# 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 i.e.credit 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
t=1
Survival            -s  (spread)                        1-q(1)                  p(1)*{1-q(1)}                  1-p(1)
Credit event     (1-R)-s                   q(1)

t=2
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}
or,
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
(1-R)

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.

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.
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
i.e.

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!

When a trader takes different position on two stocks in the market it is known as ‘pairs trade’. In pair trading the trader goes long in one stock and short in another stock. It is very pertinent to mention the selection of stocks are not that easy and it requires many statistics technique to build up the pair trade position on the selected stocks.
If executed properly, even when both stocks are up, the stock in which you were long will go up much faster than the stock in which you were short. And, when both stocks are down, the stock you were short will decline faster than the stock you were long.
Since selection of stocks in pairs trade is complex, correlation plays very important role here. Once correlation is established between the two stocks then trading is a cake walk.

Lets say, the trader zeroed down on Google and Yahoo, so if both the stocks move up and down at the same time then the correlation will be positive (+1). If Google move up and Yahoo move down at the same time then the correlation will be negative (-1). If both stocks move randomly then there will be no correlation (0).
How to get correlation? You will get correlation by dividing covariance of the percentage change in stock price by product of standard deviations of the two stock. Ideally, traders chose those stocks pair were correlation is 0.80 or above as it gives a very consistent relationship. When this correlation breaks or weakens i.e. Google moves up on the other hand Yahoo moves down, the trader bets on the price spread of these two stocks. When you decide to use correlation make sure that data taken is for more than six month or so. We can use beta as one more tool to do pair trading.  Happy trading!

# Equity long short strategy in hedge funds

Hedge funds follow unique strategies of trading in the market. Equity long short strategy is one of them. As the name suggests the strategy takes long positions in those stocks which are expected to rise and short positions in those stocks which are expected to fall in the market. So, the hedge fund or the hedge fund manager applies this strategy to buy undervalue stocks and sell overvalue stocks in the market.

An equity L/S strategy can be applied to a sector, country and region specific area. In general, the hedge fund manager makes profits by keeping the healthy margin of spreads between long and short positions. Lets say, a hedge fund manager buys \$1 million of Apple shares and sells \$1 million of Nokia shares at Nasdaq, thinking, the upcoming event at Apple’s WWDC meet will lift Apple’s shares in the market and might impact the shares of Nokia (so going short on it). Imagine, if the manager has made perfect call on both the stocks – going long on Apple will fetch profits and going short on Nokia will give profits as well. But if the manager misses the call then what? So, consider another situation where both the stocks rise due to some event/news . In this case, the manager has to make sure how he/she has allocated  money for these stocks. It depends if the manager was using “130/30” strategy i.e. 130 percent exposure to long position to long and 30 percent exposure towards the short position i.e. long bias, this formula is purely up-to the manager to decide some even take 120/20 equity L/S.  In the above mentioned case since both the stocks were from the same sector, this kind of trading is also known as “pairs trading“. Overall, this strategy works when the manager predicts a perfect call.

# Delta Hedging (Tutorial version)

A trader in option market always looks for delta hedging for his/her portfolio. A delta hedging gives an opportunity to the trader to keep his/her trading position neutral from market movement.

What is Delta?
Delta is the ratio which measures change in price of the derivative with respect to the change in price of underlying asset  . So, if delta (∆) for an option is 0.5 then it implies for every one dollar change in the price for the underlying asset (whether it is an increase or decrease), there will be a change of 50 cents to the option price.

Characteristics of Delta

For a call option, delta moves between 0 and +1 while, for a put option it fluctuates between -1 and 0. Delta will be close to zero if the option (call or put) is ‘out of the money‘. When the call option is ‘in the money‘, delta will tick close to +1 while, for put option, it will be close to -1. Options, ‘at the money‘ will have delta around +0.50 for call, and -0.50 for put.

The mechanism behind delta

A trader tries to hedge his/her portfolio by establishing delta long or delta short position in accordance with the underlying assets. For example, a trader takes a call option of \$10 which gives right to buy 100 shares of Apple Inc (trading at \$ 430) with a delta at 0.70 (i.e. in the money). Suppose if the market price of shares are now at \$450 then what will be the option price? Since, delta is 0.70 an increase in underlying price of \$20 (\$450-\$430) will increase the call option price by 0.70*20= \$1.40. So, the new call option price will be \$10+\$1.4=\$11.4.

Thus, an increase of \$20 in the Apple Inc share will increase the call option price to \$1.40 or call option price for share of Apple Inc trading at \$450 will be \$11.40.

Delta Neutral Hedging

The objective of Delta Neutral Hedging is to remove price risk regardless of how the stock moves. According to the trading jargon, an option contract with 0.50 delta is referred as “50 deltas”. So, 100 deltas are related to 100 shares thus each share will have delta value equals to 1. To sum up, if you are long on 100 deltas then increase of \$1 in stock price will give a gain of \$100 and if it fall \$1 then you will end up having loss of \$100. If a position is long on 50 deltas then increase in price of stock for \$1 will fetch you \$50 and in case of decrease in stock price, a loss of \$50.

So, if a trader buys 100 shares of a stocks to get his/her portfolio a delta neutral position, he/she has to buy 2 put contracts; at the money with a delta value of -50 per contract.

Thus, 100(delta value of 100 shares)- 100( 2 put contacts* 50 deltas)= 0 delta.

For example, if a trader held 100 shares of Apple Inc for \$400 per share on 14 March 2013. On 14 May, when Apple Inc was trading at \$430, the trader performed a delta neutral hedge against possible price change while being able to make profit. The trader bought 2 ‘contracts of July31 put’ to get the delta neutral hedge on his/her position.
100 (delta of 100 shares) – 100 (delta of 2 contracts of at the money put options of 50 deltas) = 0 delta

Now what will happen is if the stock moves up by \$1, trader will make  \$100 with shares, but loses \$50 with each put, so \$100 lost in the puts; overall no gain or loss in his position.  Although ideally it would not happen as the put option price would change with the change is stock price and since the position is long (i.e. long straddle) the trader will end up with some profits. So, if Apple rallies from \$430 put option will expire being worthless and the trader will gain from increase in the price of stock by keeping his position alive in the market and the put option loss will be offset by the profits he/she would make.
There are many permutations and combinations among call and put option to get a delta neutral hedging. We will have more on the topic later.  Keep reading and learning.