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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:
%
The bond's price is $100.00.

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

Change in yield: %
The original bond price is $100.00 and the bond price when tha yield change 0.00000% is 100.00 which is a 0.00000% difference, where the original yield is 5% and the new yield is 5.00000%.

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

āˆ’20āˆ’15āˆ’10āˆ’50510152002004006008001000
Bond Prices vs. Yields(%)Yields(%)Bond Prices

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.
12345690100110120130140
Bond Prices vs. Yields(%)Yields(%)Bond Prices

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

12345680100120140160180200220
maturity of 10 yearsmaturity of 20 yearsmaturity of 30 yearsBond Prices vs. Yields(%)Yields(%)Bond Prices

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

Assume the maturity is 30 years.
123456100200300400500
Coupon Rate 5%Coupon Rate 10%Coupon Rate 15%Bond Prices vs. Yields(%)Yields(%)Bond Prices

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 -779.4581.

Yield VS. Bo1d Price Sensitility

āˆ’5051015āˆ’8000āˆ’6000āˆ’4000āˆ’20000
Maturity: 5 yearsMaturity: 10 yearsMaturity: 20 yearsSensitility vs. Yields(%)Yields(%)Sensitility

Coupon Rate VS. Bond Price Sensitility

The higher the coupone rate the more sensivtive the bond price is when maturity is longer.
āˆ’5051015āˆ’2000āˆ’1500āˆ’1000āˆ’500
Maturity: 5 yearsMaturity: 10 yearsMaturity: 20 yearsSensitility vs. Coupon Rate(%)Coupon Rate(%)Sensitility

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.
āˆ’5051015050k100k150k
Maturity: 5 yearsMaturity: 10 yearsMaturity: 20 yearsRate of Change in Sensitility vs. Yields(%)Yields(%)Rate of Change in Sensitility

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