# fixed income -- on duration and convexity

to the extent… of nominal numbers for modified/effective duration and modified/effective convexity…is this CONTINGENT AND BASED upon the specific model/pricing function used for the particular bond? because the cfai tells us to use effective duration and convexity for embedded option bonds… but how do u even calculate MODIFIED CONVEXITY for example?//// or EFFECTIVE CONVEXITY… is the formula given in the book for the modified convex or effective?

hi, you need an option pricing model to calculate the change in price of a bond with an embedded derivattive, so I guess the price change should be stated somewhere.

Convexity will be mentioned I believe, I don’t think they’re going to ask us to find that out. There’s no mention of calculating convexity in my books, unless I overlooked it.

I pretty much agree with Matt, but you could do it with market prices if interest rates have moved.

hi, convexity is just the second derivative of the price(yield) function, divided by the price, an approximation for the calculation is shown in (69-5) on page 501 of volume 5 of these cfai-books. but it might be true that you won’t need to calculate that on the exam. cheers,

The formula for convexity was mentioned in the Stalla material and it’s close to the duration formula so easy to remember. I think it’s important to remember that convexity is only relevant for large interest rate changes. Also: 1) lower the coupon, the greater the convexity 2) longer the maturity the greater the convexity 3) Lower the YTM, the greater the convexity.