Lattice Trees by Tushar S. Chande, Ph.D.
The lattice approach to option pricing is used to build a tree, so to speak, of futures prices. The price tree can be recomputed intraday to update the expected price range. These dynamic trees can be used for risk control via price simulations and can also be used for trading. Here, we apply the various uses of lattice (or dynamic) trees to estimate prices for the Standard & Poor's 500.
Option prices can be calculated by any number of sophisticated mathematical models. All such models
make certain assumptions about the underlying security's price behavior, and these models must also
price the underlying stock before pricing the option. Thus, we can use these models to find price
estimates that may be useful for trading.
A price index can be treated as a stock that pays dividends continuously. Therefore, options on stock
indices and stock index futures can be priced using these assumptions. Mathematical models that price
options on futures must first calculate the futures price. We will examine one such model to estimate
prices for the Standard & Poor's 500 futures contract and then discuss how this approach can be used for
trading and risk control.