ABSTRACT
The simplest model in option pricing is the Binomial model. In this model, today's price can change to two different prices at a future time. The option price depends on the width of these two prices. We call delta the relationship between the amplitude of payoff prices and asset prices. Using delta we can find the option value over a period, or time step, using no-arbitrage assumptions. Alternatively, see how the corresponding option price is computed via the risk-neutral probability.
It is possible to extend the binomial trees to more periods, finding more scenarios. In particular, if we expand the tree to n periods, we will have n+1 scenarios. Once we obtain the future prices, we can calculate the option value using discounted expected values backward.
We also see how to compute the sensitivities of option prices with respect to the parameters of the market. These sensitivies are called the Greeks.
