Down Transition Probability
The probability that an asset's value will decline in one period’s time within the context of an option pricing model. The option pricing models using a down transition probability are both the binomial and trinomial option pricing models.
In a binomial option pricing model, the probability that an option's underlying asset declines in value over a time step may be denoted by 1-Qu, where Qu represents the probability that the option's underlying asset will increase over the next time step in decimal form.
Under the trinomial model, the probability of a down transition is equal to the probability of an upward transition or an equal transition over the next time step not happening. If we denote Qu as the probability of the underlying asset increasing in value over the next time step, Qd as the probability the value of the underlying asset will decrease over the next time step, then the probability that the underlying asset's value stays the same is 1-Qu-Qd.
In a binomial option pricing model, the probability that an option's underlying asset declines in value over a time step may be denoted by 1-Qu, where Qu represents the probability that the option's underlying asset will increase over the next time step in decimal form.
Under the trinomial model, the probability of a down transition is equal to the probability of an upward transition or an equal transition over the next time step not happening. If we denote Qu as the probability of the underlying asset increasing in value over the next time step, Qd as the probability the value of the underlying asset will decrease over the next time step, then the probability that the underlying asset's value stays the same is 1-Qu-Qd.
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