Credit Derivatives

Following is a reproduction from fincad.com

TYPES OF CREDIT DERIVATIVES

A credit derivative is a financial instrument that transfers credit risk related to an underlying entity or a portfolio of underlying entities from one party to another without transferring the underlying(s). The underlyings may or may not be owned by either party in the transaction. The common types of credit derivatives are Credit Default Swaps, Credit Default Index Swaps (CDS index), Collateralized Debt Obligations, Total Return Swaps, Credit Linked Notes, Asset Swaps, Credit Default Swap Options, Credit Default Index Swaps Options and Credit Spread Forwards/Options.

Credit Default Swaps

In a credit default swap the seller agrees, for an upfront or continuing premium or fee, to compensate the buyer when a specified event, such as default, restructuring of the issuer of the reference entity, or failure to pay, occurs. Buyers of credit default swaps can remove risky entities from their balance sheets without selling them. Sellers can gain higher returns from investments or diversify their portfolios by entering markets that are otherwise difficult to get into.

The value of a default swap depends not only on the credit quality of the underlying reference entity but also on the credit quality of the writer, also referred to as the counterparty. If the counterparty defaults, the buyer of a default swap will not receive any payment if a credit event occurs. We also note that if a counterparty defaults, the premium payments end. Hence, the value of a default swap depends on the probability of counterparty default, probability of entity default and the correlation between them.

Credit default swaps are composed of the following four types: credit default swaps on single entities, credit default swaps on a basket of entities, credit default index swaps, and first-loss and tranche-loss credit default swaps.

• Credit Default Swaps on Single Entities: a credit default swap on a single entity. This is the most common type of credit default swaps.
• Credit Default Swaps on Baskets of Entities: A basket default swap is similar to a single entity default swap except that the underlying is a basket of entities rather than one single entity.
• First-Loss and Tranche-Loss Credit Default Swaps: Similar to a first-to-default or an nth-to-default credit default swap, a first-loss credit default swap (FLCDS) protects its buyer from losses of a reference pool as a result of credit events. Unlike a first-to-default credit default swap, in which only the loss from the first credit event is compensated, or an nth-to-default credit default swap, in which the losses from the nth default or the first n defaults are compensated, an FLCDS compensates its buyer for any losses from credit events of the reference assets up to a certain portion of the total notional of the asset pool.
• Credit Default Index Swaps (CDS Index): A credit default index swap (CDIS) is a portfolio of single-entity credit default swaps (CDS). It can be seen as an extension of a CDS on a single-entity to a portfolio of entities. The basic difference is that in a CDS the notional is fixed during the life of the CDS and the protection buyer is compensated at most once, while in a CDIS the premium notional is variable. Whenever a default in the portfolio occurs, the premium notional is reduced by the loss amount of the defaulted entity and at the same time the protection buyer gets compensated by the lost amount. The most popular credit default index swaps are the so-called standardized credit default index swaps. In these standardized contracts the reference credit pool is homogeneous, that is, all the reference entities have the same notional and the same recovery rate. Typical examples of standardized CDISs are the CDX index and the ITRAXX index.

Total Return Swaps

A total return swap is a means to transfer the total economic exposure, including both market and credit risk, of the underlying asset. The payer of a total return swap can confidentially remove all the economic exposure of the asset without having to sell it. The receiver of a total return swap, on the other hand, can access the economic exposure of the asset without having to buy the asset. Typical reference assets of total return swaps are corporate bonds, loans and equities.

Credit-Linked Notes

A credit-linked note, also known as a credit default note, is a fixed or floating rate note where the principal and/or coupon payments are referenced to a credit or a basket of credits. If there is no credit event of the reference credit(s), all the coupons and principals will be paid in full. However, if there is a credit event, the payments of the principal and, possibly, also the coupon of the note will be reduced.

