Maximum entropy distributions inferred from option portfolios on an asset |
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Authors: | Cassio Neri Lorenz Schneider |
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Affiliation: | (1) FX Quantitative Research, Lloyds Banking Group, 10 Gresham Street, London, EC2V 7AE, UK;(2) Center for Financial Risks Analysis (CEFRA), EMLYON Business School, 23 avenue Guy de Collongue, 69130 Ecully, France |
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Abstract: | We obtain the maximum entropy distribution for an asset from call and digital option prices. A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimise a formal derivation by Buchen and Kelly (J. Financ. Quant. Anal. 31:143–159, 1996). We give a simple and robust algorithm for our method and compare our results to theirs. We present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options. Finally, we apply our approach to options on the S&P 500 index. |
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