1. Derive the formula for pricing a coupon bond that pays a coupon at the end of each period. What will the formula be if the coupons are paid at the beginning of each period (i.e. you receive a coupon immediately after you acquired the bond and only receive the face value when it matures).
The price of a bond is the PV of the expected cash flows from the |
bond if it is held till maturity, the discount rate being the market |
rate of interest (market rate may be different from the coupon rate) |
The expected cash flows from the bond are: |
1) The maturity value of the bond, which may be equal to the face |
value of the bond, and the |
2) The periodic interest payment stream which constitutes an |
annuity. The annuity may be an ordinary annuity or an annuity due. |
The formulae for finding out the price of bond would then be: |
the sum of: |
1) PV of the MV given by MV/(1+r)^n and |
2) PV of the periodic interest payments given by: |
*In the case where the interest payments are made |
at the end of each period (ordinary annuity): |
= I*((1+r)^n-1))/((r*(1+r)^n)). [This is the formula for finding |
the PV of an ordinary annuity] |
*In the case where the interest payments are made |
at the end of beginning of each period (annuity due): |
= I*r*((1+r)^n-1))/((r*(1+r)^n)). |
[This is the formula for finding PV of an annuity due] |
Where, |
MV = market value |
n = number of periods (can be year or part of the year) |
r = market rate of interest (per year or part of the year) |
I = interest in $ for a period, which is face value * |
coupon rate for a year or part of a year as the case may |
Hence, we may write the formula for the price of a bond |
as: |
1) Where the coupons are paid at the end of each |
period, |
Price of the bond = MV/(1+r)^n+= I*((1+r)^n-1))/((r*(1+r)^n)) |
2) Where the coupons are paid at the beginning of each |
period, |
Price of the bond = MV/(1+r)^n+= I*r*((1+r)^n-1))/((r*(1+r)^n)) |
1. Derive the formula for pricing a coupon bond that pays a coupon at the end...
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