Credit Default Swap Options

A credit default swap option is also known as a credit default swaption. It is an option on a credit default swap (CDS). A CDS option gives its holder the right, but not the obligation, to buy (call) or sell (put) protection on a specified reference entity for a specified future time period for a certain spread. The option is knocked out if the reference entity defaults during the life of the option. This knock-out feature marks the fundamental difference between a CDS option and a vanilla option. Most commonly traded CDS options are European style options.

Similar to the credit default swaps, CDS options can be: CDS options on a single entity with a regular payoff for the default leg; CDS options on a single entity with a binary payoff for the default leg; CDS options on a basket of entities with regular payoff for the default leg; and CDS options on a basket of entities with a binary payoff for the default leg.

Credit Default Index Swap Options

A credit default index swap option (CD index swap option, or CD index swaption, or CDS index option) is an option to buy or sell the underlying CDIS at a specified date. A payer swaption gives the holder of the option the right to buy protection (pay premium) and a receiver swaption gives the holder of the option the right to sell protection (receive premium). Unlike a CD index swap, which is a natural extension of a CDS on a single-entity to a CDS on a portfolio of entities, a CD index swaption is significantly different from a CDS option, an option on a single-entity CDS. In the case of an option on a single-entity, if the reference entity defaults before the option's expiry, the option will be knocked out and become worthless. For an option on a CDIS, when a reference entity defaults before the option's expiry, the loss will be paid by the protection seller to the protection buyer when the option is exercised. Even if there is only one entity in the portfolio, a CD index swaption is still different from a single-entity CDS option: if the entity defaults before expiry, the option's seller will pay to the protection buyer the lost amount at expiry. Clearly, a CD index swaption is always more valuable than a single-entity CDS option.

Credit Spread Options and Forwards

Credit spread options are options where the payoffs are dependent on changes to credit spreads. The transaction may be either based on changes in a credit spread relative to a risk-free benchmark (e.g. LIBOR or US Treasury) or changes in the relative spread between two credit instruments. A credit spread option may be a vanilla option or an exotic option, such as an Asian option, a lookback option, etc. The option style may be European or American. Valuation of credit spread options can be based on modeling the two underlying instruments or modeling the credit spread only.

Asset Swaps

An asset swap is a combination of a defaultable bond with a fixed-for-floating interest rate swap that swaps the coupon of the bond into the cash flows of LIBOR plus a spread. In the case of a cross currency asset swap, the principal cash flow may also be swapped. In a typical asset swap, a dealer buys a bond from a customer at the market price and sells to the customer a floating rate note at par. The dealer then enters into a fixed-for-floating swap with another counterparty to offset the floating rate obligation and the bond cash flows. For a premium bond, the dealer pays to the customer the difference of the bond price and its par. For a discount bond, the customer pays to the dealer the difference of the par and the bond price. In the swap with the counterparty the dealer pays a fixed bond coupon and receives LIBOR + a spread. The spread can be determined from the cash that the dealer pays/receives and from the difference of the bond coupon and the par swap rate.

Synthetic Collateralized Debt Obligations (CDOs)

Synthetic CDOs are credit derivatives on a pool of reference entities that are "synthesized" through more basic credit derivatives, mostly, credit default swaps (CDSs) and credit linked notes (CLNs). A common structure of CDOs involves slicing the credit risk of the reference pool into a few different risk levels. The level with a higher credit risk supports the levels with lower credit risks. The risk range of two adjacent risk levels is called a tranche. The lower bound of the risk level of a tranche is often referred to as an attachment point and the upper bound a detachment point. The most common CDO credit derivatives are CDSs on CDO tranches and CDO notes (tranche-linked notes or CLN on tranches). The most popular synthetic CDOs are the so-called standardized CDOs (sometimes are simply called standardized tranches). For a standardized CDO its reference entities are homogenous, i.e., all the reference entities have the same notional and the same recovery rate. Due to the complexity and the large sizes of reference pools of synthetic CDOs, their valuation is much more complicated and resource intensive than the ordinary single-entity or basket CDSs and CLNs. Monte Carlo methods have been the most reliable methods in CDO valuation but they are not efficient in computation. Recently, thanks in part to the standardization of the synthetic CDO market, quasi-analytic methods, such as the fast Fourier transform (FFT), are gaining popularity. These methods are much more efficient than Monte Carlo simulation for CDOs whose reference entities have "good" homogeneity and, particularly, when the one-factor copula model is used for modeling credit correlation.

