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Hello!

(the following refers to the study notes on Tuckman, Chapter 8, pages 18 through 20)

I find the volatility effect in the binomial trees that "pushes down" on the price a little confusing, from a mathematical point of view:

As usual, we are assuming a yield volatility given by (semiannual) basis point changes (e.g. up 400BP from 10% to 14% and down to 6%). By applying probabilities we get a two-year spot rate of less than 10%, which Tuckman explains with the "convexity/volatility effect".

The point that confuses me though, is that the volatility is

It seems to me then, that the effect mentioned by Tuckman stems purely from the use of a volatility in basis points that is indifferent to the yield level. If, for instance, Tuckman used a volatility-informed jump given by EXP(Sigma*SQRT(Time)) none of this would happen.

I am unsure of whether any of this made sense, but if it does, please help me to understand!

Thanks, Johannes

(the following refers to the study notes on Tuckman, Chapter 8, pages 18 through 20)

I find the volatility effect in the binomial trees that "pushes down" on the price a little confusing, from a mathematical point of view:

As usual, we are assuming a yield volatility given by (semiannual) basis point changes (e.g. up 400BP from 10% to 14% and down to 6%). By applying probabilities we get a two-year spot rate of less than 10%, which Tuckman explains with the "convexity/volatility effect".

The point that confuses me though, is that the volatility is

*given in BP yield changes*and that these will always have a "stronger impact" downwards than upwards, relative to the starting point. In contrast, if we magine a*relative volatilit*y of 40% and an initial down-jump from 10% to 6%. To get back up to 10%, the yield would have to jump 67% which is far out of its comfort zone.It seems to me then, that the effect mentioned by Tuckman stems purely from the use of a volatility in basis points that is indifferent to the yield level. If, for instance, Tuckman used a volatility-informed jump given by EXP(Sigma*SQRT(Time)) none of this would happen.

I am unsure of whether any of this made sense, but if it does, please help me to understand!

Thanks, Johannes

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