Saddlepoint approximations to option price in a general equilibrium model
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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Volume (Year): 71 (2005)
Issue (Month): 4 (March)
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- 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.
- 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.
- 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.
- 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.
- Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, vol. 55(2), pages 205-238, February.
- 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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