Consider a two-step binomial tree. A non-dividend paying stock price starts at $50, and, in each of the two time steps, the stock may go up by 20 percent or go down by 20 percent. Suppose that the risk-free rate is five percent per annum and that the time to maturity, T, is two years. We would like to find the value of a European put option with a strike price K of $52. The following diagram shows the pricing of the stock and the payoffs at the terminal nodes using a binomial tree:
Here, the nodes are calculated as follows:
At the terminal nodes, the payoff from exercising a European call option is given as follows:
In the case of a European put option, the payoff is as follows:
European call and put options are usually denoted by lowercase letters, c and p, while American call and put options are usually denoted by uppercase...
