Credit Default Swaps: Valuation

CDS valuation is done by calculating the ‘survival probability curve’.
The ‘survival probability curve’ is the very fundamental tool which gives market implied probabilities of reference entity that it doesn’t suffer a credit event prior to a give time horizon.

Lets do the maths

After every spread being paid by the protection buyer two things might happen:
1. Survival – which gives you a probability value of 1-q i.e. the reference entity survives for one more period.
2. Default – which gives you a probability value of q event occurred with deliverable obligation trading at the recovery value of R.

Probabilities build up stage

Situation            Payment               Probability          Probability of survival    Probability of Event
Survival            -s  (spread)                        1-q(1)                  p(1)*{1-q(1)}                  1-p(1)
Credit event     (1-R)-s                   q(1)

Survival            -s  (spread)                        1-q(2)                   p(2)*{1-q(2)}                 p(1)-p(2)
Credit event     (1-R)-s                   q(2)

Hence, when you calculate the NPV of a CDS then formula goes like this:

NPV= Summation {(1-R)*( probability of credit event )* risk free discount} – Summation { cash flow during survival) * probability of survival * risk free discount}
NPV= Summation [ (1-R)* { p( i-1 )-p( i ) } * d ( i ) – Summation [ s *p ( i -1 )* d( i ) ]

Here, (1-R) is assumed loss in default and d ( i ) is LIBOR

consider at t=1, NVP = 0 then solving the equation will give you  q (1) =   s

This equation tells the conditional default probability on the spread.

Lets assume 1 year  CDS at 50 bps spread having recovery (R) at 50%, what would be the probability of survival or default ?

q(1)= 0.005/(1-0.5)= 0.01

thus p(1)= 1-q(1) = 1-0.01
= 99% is the probability of survival.

So, we got to know how to calculate NPV on CDS, probability of survival on which we can make series of probabilities thus the ‘survival probability curve’ as well.


Credit Default Swaps: Trading mechanism

What is CDS?

CDS stands for credit default swap; a bilateral over-the-counter derivative contract. It transfers the risk of the loss on the face value of a reference debt issuer over a specified period (underlying asset). The core idea in CDS is to isolate the credit risk from potential default, interest rate and foreign exchange risks. One interesting point, you may enter the CDS contact even if you do not own any credit asset/ reference asset.

The trading mechanism:

When you trade in CDS there are few term which are universal and must be known.
Reference Entity-The corporate or sovereign whose credit risk is transferred.
Term– Time period of the contract/ maturity date.
Notional Amount– Amount of credit (money) being under the contact for protection i.e. $10 million. A standard contact will have $10 million as notional amount.
Premium– The money being paid by the protection buyer to the protection seller. In trading term it is known as “spread”.
Credit Event– An event of default.

Once the protection buyer enters the contact he/she makes timely payments to the protection seller which is called “spread”. The spread is calculated on notional amount of the contact. When the contract ends i.e. at the end of maturity or in case of credit event the buyer stops premium payment aka spread to the seller.

There are two mode of settlement- 1) Physical and 2) cash.
In physical settlement, buyer delivers a basket of deliverable obligations with face value equal to the notional to the seller in exchange of Notional amount ( in simple term buyer has to deliver the bond). While in cash settlement, seller pays notional minus price assigned to the reference obligation ( in simple term seller will pay notional minus recovery rate aka existing spread on the CDS).


To make it more clear, lets assume you buy a protection on $10mln at 100 bps. Now the next day spread widens to 150 bps. So, in mark to market term you made a profit of :

$10mln* (0.0150-0.0100)*4.10= $205,150
Notional amount*(change in spread)*spread PV01

Note: Spread PV01 is the change in CDS value caused by a 1basis point of spread move; a tedious calculation. Spread PV for particular CDS are available in many financial databases.

Tomorrow we will have calculation of spread PV and CDS pricing in detail. Keep reading!

Fee-based income holds the key for Banking system

ImageIn the era of quantitative easing and significant market competition, maintaining profitability through interest-based income is becoming very tough for banks. In the last two decades, interest margins have come under tremendous pressure. In modern times, banks prefer non-interest income i.e. fee based income to drive profitability and return on capital.

The 2008 financial crisis was a big blow for banks, especially for those depending broadly on interest-based income. As the global economic recovery still looks fragile, banks are finding it hard to do loan- and mortgage-based business i.e. interest-based business. The ultra-low central bank interest rate regime was supposed to spur economic activity, as it (theoretically) supports more lending activity, but many banks are hesitant in lending due to potential bad loan losses and slow demand for loans. It would be worth to mention the ultra-low interest rate regime has also dampened savings account activities in banks.

Most of the fee-based incomes (advisory and management fees) are fairly risk-free, as these services don’t involve significant capital investment.

In recent times, banks have reported handsome revenues from fee-based income; thanks to the spur in M&A activities and private equity deals (mainly in US). Since we are living in a globalized society, there are no boundaries for banks and they can reach out to any corner of the world, thus making many potential M&A and private equity activities lucrative.

It would be pertinent to mention that fee-based driven income cushions banks against market competition. In coming days, implementation of new banking rules and regulations are going to take a paradigm shift (Dodd Frank rule, Basel III). This might curb the freedom of leverage banks take on their reserves and provisions, which in turn will leave banks with limited capital or liquidity to do the traditional business of loans and advances –further constraining interest-based income.

Fee-based income is more volatile than interest-based income, but a range of services like wealth management, transaction banking, treasury, and investment banking are covered under fee-based income. The wide spectrum of fee-based service provides room for banks to shuffle service strategies.

In the prevailing economic situation, banks would look for more fee-based income, but they won’t be able to ignore interest-based income completely. They have to build up modus operandi for various possible economic situations. For example, they will have to understand, what would be good for business if the Fed will increase the short-term interest rate or possible ‘tapering’ in coming months? How to benefit from the global corporate houses’ quest for M&A?