Bootstrapping Discount Factors from Deposits, FRAs, and Swaps

Summary

The document raises a practical curve-building question: how to bootstrap discount factors from a deposit, forward rate agreements, and longer-dated swap quotes. The student reports discount factors for the short instruments but is unsure how to derive the two-year and three-year swap discount factors, using a stated start date and day-count convention.

The response points to a reference on interest-rate swaps and flags that the quoted two-year swap rate appears inconsistent with the earlier forward rates. It uses a simple average as an intuition check and asks what the implied forward rate would need to be. No swap cash-flow schedule, payment frequency, day-count details for the swaps, or step-by-step bootstrap is provided, so the quoted information is insufficient to reproduce the requested discount factors. The main lesson is to check quote consistency and instrument conventions before solving the swap equations.

Key ideas

• Swap discount factors are bootstrapped using the swap's scheduled cash flows and market conventions.
• The response recommends checking whether longer swap quotes are plausible given earlier deposit and forward rates.
• A simple average can serve as a rough intuition check, but it does not replace curve bootstrapping.
• The document does not provide enough swap conventions or calculations to determine the requested discount factors.

Tags

# Curve building for a swap


# Curve building for a swap












I'm a student learning how to build a swap curve, I've deposit 6m rate = 5%, fra 6-12m rate = 5.8% and 12m-18m rate= 6% and swap 2y =7% and 3y swap rate = 7.5%. I get the correct discount factors for the deposit and fras but for swaps I get wrong values..

DF6m =0.97547758 DF6-12m =0.94709626 DF12-18m =0.91921345 DF 2y swap =?? DF 3y swap =??

For this example starting date is 10/09/2010 using day conv act/360. Can you help me get the right discount factors for 2y and 3y swaps. or direct me to book with examples of curve buildings ? thank you

## Answer by user42108 (score 1)

https://quant.stackexchange.com/a/49454

Try Howard Corb's book ["Interest Rate Swaps and Other Derivatives", Columbia Business School Publishing, 2012].

And your 2y rate looks odd which should be intuitively obvious - simple arithmetic mean of your 6m, 6mf6m and 12mf6m rates is 5.6%. What does that suggest about your 18mf6m rate for the 2y rate to be 7%?!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.