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Volatility effect on bond yields (Tuckman, Chapter 8)

JDGutzmann

Member
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 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 volatility 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.

Thanks, Johannes

ShaktiRathore

Well-Known Member
Subscriber
Hi,
Yes tuckman is using bps addition to yield to express volatility,that iis why convexity effect shows ufup of reduced effective spot rate ,if he had used volatility like u mentioned(40up and 67 down)then spot rate would not be affected.400bpd add. Shall decrease disc. Factor less than increase in disc fac. Due to 400 bps deletion from yield so overall increase ibn disc. Factor thus reduced eff. Spot rate.
Thanks

JDGutzmann

Member
Thank you, that made the implications of using BP shift clearer to me.
However, I still don't understand why we are using an absolute measure of volatility (+/- Basis Points) instead of a relative one (+/- percent), like in any other application of standard deviates. Why is the variation of yields measured in absolute terms and not relative?
All the best, Johannes

Aenny

Active Member
Subscriber
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.
for understanding it helped me thinking of the geometric bronian motion with its lognormal parametrs
and
.
Maybe it's useful for you too.