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What is the 2x5 swap rate? here 2x5 swap rate refers to the 3-year swap, 2 years forward.

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  • $\begingroup$ any comment guys ? $\endgroup$
    – Dylan Zhu
    Jun 5, 2016 at 15:32
  • $\begingroup$ this is homework, right? What about: bootstrapping the yield curve and then applying the formula for the fair rate in a forward starting swap? If you google the terms then you find the formulas. $\endgroup$
    – Richi Wa
    Jun 6, 2016 at 7:31

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Give or take, should be 6.50%. I got this result by applying (5 * 5y swap - 2 * 2y swap) / (5 - 2). Clearly this is not exact and I feel a bit ashamed to publish it on a quant forum.

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Assuming these are par rates for annual swaps, if you bootstrap the curve with DF = (1 - par * sum of dfs from prev annual payments) / (1 + par), you get:

1y 0.952381
2y 0.902613
3y 0.851161
4y 0.798483
5y 0.745020

The 2y3y swap rate would be (df2y - df5y) / sum(df3y, df4y, df5y), i.e., 6.581%

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