## DEFINITION of 'Down Transition Probability'

Down transition probability is the probability, in the context of an option pricing model, that an asset's value will decline in one period's time. Both binomial option pricing models and trinomial option pricing models use down transition probabilities.

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## BREAKING DOWN 'Down Transition Probability'

In a binomial option pricing model, the probability that an option's underlying asset declines in value over one period may be denoted by 1-Qu, where Qu represents the probability that the option's underlying asset will increase over the period. Under the trinomial model, the probability of a down transition is equal to the probability of an upward transition or an equal transition not occurring over the next period. If we denote Qu as the probability of the underlying asset increasing in value over the next time step and Qd as the probability the value of the underlying asset will decrease over the next period, then the probability that the underlying asset's value stays the same is 1-Qu-Qd.

Binomial option pricing models can become unwieldy, trinomial option pricing models can produce equivalent results while also being easier to build, more intuitive and more rapidly calculated.

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