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Bond Pricing with No Default Risks and a Fixed Interest Rate

A Bond's price is valued based on its face value, coupon rate, expiration date, term and interest rate.

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Assuming a bond pays semiannual coupons, its price is calculated as follows:
Face value:
dollar(s) 
Coupon  rate:
 % 
Maturity:
 year(s) 
Yield:
%

How much does the above bond price change when yield change instaneously?

Change in yield: %

The chart bellow shows the affect of instant change in yield to bond prices with fave value, maturity and coupon rate as your inputs above

The Higher the Interest Rate, the Cheaper the Bond Price

For a 10-year bond with a fave value of $100 and a coupon rate of 5% that pays coupons annually, the prices by interest rates are bellow.

The Longer the Maturity, the More Sensitive the Bond Price with Interest Rate

The Higher the Coupon Rate, the More Sensitive the Bond Price with Interest Rate

Assume the maturity is 30 years.

Bond Prices' Sensitivity to Change in Yield

The reasons I want to know the sensitivity to yeild is
  1. Find the downside risk of the bond.
  2. Find the upside potenttial of the bond.
  3. Locate the best price point of the bond in terms of yield, price, coupno rate and maturity.

Bond Price Sensitivity Using the Previsous Put In Data

The following chart is the sensitivity of bond prices relative to the data put in at the begining of this website. The current date are:
  • The face value is $100.
  • The coupon rate is 5%.
  • The maturity is 10 years.
  • The yield is 5%.
  • The sensitivity of bond prices is -679.155..

Yield VS. Bo1d Price Sensitility

Coupon Rate VS. Bond Price Sensitility

The higher the coupone rate the more sensivtive the bond price is when maturity is longer.

Bond Price Sensitivity Math Formula

Bond price sensitility to change in yield is the slope of the price which is first derivitive of the price formulate. The result divided by the bond price is called modified duration.

What about the second derivative?

The above examples show bond prices' seneitivitiy to change in yeidls. But what the rate of change in sensitivity?
The higher the yeild, the samller the rate of change in duration although bond's price are less sensitive when yields are higher. The longer the maturity the rate of change in duration drops faster.
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