Bond Pricing Function Details
You can use the GovBondPrc function to value corporate bonds and government bonds. The following variables are required to calculate the value of a given bond:
- ValDate – the date from which the bond is valued, also known as the valuation date. For example, if you want to calculate today’s value of a bond, set ValDate to today’s date. You can also evaluate the bond at dates in the past or in the future within the life of the bond. However, setting ValDate to a date after the maturity date results in a valuation of 0.
- ParValue – the face value of the bond, denominated in the same currency in which the bond was issued.
- Freq – the number of months between coupon payments. For example, if payments are made semi-annually, then freg=6. Freq can be any integer from 1 to 12. If the bond has no coupon, set freq=1.
- Coupon – the coupon rate per annum for the bond in decimal form. For example, if a bond has a coupon rate of 5%, then coupon=0.05. If the bond has no coupon, set coupon=0.00.
- MatDate – the date on which the bond matures.
- SpotVal[*] – an array that contains the spot value of interest rates of different maturities. For example, if a three-month interest rate has a value of 4%, then spotval=0.04. SpotVal can have from 1 to 50 elements.
- Maturity[*] – an array that contains the maturities for the interest rates found in SpotVal, measured in years. For example, a three-month interest rate has maturity=0.25. Maturity can have from 1 to 50 elements.
To price a bond, the GovBondPrc function first calculates the present value of any coupon payments. Coupon payments are discounted to the valuation date, based on the assumption of continuous compounding. After the coupons have been discounted, the present value of the par value is calculated. The price of the bond is the sum of the present values of the coupon payments and the present value of the par value.
For zero coupon bonds (such as US Treasury strips), the value of the bond is the present value of the par value. To value zero coupon bonds, set freq=1 and coupon=0.00. Because interest rates of different maturities have different values, the present value calculations of the coupon payments should be made with the interest rates of the appropriate maturity.
To understand how the GovBondPrc function works, consider a corporate bond with a par value of $100,000 and a one-year maturity. The bond has a coupon rate of 5%, and coupon payments are made semi-annually. Assume that the six-month maturity interest rate is 3% and that the one-year maturity interest rate is 5%. The value of this bond on the day on which it was issued would be as follows:
The GovBondPrc function has the ability to discount coupons over time periods shorter than the full time period. For example, suppose that you want to determine how much the same corporate bond is worth two months after it has been issued. At that time, there are four months remaining until the next coupon payment. The GovBondPrc function automatically accounts for the irregular payment interval and calculates the correct present value for that coupon payment.
To calculate the present value of a coupon payment, you must specify an interest rate with the correct maturity. For example, suppose that SpotVal contains spot values for a three-month and a twelve-month interest rate. If the next coupon payment occurs in five months from the valuation date, neither rate is appropriate for finding the present value. The GovBondPrc function calculates an appropriate rate using linear interpolation.
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