R19.P1.T3.HULL Ch7 Currency Swap Valuation XLS

[gargi.adhikari]

In reference to R19.P1.T3.FIN_PRODS_HULL_Ch7_Currency_Swap_Valuation
Eg2:-

Currency Swap Valuation -Eg 1 in the prior tab is perfectly good. But I had some questions on the 2nd Example for the Currency Swap Valuation. I see 2 different Net Swap Values for the 2 methodologies - $ 2.71 in the Bond Methodology and $ .6121 in the FRA Method. Also, in The Bond method, the valuation is just for Time = 10...where are the other years..? Why are we not factoring them in..?

Also why are the Time values Row 16 ( F16 to K16 ) = Row 17 ( F17 to K17 ) - 5 ...?

Much gratitude.

 

[David Harper CFA FRM]

Hi @gargi.adhikari It took me a while to figure out how the heck this sheet got so messed up, sorry. I probably need to remove this sheet or clean it up. I finally discovered it was my hasty attempt to answer Hull's Question 7.12, which I probably should not have shared to the learning XLS. Here is Hull's question which I was attempting to answer:

7.12. A financial institution has entered into a 10-year currency swap with company Y. Under the terms of the swap, the financial institution receives interest at 3% per annum in Swiss francs and pays interest at 8% per annum in US dollars. Interest payments are exchanged once a year. The principal amounts are 7 million dollars and 10 million francs. Suppose that company Y declares bankruptcy at the end of year 6, when the exchange rate is $0.80 per franc. What is the cost to the financial institution? Assume that, at the end of year 6, the interest rate is 3% per annum in Swiss francs and 8% per annum in US dollars for all maturities. All interest rates are quoted with annual compounding.

... although I didn't switch the Yen to Swiss francs.
... further, this version commingles annual compound frequency (with respect to inferring forward rates) and continuous frequency (with respect to discounting), so I have adjusted this so that all is annual compounding (because Hull's answer does that).
... you can see now they do match, although it requires further clean up (I did format the currencies).
... Hull's solution gives an answer of 679,800 which I basically have matched (0.680 = 680,000) after, also, realizing that the discounting starts at year 0 rather than year 1; i.e., the default occurs at the end of year 6 and the immediate settlement is not received (this sort of timing issue arises in this sort of problem). The question concerns a 10-year swap that defaults at the end of year 6, so it is solved according to the beginning (time 0) of a 4-year swap.

Here is a revised version https://www.dropbox.com/s/j095cqxai22uhqi/Hull-QA-7-12-currency-swap.xlsx?dl=0

Screen below. I hope that clarifies. Thanks for spotting the mess of an XLS that I had in there, yikes!

 

[gargi.adhikari]

@David Harper CFA FRM Thanks so much as usual for looking into this. Much gratitude Will dig back into this one shortly

 

[gargi.adhikari]

@David Harper CFA FRM Hi -Hope you all had a Happy and blessed Easter ! I was re-visiting this topic and this revised example...
in this example, why are are we discounting at Year 0 instead of Year 1...?

The above explains that-
" The question concerns a 10-year swap that defaults at the end of year 6, so it is solved according to the beginning (time 0) of a 4-year swap."

So why are not just evaluating this as a 4 year Swap starting at the beginning of Year 7..? Why are we factoring in the 6th year's payments as it defaults at the end of Year 6...?

 

[David Harper CFA FRM]

Hi @gargi.adhikari Yes, it's a good question: this is a classic issue raised (which has been raised here in the forum many times over the years, especially when the questions are imprecise) around the case of a question about an interest rate swap that defaults on the swap payment date. My view is that your suggested alternative approach is not incorrect; it's not Hull's solution, but the problem that we've observed (in my opinion but confirmed over years of conversation here in the forum) is that technically this assumption is ambiguous that states "Suppose that company Y declares bankruptcy at the end of year 6" because it does not explicitly state whether the payment (coupon) exchange at the end of year 6 has been completed or not. For this reason, our feedback (to GARP) and our view is that the question needs to explicitly say something, in a situation like this, like ""Suppose that company Y declares bankruptcy at the end of year 6 but immediately before the imminent exchange of end-of-year swap payments." Because, you are correct to suggest that, if the question wrote something like "Suppose that company Y declares bankruptcy at the end of year 6 immediately after the (end-of-year) exchange of swap payments," then this should be valued "as-if" it were a swap with four years remaining (which is true regardless) and four cash flows (instead of five given by the solution because year zero is included). This question makes an assumption, so i would consider it imprecise.

