Bond Pricing

Bond Pricing

A bond is a fixed-income instrument that pays periodic coupon payments and returns the face value at maturity.

Bond Price Formula

$P = \sum_{t=1}^{n} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^n}$

Where:

• $P$ = bond price
• $C$ = coupon payment = Face × Coupon Rate
• $F$ = face value (par value)
• $y$ = yield to maturity (YTM)
• $n$ = number of periods

Price vs. Yield Relationship

• At par: Coupon rate = YTM → Price = Face value
• At discount: Coupon rate < YTM → Price < Face value
• At premium: Coupon rate > YTM → Price > Face value

Example

Bond: Face = 1000, Coupon = 5%, YTM = 6%, 10 years: $$P = \sum_{t=1}^{10} \frac{50}{1.06^t} + \frac{1000}{1.06^{10}} = \926.40$$

The bond trades at a discount because its coupon (5%) is below the market yield (6%).