{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture_16

# Lecture_16 - InterestRate Management The Price-Rate...

This preview shows pages 1–8. Sign up to view the full content.

Interest Rate  Management Professor Ruslan Goyenko

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Fall 2010 Investment  2 The Price-Rate Function for a Zero 100 bp At a rate of 5%, the price is 0.2273 If rates fall to 4%, the price is 0.3048 The actual change is 0.077 Using a linear approximation, the change is about 0.0665
Fall 2010 Investment  3 Computing dollar duration for a zero. .. Recall By this definition, the dollar duration of the zero is directly related to the slope of the price-rate function. Example: The dollar duration of \$1 par of a 30-year zero at an interest rate of 5% is 6.65, as illustrated in the last slide: -0.0665/(-0.01)=0.0665/0.01=6.65. We can use calculus to compute the slope of the price-rate function and get an explicit formula for the dollar duration of any zero.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Fall 2010 Investment  4 Duration Duration approximates the percent change in price for a 100 basis point change in rates:
Price Approximation Using Duration Price Yield y 3 p * Actual Price Tangent Line at y* (estimated price) y * y 1 y 2 y 4 Error in Estimating Price Based only on Duration Error in Estimating Price Based only on Duration

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Fall 2010 Investment  6 Taylor Series A theorem from calculus says that the value of a function can be approximated near a given point using its "Taylor series" around that point . Using only the first two derivatives, the Taylor series approximation is: 2 0 0 0 0 0 ) ( ) ( ' ' 2 1 ) ( ) ( ' ) ( ) ( : x x x f x x x f x f x f or - × + - × -
Fall 2010 Investment  7 The Convexity Correction Change in price = ΔP = - \$D x Δr + 0.5 x \$C x (Δr)2 = - dollar duration x change in rates + (1/2) x dollar convexity x change in rates squared 2 0 0 0 0 0 ) ( ) ( ' ' 2 1 ) ( ) ( ' ) ( ) ( x x x f x x x f x f x f - × + - × -

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 18

Lecture_16 - InterestRate Management The Price-Rate...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online