The duration itself will also change with the change of interest rate. Therefore, it cannot fully describe the sensitivity of bond prices to changes in interest rates. In 1984, Stanley Diller introduced the concept of convexity.

Duration describes the slope of the price-yield curve, and convexity describes the bending degree of the curve. Convexity is the second derivative of bond price to yield.

[Edit] The calculation of convexity

According to the bond pricing theorem 1 and 4, the bond price-yield curve is a curve that slopes from top left to bottom right and is convex downward. B> in the figure below; Answer.

Bond pricing theorem 1;

Bond prices are inversely proportional to yield to maturity.

If yield to maturity is larger than coupon rate and the bond price is lower than the face value, this bond is called a discount bond.

If yield to maturity is smaller than coupon rate and the bond price is higher than the face value, this bond is called premium bond.

If coupon rate is equal to yield to maturity and the bond price is equal to the face value, this is the so-called parity bond.

For redeemable bonds, this relationship does not hold.

Bond pricing theorem 4:

If the term of a bond is fixed, under the same change of yield, the increase of bond yield will lead to the decrease of price, and the decrease of yield will lead to the increase of price.

Example: The face value of the three-phase bonds is 65,438+0,000 yuan, with a maturity of 5 years and coupon rate 7%. When yield to maturity changes.

Yield to maturity (%) 6 7 8

Price1042.121000 960.07

Bond price change rate (%) 4.2 1 0 -4.00

[Edit] The property of convexity

1, convexity increases with the increase of duration. If the yield and duration remain unchanged, the greater the coupon rate, the greater the convexity. When the interest rate falls, the convexity increases.

2. For bonds without implied options, the convexity is always greater than 0, that is, if the interest rate drops, the bond price will accelerate; When interest rates rise, bond prices will slow down and fall.

3. The convexity of bonds with implied options is generally negative, that is, the price slows down and rises with the decrease of interest rate, or the effective duration of bonds shortens with the decrease of interest rate and extends with the increase of interest rate. Because when the interest rate falls, the possibility of buying options increases.

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