Currency swap and CTD

[prasadhegde1]

Hi David

Could you please help me understand the cheapest to deliver (CTD) bond , I am finding it hard to see the intuition.

Also I was reading Hull - Chapter 7 Swaps in the currency swaps section Valuation of currency swaps in terms of bond prices I somehow find that there is some problem with the formula

Vswap= Bd - So Bf

where as Bd is value measured in domestic currency defined by domestic cashflows

Bf = value measured in foreign currency defined by foreign cashflows
So = Spot exchange rate (expressed as number of dollars per unit of foreign currency )

but as per a illustration given by Hull the formula states as Vswap = Bd - Bf / So

bc to get the value of the swap the foreign currency has to be converted in terms of USD .

Am I missing something here ?

 

[David Harper CFA FRM]

Hi prasad,

Hi

The CTD is a bit involved, but last year I recorded two brief freebies:
http://www.bionicturtle.com/learn/article/conversion_factor_for_treasury_bond_futures_contract_7_min_screencast/
http://www.bionicturtle.com/learn/article/cheapest_to_deliver_ctd_bond_6_min_screencast/

If we step back, the basic idea is:

Unlike most futures, the short can "select" the "commodity" to deliver (in this case the short selects among several eligible bonds)

Why many eligible? Tuckman Ch 20 gives much better detail; e.g., "The design of bond futures contracts purposely avoids a single underlying security. One reason for this is that if the single underlying bond should lose liquidity, perhaps because it has been accumulated over time by buy-and-hold investors and institutions, then the futures contract would lose its liquidity as well. Another reason for avoiding a single underlying bond is the possibility of a squeeze."

Then, I think my brief video above does a decent job of showing: the short must purchase a bond to deliver, then delivers that bond and receives [settlement * CF]. In a nutshell, the short wants to maximize benefit/cost.

On the currency swap formula, i don't recognize the instance but I am confident it is just a ratio change: both of the formula can be correct. Both of these are correct:

Vswap= Bd - S0 * Bf
Vswap= Bd - Bf / S0

If in the first, S0 = USD $ / 1 unit foreign, and
in the second, S0 = Foreign / 1 USD$

see how the illustration, instead of multiply, is dividing by reciprocal (we can express the spot either way)? You know you want dollars, so Bf needs to multiply by $/foreign in order for the foreign to cancel...

Hope that helps

David

 

[SURAJM]

Hi David,

One of the difficulties that i have faced with your website is that you have lots of useful articles from past year out there but its very difficult to find them because there is no index to search for .

Suraj

 

[David Harper CFA FRM]

Hi Suraj - I agree, our developer starts a third round of site changes this week, and this includes relating/tagging entries. So after he adds some technical functionality then we will reactroactively tag and I hope to improve this greatly (alas it cannot be done for the forums, I wanted to tag forum threads too)...David