Expected Exposure Calculation

Can someone please help me understand how did we calculate these Expected Exposures values? I’m not getting it via spot rates or forward rates as mentioned in exhibit 9-10. I’m stuck at this exposures calculation.

@S2000magician could you please help?

It’s the weighted average of the bond values (plus coupon) in the binomial tree used to value the bond.

Here, they don’t give you the tree, so you can’t compute those values yourself.

If you go back to Exhibits 12 and 13, you can see how it’s done. In Exhibit 12, at time t = 1, there are two possible bond values – 98.4920 and 101.0803 – each with a weight of 1/2, plus a coupon of 3.50. The expected exposure is:

\left(\frac12\right)98.4920 + \left(\frac12\right)101.0803 + 3.50 = 103.2862

which is the value we see in Exhibit 3 at time t = 1.

Note that at time t = 2, the weights are 1/4, 1/2, and 1/4, respectively: one path to get to 95.6703, two paths to get to 98.1435, and one path to get to 100.2352. The expected exposure is:

\left(\frac14\right)95.6703 + \left(\frac12\right)98.1435 + \left(\frac14\right)100.2352 + 3.50 = 101.5481

which is the value we see in Exhibit 3 at time t = 2.

At time t = 3, the weights will be, in order, 1/8, 3/8, 3/8, and 1/8.

And so on.

I wrote an article on this: Valuing Risky Bonds | Financial Exam Help 123

You can get access to it (as well as all of my other articles on Level II Fixed Income) here: CFA® Level II Fixed Income Membership | Financial Exam Help 123

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Thanks Bill, it is much helpful. :slightly_smiling_face:

My pleasure.

Good to hear.