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Value a forward-starting coupon schedule

A year-one value uses relative factors D2/D1 and D3/D1 for payments due at years two and three.

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Specify what is being valued

A fictional schedule pays 5 at year two and 105 at year three, with no payment at year one. Compute its curve-implied value at year one, then convert that value back to today. This is a stated future settlement-value calculation, not an observed future market price.

Use factors relative to the valuation date

With today’s factors from 4%, 5%, 6% annual zeros, the year-one value is 5D2/D1 + 105D3/D1 = 96.402979. These ratios discount from the payment dates to year one under the implied curve.

V1=5D2D1+105D3D1V_1=5\frac{D_2}{D_1}+105\frac{D_3}{D_1}

The schedule contains only the year-two and year-three payments.

Return to today

Multiplying V1 by D1 gives 92.695172, equal to pricing the two payments directly today. The year-one date is a valuation date, not an extra 5 coupon. Adding a payment there would change the contract.

Label the forward-implied value

Future realized valuation will depend on information and the curve then prevailing. The present curve fixes this conditional forward calculation; it does not establish what a buyer will quote at year one. Keep contractual settlement terms separate from a price forecast.

Further references