# How to calculate this swap rate

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

• any comment guys ? – Dylan Zhu Jun 5 '16 at 15:32
• 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. – Ric Jun 6 '16 at 7:31

## 2 Answers

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.

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%