Derivatives - IX

Pricing of options, that is calculation of premium, can be done under various methods. Black-Scholes Model and the Binomial Model are the most commonly used methodologies for theoretical calculation. If actual premium is different, derivative traders become active enough to make the actual price converge with the model outputs. However, the assumptions regarding interest rate and volatility may be different for some traders. Such traders are normally more active.

Many calculators are available for finding the theoretical premium for call and put options. Here is one such:

http://www.fintools.com/resources/online-calculators/options-calcs/options-calculator/

It will be interesting to modify various assumptions and look at the impact on option prices.

Derivatives - VIII

1) Futures contracts create obligations, not rights.

2) Only the option buyer gets rights.

3) Options seller is also known as writer.

4) Futures price = Cash price + carry charges

5) Cash price minus Futures price = Basis.

6) Maximum possible profit to the option seller = Premium

7) Neither intrinsic value nor time value can be negative.

8) Beta is a measure of systematic risk.

9) Longer the time to expiry, more will be the time value.

10) Short Futures = Long Put + Short call.

Derivatives - VII

The long and short of Hedging:

Hedging through futures may involve either buying or selling an asset in the futures market. Purchase in the Futures market is called as 'Long Hedge'. If hedging is done by selling in the futures market, it is called as 'Short Hedge'.

For example, you may have a lot of money with you and you may also want to buy a particular share. If you buy in the spot (cash) market, the price may go up immediately and you may get less number of shares. So, you buy from the futures market. Then, slowly as and when you make cash purchases, you unwind your futures position. This is 'long hedge'.

Similarly, if you have many shares to sell, you may sell them in the futures market so that the cash price is not brought down. This is 'short hedge'.

If there is no futures market for a particular item, you may enter into contracts for a similar product like diesel instead of aviation turbine fuel (ATF). This is called as 'Cross Hedge'. The assumption is the prices of diesel and ATF will move in a similar fashion.

Derivatives - VI

Hedging through Futures: Hedging means protecting one's portfolio from impact of market changes. This amounts to giving up or shedding risk.

Any asset (including an equity share) is subject to two kinds of risk: one is called Specific Risk that relates to its inherent risk and the other is Systematic Risk or Market Risk. If you own Tata Steel share, consequences of Tata Steel management's business style is the specific risk. Consequences arising from factors which affect all companies and not Tata Steel alone form the Market Risk or Systematic Risk.

If you want to give up specific risk without selling the share, you will have to 'diversify' your holdings (portfolio) so that you are less affected by factors that impact Tata Steel exclusively. If diversification is random and large enough, you may completely shed the specific risk of owning Tata Steel share.

But, diversification does not reduce market risk. One indicator of market risk in the equity market is what happens to a particular share's price when the index (say Nifty) moves up or down. This indicator or relationship is called 'beta'. Beta of a share is 1 if there is the same percentage change in the price of share as the change in index, say Nifty. If Nifty increases by 5% and the share's price also increases by 5%, we say that the beta of this share is 1. If the price of share goes up by 10%, it means beta is 2.

Nifty index can be bought and sold in the market. Suppose the Nifty index is now Rs.8,000. If Nifty moves up by 5%, Nifty index will be worth Rs.8,400. If you had shares worth Rs.4,000 when Nifty index was Rs.8,000 and beta of your shares is 2, your shares will be worth Rs.4,400 after Nifty has increased by 5%. This means that the increase in the value of your shares is the same as increase in the price of Nifty index.

Concept of 'beta' is made use of to hedge against market risk. In the example given above, if you sell one Nifty index in the Futures market (i.e. short one Nifty index futures), what you gain from owning shares would be offset by what you lose in the Nifty Futures sold. Similarly, if you lose from your share holdings, you will gain the same amount from the Nifty Futures sold. This is an example of 'perfect hedge'. Depending on your capacity and willingness to absorb market risk, you may opt for partial hedges.

