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Saddlepoint approximations to option price in a general equilibrium model

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

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.

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

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    1. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
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    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    2. E. Nicolato & D. Sloth, 2014. "Risk adjustments of option prices under time-changed dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 125-141, January.
    3. Rong Yuan & Debiao Meng & Haiqing Li, 2016. "Multidisciplinary reliability design optimization using an enhanced saddlepoint approximation in the framework of sequential optimization and reliability analysis," Journal of Risk and Reliability, , vol. 230(6), pages 570-578, December.
    4. Mengzhe Zhang & Leunglung Chan, 2016. "Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-20, December.
    5. 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.
    6. Takashi Kato & Jun Sekine & Kenichi Yoshikawa, 2013. "Order Estimates for the Exact Lugannani-Rice Expansion," Papers 1310.3347, arXiv.org, revised Jun 2014.
    7. Dilip B. Madan & Wim Schoutens, 2019. "Arbitrage Free Approximations to Candidate Volatility Surface Quotations," JRFM, MDPI, vol. 12(2), pages 1-21, April.

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