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SPEPS Preprint

Author(s): Alan J. King, IBM Thomas J. Watson Research Center
Matti Koivu, Helsinki School of Economics
Teemu Pennanen, Helsinki School of Economics
Title: Calibrated option bounds
Date of Acceptance: 13.03.2003
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): calibration, Options, pricing, convex optimization
Appeared in: International journal of theoretical and applied finance : IJTAF 2 (Vol. 8, 2005)
World Scientific (Singapore)
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Abstract (eng):
This paper proposes a numerical approach for computing bounds for the arbitrage-free prices of an option when some options are available for trading. Convex duality reveals a close relationship with recently proposed calibration techniques and implied trees. Our approach is intimately related to the uncertain volatility model of Avellaneda, Levy and Parás, but it is more general in that it is not based on any particular form of the asset price process and does not require the seller's price of an option to be a differentiable function of the cash-flows of the option. Numerical tests on S&P 500 options demonstrate the accuracy and robustness of the proposed method.
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