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Frontiers in Finance and Economics is a UGC APPROVED International Journal of Research

Call and Put Implied Volatilities and the Derivation of Option Implied Trees

  1. Moriggia S. Muzzioli C. Torricelli
Resting on the stylized fact that call and put prices imply different volatilities, the present paper proposes a methodology for the derivation of  an arbitrage free implied tree that takes into account the information in both option classes. Specifically, we derive an implied tree that is characterised by interval values for the stock prices and we endogenously imply the corresponding artificial probabilities based on the risk neutral valuation argument. The implied tree obtained is then calibrated to market option prices by means of a non-linear optimisation routine. The methodology proposed is tested both in and out of sample using DAX index options data. Numerical results are benchmarked to the Derman and Kani’s approach. The comparison suggests that the methodology proposed in this paper, by taking into account the informational content of both call and put prices, highly improves both the in sample fitting and the out of sample performance.
Keywords: Implied Binomial Tree, Smile Effect, Interval Tree.
JEL classification: G13, G14.
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Frontiers in Finance and Economics

FRONTIERS IN FINANCE AND ECONOMICS with ISSN no. 1814-2044 Multi-Disciplinary Journal of Economic, Finance and Business and Management Sciences. Frontiers of Finance and Economics, a bi-Annual UGC Approved Journal. Send papers for publication to editor@ffejournal.org

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