Convexity

[Paras Chhabra]

Hi David
Into Duration, Dv01 and convexity since yesterday and finally today am starting to get Some sort of confidence. Just struggling in the attached question and it’s second derivative calculation and convexity. Am getting a slightly different answer by applying the formula
Would be lovely if u can help
Apologies but I can’t seem to find a place where I can attach the file..so providing a reference

VRM Chapter 12 Applying duration and convexity..Page 24. Tuckman example.
Thanks

 

[David Harper CFA FRM]

Hi @PaParas Good for you for engaging with the calculations! Maybe the best way to figure out the difference is to share with you my spreadsheet. Here it is, I trust you can open this in Excel https://www.dropbox.com/s/vap6tnjbeemkldu/080720-option-dv01.xlsx?dl=0

The exercise is shown below. Most often, the difference is rounding.

In this example, the estimated price at 2.50% is given by $1.738300 + $0.946350 + $0.174990 = $2.8596, where I expanded decimals only to identify potential rounding difference, and:

• $1.7383 is given as the price at 2.77%
• $0.946350 = -$350.50 × -0.2700%
• $0.174990 = 0.5 × 48,008.285 × -0.2700%^2

Let me know? Thanks!

 

[Paras Chhabra]

Thanks a lot David for taking out time for this..I did manage to open the excel file. Still can’t seem to get hold of the 48008 figure of telnet second derivative. Somehow I keep getting 46800..I am definitely doing something wrong I guess
Would love to get myself corrected
Thanks

 

[David Harper CFA FRM]

Hi @PaParas The second derivative is super-sensitive, that's very close. Often it is rounding but notice that $1.73830 * 27,618.0 = 48,008.4 per the second derivative, d^2P/dy^2 as simply equal to the product of Convexity and the Price, C*P. So my own rounding is infinitesimal. I hope that's helpful,