rice Expansion," Papers 1310.3347, arXiv.org, revised Jun 2014.
    2. Dennis Kristensen & Antonio Mele, 2009. "Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models," CREATES Research Papers 2009-14, School of Economics and Management, University of Aarhus.

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