# Binary options binom

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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 binary options binom 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 their 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 holder 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.