When you own a collection (portfolio) of shares of different companies, beta of the portfolio is the weighted average beta of all shares, the weights being the market values of shares.

'Hedge Ratio' means the number of Nifty indices you need to short in order to neutralise or shed market risk totally. This is equal to Market value of portfolio multiplied by beta of portfolio and divided by value of Nifty index. (Note: Nifty index is taken as an example. Similarly, you can consider Sensex as an index or midcap index or any other index. It should however be noted that beta of a share will be different depending on the index. In addition, beta changes over time.)

Derivatives - V

Synthetic Options: A synthetic option is a combination of two or more options to yield a particular risk profile. That is, the risk profile that will be generated by one option is sought to be generated by combining multiple options. This enables greater flexibility in owning different risk profiles by withdrawing from certain options depending on evolving situations.

Different risk profiles and their synthetic options are given below:

1) Long Call = Long Put + Long Future

2) Short Call = Short Put + Short Future

3) Long Put = Long Call + Short Future

4) Short Put = Short Call + Long Future

5) Long Future = Long Call + Short Put

6) Short Future = Short Call + Long Put

Note: Above equations show the relationship among Call option, Put option and Futures. Cost in the form of premium is ignored. We are considering only the gross pay-off profile. Long means purchase, Short means sale.

Derivatives - IV

Options: An option contract is said to be ITM (in-the-money) if the option holder would exercise the option if it is the expiration day. Thus, a call option with strike price of Rs.40 is ITM if the ruling spot price is more than Rs.40. This means that the option holder will but the asset at Rs.40 and sell it at the prevailing price and thus make profit.

For a put option to be ITM, spot price has to be lower than the strike price. The following table explains the terms ITM, OTM (Out of - the - money) and ATM (at - the - money).

Situation                                                   Call option                                            Put option

1) Strike price > spot price                             OTM                                                 ITM

2) Strike price = spot price                             ATM                                                 ATM

3) Strike price < spot price                             ITM                                                   OTM


Premium: Premium is the price paid by the option buyer to the option seller.Premium is Value of the option.
Option's value consists of two elements namely intrinsic value and time value also known as extrinsic value.

Intrinsic value means the amount to which an option is ITM. Time value represents the additional profit potential that the remaining time to expiry of option is likely to create for the option holder. Hence, as time to expiry nears, time value drops.

Premium = Value = Intrinsic value + Time value. (If a call option premium = Rs.6, Strike price = Rs.40, Spot price = Rs.42, then Intrinsic value of the call option = Rs.2, time value = Rs.4)

Neither intrinsic value nor time value can be negative. They are either positive or zero.

For an OTM or ATM option, there is no intrinsic value. So, for an OTM or ATM, premium = time value.

Following consequences are note-worthy:

1) When an option is ATM, it commands the highest time value.
2) At the time of an option's expiry, the entire value is intrinsic only.
3) Fall in time value occurs at an accelerated pace as expiry draws near.
4) Extreme ITM or OTM option commands negligible time value.

Derivatives - III

Futures Contracts: A buyer gets into the Futures market in order to ensure that a particular asset will be available at the expected time of his need. Similarly, a seller participates in the Futures market to be in a position to dispose of an asset at a time convenient to him.

A manufacturer who needs a raw material for production two months from now may decide to ensure availability of the raw material with a definite price through a two-months Futures contract. What will be the price specified in this contract?

The manufacturer has two choices: 1) He can buy the raw material right now and preserve it for two months before using it or 2) He can get into the Futures contract in which case he will pay the price after two months. If he buys it right now, he has to pay the spot price, incur interest on this price for two months and also bear storage charges.

These two choices will involve the same cost because otherwise the costlier choice is no choice at all. (If the cost is different in these two choices, there will be 'arbitrage' possibility.)

