Price & Yield

Par, Premium & Discount

The same fixed bond at different yields can trade above face, at face, or below face value.

highlighted = computed this step

Yield and price direction

For the same bond, yield and price move in opposite directions. At 10% the price is $1,000.00; at 5% the price is $1,136.16; at 20% the price is $789.35.

$1,000.00,$1,136.16,$789.35\$1,000.00,\$1,136.16,\$789.35
Par, premium, and discountSame bond, different yields.PeriodCouponPrincipalCash flowPV1$100.00$0.00$100.00$95.242$100.00$0.00$100.00$90.703$100.00$1,000.00$1,100.00$950.22Price = Σ PV$1,136.16

Exact premium-price fraction

The exact premium-yield price in cents is 1052200000/9261, which rounds half-up to $1,136.16 at this display level.

1052200000/92611052200000/9261

Conventions

This book uses one fixed yield and fixed timing. Real prices also depend on spread assumptions, liquidity, and model choice. Institutions or regulations may use different rounding and disclosure conventions.

P>face: premium, P=face: par, P<face: discount\text{P>face: premium,\\ P=face: par,\\ P<face: discount}