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OneBasisPoint
Topic Author
Posts: 3
Joined: February 4th, 2020, 4:22 pm

Basic curve building - estimation curve

April 4th, 2022, 2:14 pm

Hi,
can't get my head round this - trying to duplicate values generated by a computer system, building an IR curve, calibrating by 3M currency swaps, say TRY-USD.
The curve in question is used as the estimation curve, with another TRY curve for discounting.
I've managed to find all the currency swap coupon rates on the TRY legs that make them par when discounted with the other TRY curve.
For the first, 1M pillar, I can just convert the coupon rate from linear to continuous compound and I get the first zero rate.
For the second, 2M pillar that doesn't match.
I can't quite get the correct way to think about it - don't quite get what the coupon rate represents, and how I should calc the next zero rates - some kind of bootstrap?
31 day coupon rate = -0.11340; zero rate = -0.1139546714 = ln(1+(cpn rate)*(day count))/(day count)
61 day coupon rate  = -0.054675; zero rate = -0.0558783977 ???
forward linear interpolation
Any help gratefully received!!
 
Mercadian
Posts: 37
Joined: July 24th, 2020, 4:22 pm

Re: Basic curve building - estimation curve

April 5th, 2022, 2:14 pm

Hey 1bp,

Do you think you can add a couple of screenshots of what you're looking at? a picture is worth a thousand words.

Some questions that might help:

1. Is it a USD-TRY FX Curve? built with Xccy Swaps? or FX Swaps? both?
2. What do you consider your base/funding/risk-free currency? USD or TRY? is it onshore/offshore Turkey?
3. What curve do you use to compute FX Forward Rates? is it the same curve?
4. What is the interpolation method and over which variable?
5. Do you have the following data you could share:

- FX Spot Rate (spot delay)
- Curve Instrument details (start delay, payment frequency, rate conventions)
- Par and target zero rates

Rgds,
M
 
OneBasisPoint
Topic Author
Posts: 3
Joined: February 4th, 2020, 4:22 pm

Re: Basic curve building - estimation curve

April 5th, 2022, 5:26 pm

Hey 1bp,

Do you think you can add a couple of screenshots of what you're looking at? a picture is worth a thousand words.

Some questions that might help:

1. Is it a USD-TRY FX Curve? built with Xccy Swaps? or FX Swaps? both?
2. What do you consider your base/funding/risk-free currency? USD or TRY? is it onshore/offshore Turkey?
3. What curve do you use to compute FX Forward Rates? is it the same curve?
4. What is the interpolation method and over which variable?
5. Do you have the following data you could share:

- FX Spot Rate (spot delay)
- Curve Instrument details (start delay, payment frequency, rate conventions)
- Par and target zero rates

Rgds,
M
Hi Mercadian,
thanks for your interest - I actually found the problem myself - basically a few things like, discount the pillar instrument cashflows to the spot date of the pillar instrument start date, plus use the correct day count conventions, plus use the proper interpolation formula for points between the previously-derived rates.
In short a lot of dull detail but got most pillars to accuracy 10^-8 and better, just got the long end out past 10 years to debug.
many thanks,
OneBasisPoint
 
 
Mercadian
Posts: 37
Joined: July 24th, 2020, 4:22 pm

Re: Basic curve building - estimation curve

April 5th, 2022, 6:37 pm

Hey 1bp,

Great to hear, curious about what system you were using is it a Vendor solution or inhouse? 

Rgds,
M
 
OneBasisPoint
Topic Author
Posts: 3
Joined: February 4th, 2020, 4:22 pm

Re: Basic curve building - estimation curve

April 11th, 2022, 5:36 pm

Hey 1bp,

Great to hear, curious about what system you were using is it a Vendor solution or inhouse? 

Rgds,
M
Hi - it is Vendor - Murex.
Actually still stuck on something - I have 3M coupons that I'm using to generate a forward estimation curve, for <3M I just convert the coupon rate from simple to continuous compounding, calc the discount factor over the coupon length, mult by the discount factor between the start of the curve and the start of the coupon, and convert that back into a continuous compounded rate.
Unfortunately that doesn't match for >3M pillars, there's then more than 1 coupon, my calc  doesn't work - tried several things but no joy.
Some figures;
Curve date 17/03/2022

The first 4 pillars are, just cpns;
start;end;curve output DF;curve output rate;instrument coupon rate
18/03/2022;18/04/2022;1.010040619;-11.39546714;-11.3405
18/03/2022;18/05/2022;1.009536862;-5.58783977;-5.4675
18/03/2022;21/06/2022;1.004647416;-1.762892873;-1.65791
18/03/2022;18/07/2022;0.990829309;2.733939251;7.776955288

4M pillar instrument has 2 cpns - flow is calculated from coupon rate just nominal*(rate+margin)*time;
start;end;nominal;flow;coupon rate;margin
18/03/2022;18/04/2022;102,250,000;-3,724,406.75;-11.3405;54.22743
18/04/2022;18/07/2022;102,250,000;-15,806,446.69;7.776955288;54.22743

The curve output that I'm trying to match is;
offset days;discount factor;rate
32;1.065496376;-11.39546714
62;1.117108784;-5.58783977
96;1.165126197;-1.762892873
123;1.185361274;2.733939251

Tried things like adding the 2 coupon flows & finding the average rate that gives the same total etc etc but not sure what I'm doing.
For the 1st 3 pillars the curve rate is Ln(1+(cpn rate)/100*(cpn length)/365); convert to discount factor exp(-rate*(cpn length)/100) adjust by 1 day (17-18th = 1.000312253) then convert back to continuous compounding rate (using (17th-cpn end)/365) to get the curve output rate.

That doesn't work for the 4M pillar with 2 coupons.
Any help gratefully received
best regards,
1BP