So spot price + interest + storage charges = Futures price.

Sometimes, the asset under consideration may produce some income in the interval between now and the Futures period. A typical example is an equity share which may generate dividend in the intervening period. This income is to be deducted from cost to arrive at the Futures price. To calculate the Futures price more accurately, compounding at relevant interest rate has to be done for costs incurred and incomes received at different times.

Futures price will normally be higher than the present spot price. The difference between the spot price and the Futures price is called the 'Basis'. In a normal market , also called as 'contango' market, Basis is negative. If Futures price is less than present spot price, Basis is positive and such a market is called as 'backwardation' market.

Derivatives - II

Futures / Forward contracts are agreements to buy and sell (one party will buy and another will sell) an asset at a pre-determined price on a fixed future date. Agreements transacted through an exchange are called Futures contracts whereas agreements between two parties, that is a buyer and a seller, without the intervention of an exchange are known as Forward contracts.

Option contract is a right that the option buyer gets from the option seller also called the option writer to buy or sell an asset at a pre-determined price called the strike price during or at a particular time in future. Thus, the option buyer gets a right to buy or sell depending on the contract. Option contract that gives the right to buy an asset is known as call option; the contract that gives the right to sell an asset is called as put option. The option buyer purchases the right from the option writer by paying a price to the writer. This price is called the premium of the option. The day on which the option contract expires is called expiration day of the option. If the right to buy or sell can be exercised only on the expiration day, such an option is termed as 'European option'. If the right is exercisable on any day upto the expiration day, the option is called as 'American option'. So, the option buyer gets a wider window of time to exercise his / her option under American option.. Therefore, it stands to reason that American options attract higher premiums. In the Indian stock markets, only European options are allowed. Exercise day is the day on which the option is exercised. In case options are not exercised (this happens when the price movement is not favourable to the option buyer or the option holder), exercise day does not arise.

Swaps*
Another important class of derivative security are swaps, perhaps the most common of which are interest rate swaps and currency swaps. Other types of swaps include equity and commodity swaps. A plain vanilla swap usually involves one party swapping a series of  fixed level payments for a series of variable payments.
Swaps were introduced primarily for their use in risk-management. For example, it is often the case that a party faces a stream of obligations that are floating or stochastic, but that it will have to meet these obligations with a stream of fixed payments. Because of this mismatch between floating and fixed, there is no guarantee that the party will be able to meet its obligations. However, if the present value of the fixed stream is greater than or equal to the present value of the floating stream, then it could purchase an appropriate swap and thereby ensure that it can meet its obligations. (*Acknowledgement: Description of Swaps is taken from www.columbia.edu IEOR E4706: Financial Engineering: Discrete-Time Models °c 2010 by Martin Haugh)

Derivatives - I

What is a derivative? It is a contract whose value depends on an underlying asset. This means that a derivative does not have an independent value. It gains more value as the underlying asset gathers value.

What is an underlying asset? The underlying asset is the subject matter of derivative. Such an asset may be an equity share, a currency, a commodity, a fixed rate debt instrument or a loan (credit).

Derivatives can be broadly classified into financial derivatives and commodity derivatives.

In addition to classification based on type of underlying asset as above, we may classify derivatives in the following ways also:

1) Relationship between the underlying asset and the derivative: Forwards / Futures, Options and Swaps.

2) Market: Exchange-traded derivatives and Over the Counter (OTC) derivatives.

3) Purpose: Speculative, Hedge and Arbitrage

4) Payoff profile: In the Money (ITM), Out of Money (OTM) and At the Money (ATM) derivatives.

5) Payoff profile II: Linear and Non-linear derivatives.

Objective: Derivatives are normally considered as tools for Risk Management. When they are misused, knowingly or unknowingly, they have the potential to become what Warren Buffett calls as 'Financial Weapons of Mass Destruction'. Examples: 1) Nick Leeson of Barings Bank (1995), 2) Jerome Kerviel of SocGen (January, 2008), 3) Kweku Adoboli of UBS (Sept., 2011)