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DMT exercise. Chapter 14 page 27 (of Sure's notes)

+2 votes
asked Oct 18, 2016 in BUS 2016H - Financial Mathematics by Kelly (970 points)

The solution gives DMT(i=5%) = 7.54. 

From what I understand, 7.54 is the answer to the volatility and not the DMT. 

This is because 7.54 is the solution to substituting 5% into the DMT formula on the previous page (which is calculated by differentiating the PV wrt delta). Shouldn't 7.54 be multiplied by (1+i)=1.05 (the Jacobean) if we want to substitute i directly into that DMT formula in order to calculate the true DMT rather than merely the volatility. 

Also, it is given in the notes that DMT(delta)=Vol(i)(1+i).

Are the solutions wrong? If not, please explain to me where I am getting confused. 


1 Answer

+2 votes
answered Oct 18, 2016 by Richard van Gysen (3,180 points)
Best answer

The answer uses the DMT derivation of a redeemable bond that pays coupons on page 26. This formula results in DMT being defined in terms of i and is specifically:

\((C/(P*i) )*\ddot{a}_{\bar{n|}i} + n*(1 - C/(P*i) )\)

So we must use i to find the DMT as this is what the formula requires.

It is confusing because we define DMT in terms of delta and not i. However, we manipulated the above formula to be in terms of i and not delta and thus should involve i. You can find another form of the page 26 formula in terms of delta and find DMT also.