This typically arises in credit exposure questions because, you will notice, this question may as well be a current (credit) exposure question. What I mean is that the imminent cash flow exchange (at the end of year six) is -$320,000 to the financial institution (ie, at the end of year 6, the FI is paying $560,000 and receiving USD-after-translated $240,000, for a net cash outflow of -$320,000). If the counterparty defaults after this exchange, the "cost" to the FI becomes $1.0 MM, and that would also be the FI's current exposure at that time. (but notice how that fits!? In that case, the FI would have just paid an additional net $320,000 toward which is sort of like an "investment into" the final swap where it regains its value).

So I do agree with you, this assumption here matters. FWIW, here is an example from the handbook https://forum.bionicturtle.com/threads/interest-rate-swap.5782 where the assumption is not given; in this case, because the default happens to be on the first coupon, it's the one time where it actually doesn't matter because it's not a currency swap and the first coupon exchange nets to zero, anyway. I hope this helps! Thanks,

 

[gargi.adhikari]

Got it @David Harper CFA FRM Thanks so much for the clarity on this !

 

[gargi.adhikari]

I was revisiting this topic-Eg 2 of Currency Swap and had a follow up question -Please refer to the screenshot below:-

Below we are trying to find the Swap Value using the Bond Method -that is, treating the Domestic and Foreign Cash Flows as 2 Bonds as illustrated below.

However, in order to save time in the exam I was trying to trying to find the Bond Values using the Calculator plugging in the values as:-
For the 1st Bond-Value: N=4 , I/Y = 8% , PMT = 560,000, FV= 7,000,000 => CPT PV- But I am getting PV as 7,000,000 instead of $ 7.56 Mil
For the 2nd Bond-Value: N=4 , I/Y = 3% , PMT = 30,000, FV= 10,000,000 => CPT PV- But I am getting PV as 7,449,662 instead of $ 10.3 Mil

What am I missing here ...?

 

[Nicole Seaman]

I was revisiting this topic-Eg 2 of Currency Swap and had a follow up question -Please refer to the screenshot below:-

Below we are trying to find the Swap Value using the Bond Method -that is, treating the Domestic and Foreign Cash Flows as 2 Bonds as illustrated below.

However, in order to save time in the exam I was trying to trying to find the Bond Values using the Calculator plugging in the values as:-
For the 1st Bond-Value: N=4 , I/Y = 8% , PMT = 560,000, FV= 7,000,000 => CPT PV- But I am getting PV as 7,000,000 instead of $ 7.56 Mil
For the 2nd Bond-Value: N=4 , I/Y = 3% , PMT = 30,000, FV= 10,000,000 => CPT PV- But I am getting PV as 7,449,662 instead of $ 10.3 Mil

What am I missing here ...?

View attachment 1671

Hello @gargi.adhikari

Here are a few other threads in the forum that might help you:

• https://forum.bionicturtle.com/thre...-bond-prices-hull-chapter-6.10627/#post-51741
  
• https://forum.bionicturtle.com/threads/practice-to-find-spot-rate-for-bonds.9406/#post-40844
  
• https://forum.bionicturtle.com/thre...nd-zero-coupon-bonds-fabozzi.8837/#post-36982
  
• https://forum.bionicturtle.com/threads/which-calculator-do-you-recommend.6577/#post-21648 (this has some discussion on bond functions)

 

[gargi.adhikari]

Thanks @Nicole Seaman for the links above - I did check them out... I was trying to use the same techniques to calculate the Prices of the 2 Bonds for the Currency Swap Valuation- but the answer I am getting is way different than if worked out by hand somehow....and so I was trying to see if I was plugging some no wrong or was it because the PMT = 560,000 is such a minuscule fraction of the FV Value of $7 Mil that the calculator is approximating the Bond Price to 7 Mil.

I also am getting the 2nd Bond Price as 7,449,662 instead of $ 10.3 Mil


I did try changing the Decimal Precision settings on my calculator to different decimal places- but that did not help....what else am I doing wrong- because for Currency Swap Valuations in the exam I would prefer to use the Bond approach and then would prefer to find the Bond Prices on the calculator (instead of spending time on doing them manually)and then just find the Net Swap value as the difference of those 2 Bond prices..

 

[David Harper CFA FRM]

@gargi.adhikari your TVM assumes the first payment at the end of the first year (aka, end-of-payments, or in arrears) but notice how the first 560,000 pays immediately and has the same PV. So your timing doesn't match. I'm in a total rush at the moment but if i get a chance i'll post later with keystrokes. The beginning/end is changed in the calculator with: [2nd] [BGN] [2nd] [SET]

 

[gargi.adhikari]

SPOT ON !! THANKS YOU !! I see the point I was missing !! THANK YOU !!