let’s try to understand this in parts so that we all are on same page. Duration = % change in price for 100 bps change in interest rate. Assume an option free bond. Duration will measure the change in price very good for small yield changes. but it will produce wider margin as the yield becomes large. (this is all straight from the book and can be seen clearly in a graph) My problem is. if current price is 100. intrst rate shock let’s say for 200. and let’s say the new price is 105, and 96 however based on duration we get the new price to be 103. so the underestimation happened by 3 bucks. now my question is will the new price due to decline equal 93, or 94, or 92. Q. will it be $ 2 off is the question. or less than $2 or more than $2.

i think that for the most part, with duration, there will be -more error when you are trying to value a price appreciation than price depreciation- due to the fact that prices increase more sharply than they drop and there is more room for error when using duration (secant line or tangent) so if the duration estimate underestimated the price increase by 2 dollars it will overestimate the price decrease by less than 2 dollars

Super, is that for option and option free bonds?

sorry, option free bonds, positive convexity

They acted like option bonds were so complex that it was beyond level 1 in the book, they didn’t really go into it from what I can see.

you can figure out the relationship by drawing a price-yield curve for a bond with options embedded, mark down the put price or call price on the diagram, and draw a secant or tangent line to see how the error works in fact, that’s what i would recommend doing every time you encounter a conceptual problem dealing with convexity, price-yield curves, duration, etc.