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What's the difference between a spot curve and a par curve?

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posted Jul 10 by Vijay

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1 Answer

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At the risk of being too concise and omitting the exhaustive development that characterizes many popular Quora answers to avoid (perhaps) needlessly introducing the taxonomy of interest rates in the hope that you already have foundational knowledge in things like present value, discount rates, bond pricing, etc., the short answer is...

the spot curve (or zero-coupon curve), unlike the par curve, reflects the term structure of interest rates absent re-investment risk/assumption.

There's an implicit assumption that coupon payments, when received, are re-invested at the contemporaneous-maturity, spot yield, which is almost never true. The assumption is avoided in the spot (zero-coupon) curve since there are no coupons to re-invest. The spot and par yield curves are related via:

cn=1−1(1+rn)n∑nk=11(1+rk)kcn=1−1(1+rn)n∑k=1n1(1+rk)k

where cncn is the par yield at maturity (tenor) nn and rkrk is the spot yield at tenor kk.

answer Jul 11 by Tanmay
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