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The Volatility Smile and Its Implied Tree

PublisherGoldman Sachs & Co.
Format341.0KB PDF, requires Acrobat Rdr 5Date added27 Aug 2003
Topics International Standards, Currency Conversion, Online Trading
Downloads50

In this paper we show how you can use the smile – the prices of known, liquid, European-style index options of all available strikes and expirations – as inputs to deduce the form of the index’s random walk. More specifically, we show how you can systematically extract, from the smile, a unique binomial tree for the index corresponding to the modified random walk mentioned above. We call this the implied tree. When you use this tree to value any of the options on which it is based, it produces values that match the observed market prices. From this tree you can calculate both the distribution and the volatility of the index at future times and market levels, as implied by options prices.

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