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A New Binomial Model for Discrete Lookback Options using Mathematica

Michael Kelly
Organization: University of Western Sydney

2006 Wolfram Technology Conference
Conference location

Champaign IL

Lookback options are a special case of exotic derivatives where the value of the derivative depends upon some function of all of the previous underlying asset prices. In particular it attempts to mimic the optimal situation where one can purchase stocks at the minimum price and sell stocks at the maximum price, ie buy at the low and sell at the high. There are two types of call and put Lookback options, depending upon whether the strike or the final asset price is replaced by the optimal asset price. Using the standard notation where S is the asset and K is the strike price that one pays for the asset at some future date, then the Floating strike or Standard Lookback call has the value a, whereas the Fixed strike Lookback call or call on the Max has the value a. Standard Lookback options were first evaluated by Goldman, Sosin and Gatto (1979) and probabilistic models for all types of Lookback options were later calculated by Conze and Viswanathan (1991). All of these models were determined within the continuous framework, where the value of the underlying security is modeled as changing continuously with time. However such prices were found by Babbs (2000) and others to significantly overprice the true value of the market Lookbacks, because the actual Lookback options were determined from asset prices valued at discrete intervals of a fraction of a day. This paper derives two new methods for determining discrete Lookback options by using Mathematica's powerful symbolic capabilities to find simplified expressions for the optimal asset prices in each asset path in a binomial tree model.

*Business and Economics

finance, lookback options, binomial models
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DiscreteLookbackOptionsPaper.nb (487.3 KB) - Mathematica Notebook [for Mathematica 5.2]