Valuation IR Swap - Schweser Example from errata

[Mercutio]

Valuation of derivatives, what a wonderful world! I am struggling to find the error in my computation.

Schweser has provided a correction regarding valuation of a fixed for floating IR Swap, with the formula

((SFR_new - SFR_old)/# of settlements per year) * Sum of discounts * Notional Principal.

I for now would like to reside to to old fashioned doing it by hand version and value the two legs separately.

Swap rate at initiation: 4,4%, for a 1y quarterly pay swap with notional amount of 5*10⁶. Now after 180 days the Libor is flat at 3,5%. Find the current value of the swap at t=180.

Schweser is getting a value of -$22, 209.

When I value the fix leg, I get v_fix=[0,011/(1+ 0,035*90/360) + 1,011/(1+ 0,035*180/360)] * 5*10⁶

v_floating = 5*10⁶, since we have just settled.

This leads to a value of the swap of v = v_floating - v_fix = -$22, 575

Are these just rounding errors / is my approach incorrect at some step?

[S2000magician]

I get $22,582. Your methodology is correct; I don’t know how Schweser is getting their number.

[Mercutio]

For completeness: Schweser is calculating via the formula

((SFR_new - SFR_old)/# of settlements per year) * Sum of discounts * Notional Principal = (0.035 - 0.044)/4 * 1.9741 * 5 * 10^6 = -22,209

where 1.9741 = 0.9913 + 0.9828 = Z_1 + Z_2

As far as I can see no errors in the computation itself, so maybe the formula is a bit of an approximation, or it is indeed some rounding error.

Thank you anyways!!

[wolfpacker88]

In case anyone is struggling with this like I was. S2000magician is almost correct. When discounting the 2 remaining fixed and floating payment leg, be sure to use discount factor 1 for the first legs and discount factor 2 for the second. He likely used the second discount factor for the remaining floating payments 1 and 2.

The two legs look like this:

v_fix=[0,011/(1+ 0,035*90/360) + 1,011/(1+ 0,035*180/360)] * 5*10⁶

v_float=[0,0875/(1+ 0,035*90/360) + 0,0875/(1+ 0,035*180/360)] * 5*10⁶

^{fixed payer pays $22,209 since rates dropped over the 180 days.}

^{Kaplan really should consider explaining their formula shortcuts in a bit more depth.}

All the best!

[S2000magician]

@wolfpacker88

In case anyone is struggling with this like I was. S2000magician is almost correct. When discounting the 2 remaining fixed and floating payment leg, be sure to use discount factor 1 for the first legs and discount factor 2 for the second. He likely used the second discount factor for the remaining floating payments 1 and 2.

The two legs look like this:

v_fix=[0,011/(1+ 0,035*90/360) + 1,011/(1+ 0,035*180/360)] * 5*10⁶

v_float=[0,0875/(1+ 0,035*90/360) + _ 1,011 _/(1+ 0,035*180/360)] * 5*10⁶

^{fixed payer pays $22,209 since rates dropped over the 180 days.}

^{Kaplan really should consider explaining their formula shortcuts in a bit more depth.}

All the best!

How did you get the highlighted number for the floating leg?

[wolfpacker88]

I meant to write 0,0875. I corrected it in my original post. However, I’m still back and forth about this problem. Other solutions to similar problems ignore the last floating cash flow since we don’t know what the future reset will be, even though we do know that par will be 1. If we proceed in this manner, discounting the only cash flow for the floating leg (floating rate coupon + par of 1) by the new 90-day rate, then I arrive at a value of $22,582

[S2000magician]

@wolfpacker88

I meant to write 0,0875. I corrected it in my original post. However, I’m still back and forth about this problem. Other solutions to similar problems ignore the last floating cash flow since we don’t know what the future reset will be, even though _ we do know that par will be 1 _.

That’s the point: the floating leg will reset to par on a settlement date, so you don’t need to know the remaining floating payments.

@wolfpacker88

If we proceed in this manner, discounting the only cash flow for the floating leg (floating rate coupon + par of 1) by the new 90-day rate, then I arrive at a value of $22,582

Which is remarkably close to the value at which I arrived.

Apparently you’re almost correct.

[wolfpacker88]

I’ve benefited from your help enough in the past to know better. This material is hard enough for some of us as it is. Maybe I should give the folks at Schweser a call.

I think I saw you’ll be at the UCI review in a few weeks. I’m looking forward to it.

[S2000magician]

As am I, sir!