Risk-Neutral Probabilities in Binomial Short-Rate Models

Summary

The document asks why binomial short-rate models often assign equal risk-neutral probabilities to up and down moves, and whether model properties such as no drift or a flat volatility term structure depend on that choice. It highlights a concern: if changing the probability changes those properties, can they be treated as general features of the model?

The text presents questions rather than a resolution. It gives no derivation or evidence explaining when equal probabilities are justified, how risk-neutral probabilities should be calibrated, or whether the cited model characteristics hold under alternative specifications. Its value is in identifying the distinction between assumptions used to construct a model and properties that follow from the model itself; conclusions require further explanation of the particular tree and parameterization.

Key ideas

• Equal up and down risk-neutral probabilities are sometimes assumed in binomial short-rate models.
• The document questions whether the equal-probability choice is conventional or mathematically necessary.
• It asks whether claims about drift and volatility structure depend on the selected probabilities.
• The text raises the issue but does not provide a derivation or answer.

Tags

# Why do we simply assume the risk neutral probabilities to be "0.5"?


# Why do we simply assume the risk neutral probabilities to be "0.5"?












I am aware that there was a question similar to this but my question is a little different.

Firstly, in context of binomial short rate, why do we simply assume the risk neutral probabilities p=1-p=0.5? Is this some kind of common practice or helps somehow?

Taken from a paper, "Let us also assume that under the risk-neutral probability measure (not necessarily the actual measure), that the probability of an up or down move is the same, equal to 0.5." Is there a rationale behind this?

Secondly and more importantly,

I have an introductory textbook, where basic characteristics of one factor interest rate models are explained like no-drift, flat volatility term structure specific to models. But here as well, 0.5 is taken to be risk neutral probability. But the problem is as soon as you change it from 0.5 to anything else, the so called "characteristics" of the models fall apart. So how can we generalise the behaviour of a model on the basis of a specific probability, i.e, 0.5? Isn't that wrong to say that a model has flat volatility term structure when it only exhibits so, if we were to choose risk neutral probabilities as 0.5?

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