Spot Rates & Discount Factors

Spot Rates & Discount Factors

The rational spine of the curve is the discount factor.

highlighted = computed this step

Spot rates to discount factors

A spot rate belongs to one maturity. For year 1, the spot rate is exact 1/24, shown rounded as 4.17%. Its discount factor is 24/25.

dt=1(1+st)td_t=\frac{1}{(1+s_t)^t}

Price a zero

A zero-coupon payment of $100.00 in year 1 is worth $96.00 today because the discount factor is 24/25.

PV=$100.00⋅24/25=$96.00\text{PV}=\$100.00\cdot 24/25=\$96.00
Zero price from the curveThe discount factor prices one future payment.Zero-coupon pricingPeriodCash flowDiscount factorPV1$100.0024/25$96.00Price = Σ CF × d$96.00

Curve inputs

This curve is a set of stated model inputs. It ignores credit spreads, liquidity spreads, taxes, and trading frictions.

discount factors are model inputs here\text{discount factors are model inputs here}