Under the binomial model, current value of an option equals the present value of the probability-weighted future payoffs from the options.
It is different from the Black-Scholes-Merton model which is most appropriate for valuing path-independent options. At any point of time, the underlying can have two price movements: either an up move or a down move.
Similarly, in case of a down move, the ratio of the new price S- to S is called the down-factor d. The call option is in-the-money when the spot price of the underlying is higher than the exercise price of the option.
On the other hand, in case of a down movement, the call option payoff c- equals the higher of 0 or dS — X. The binomial model effectively weighs the different payoffs with binary options binomial input associated probability and discounts them to time 0.
The following binomial tree represents the general one-period call option.
The payoff pattern of a put optionan option that entitles the binary options binomial input to sell the underlying at the exercise price is exactly opposite, i. The terminal pay-off of a call or put option after different price movements can be worked by multiplying the up and down factor for every price move.
The following table summarizes the different pay-off situations Period 1 Price.