Example 6.3 credit risk measurement and management : computing z spread

[Bernard57950]

Hello,

May someone help me with the 6.3 example regarding the computation of the spread 01 (p.155).

In fact, I don't understand the way it is calculated.

0.07/2 * e-(0.0347+0.04605-0.00005)i1/2 + e-(0.0347+0.04605-0.00005)*5

Where i = 2 to 5?

I don't manage to find the results could someone detail the way of doing it?

Thank you very much for your help

Best regards

Bernard

 

[Nicole Seaman]

Hello,

May someone help me with the 6.3 example regarding the computation of the spread 01 (p.155).

In fact, I don't understand the way it is calculated.

0.07/2 * e-(0.0347+0.04605-0.00005)i1/2 + e-(0.0347+0.04605-0.00005)*5

Where i = 2 to 5?

I don't manage to find the results could someone detail the way of doing it?

Thank you very much for your help

Best regards

Bernard

Hello @Bernard57950

It is helpful for us if you let us know which reading you are referring to and if you are referencing our BT notes or the GARP books. We just don't have a lot of time to search for the reading that is being referenced in the question, especially with the exam getting close.

Thank you,

Nicole

 

[Bernard57950]

Hello,

Thank you very much for your answer.

I totally understand and should have mentioned that I made reference to the garp book, FRM Part 2, Credit Risk Measurement and Management, page 155 (chapter 6 : spread risk and default intensity models), example 6.3.

Thank you very much for your help.

Best regards;

Bernard

 

[David Harper CFA FRM]

Hi @Bernard57950 First Malz finds the z-spread in example 7.2, please see my screenshot below. Given an observed trading price of 95.00 the z-spread is the value that adds to the riskfree spot rate of 3.47% such that the cash flows, when discounted at (3.47% + Z-spread) equal the observed price of $95.00; see sum of PV = $95.00 below. The coupon cash flows are $3.50 every six months so that discounted continuously that PV = $3.50 * exp[-(r + Z)*T]. The final cash flows includes the principal so its PV = $103.50 * exp[-(3.47% Rf + 4.605% Z-spread)*5.0 years] = $69.12.

Then the spread 01 simply shocks the discount rate by +/- 0.5 basis points, see final four columns. For example, the final cash flow:

• PV (shock - .5 bps) = $103.50 * exp[-(3.47% Rf + 4.605% Z-spread - 0.0050%)*5.0 years] = $69.1335,
• PV (shock + .5 bps) = $103.50 * exp[-(3.47% Rf + 4.605% Z-spread + 0.0050%)*5.0 years] = $69.1009. I hope that helps!

 

[Bernard57950]

Hello David,

Thank you very much for this really clear answer.

Thanks to your excel table, I have totally understood the concept.

The Z-spread has to be found by iteration (example 7.2), then regarding the example 7.3, we can calculate different bonds values considering an increase/decrease of the spread of 0.5 bp. This Z-spread has to be added to the rf rate so that we can find the bond's price, the later being the sum of the present values of the cash inflows : " the z spread being the spread that must be added to the Libor spot curve to arrive at the market price of the bond".

By the way, I enjoy this opportunity to thank you for all your Youtube videos covering many different financial topics. They have always been very helpful for me.

Best regards,

Bernard

 

[Gasthron]

Hi David,
I was wondering how you calculated the spot rate. Would be great if you or someone else could explain.

Thank you in advance!

 

[David Harper CFA FRM]

Hi @Gasthron My XLS above is just my replication of Malz Ex 7.2 and, for him, it's just a compound frequency adjustment: LN(1+3.50%/2)*2 = 3.47%. So, without checking the text, it looks like he assumes a flat 3.50% semi-annual yield curve. A flat yield curve is a common assumption with high convenience because swap = spot = forward = yield when the curve is flat (huge simplification!). So this is just translating a (discrete) semi-annual 3.50% into a continuous 3.47% which is used in the PV.

For the more sophisticated translation of swap rate (aka, par yield) to spot/discount factor, I recently performed that math (see the XLS) at https://forum.bionicturtle.com/thre...rsus-spot-rates-tuckman-ch-2.22090/post-90249