Apr
6

## Implied Binomial Tree

Black Scholes model assumes stock price follows GBM with constant volatility, however, the market implied volatilities of stock options often show "the volatility smile", which decreases with the strike level, and increases with the time to maturity. There are various proposed extensions of this GBM model to account for "the volatility smile". One approach is the

Download the paper and accompanying excel file at http://www.kelleyschool.com/papers.html.

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**implied binomial tree**technique proposed by Rubinstein (1994), in which the author assumes the stock prices are generated by a modified random walk where the underlying assets volatility depends on both stock price and time, therefore it is an modification of basic Binomial tree method.**Implied binomial tree**uses the observable market option prices in order to estimate the implied distribution, to construct such a tree, optimization routine generally applies and technically it is more difficult than a basic Binomial tree. Here is a good paper implementing the implied binomial tree using an Excel spreadsheet without VBA. It demonstrates both the optimization needed to generate implied ending risk-neutral probabilities from a set of actual option prices and the backwards recursion needed to solve for the entire implied tree.Download the paper and accompanying excel file at http://www.kelleyschool.com/papers.html.

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