1. Derivatives and it’s variants

2. Derivative - Definition
A derivative is a financial instrument which derives its value of some other financial instrument or variable
The value from which a derivative derives its values is called an underlier
Primary instruments or Cash Instruments are in contrast directly determined by markets
Example of derivatives: Stock Options, Interest rate swaps, equity options
Stock option is a derivative because it derives its values from the value of stock
An interest rate swap is a derivative because it derives its value from one or more interest rate indices
A cash instrument is an instrument whose value is determined directly by the markets
Stocks, commodities, currencies and bonds are all cash instruments
The distinction between cash and derivatives are not always precise

3. Categories Derivatives are categorized in various ways.
Linear derivatives
Non-linear derivatives
Another category
Vanilla derivatives
Exotic derivatives
Another Category
Standalone
Embedded
Linear derivatives have payoffs that are linear or somewhat linear and the others are non-linear
Nonlinear is always due to the derivative either being an option or having an option embedded in its structure
Vanilla derivatives tend to be simple and more common the latter more complicated
There is no definitive rule to distinguish one from the other.

4. Standard Derivatives Asian option- non-linear – exotic
Barrier option – non-linear – exotic
Basket option – non-linear – exotic
Binary option – non-linear – exotic
Call option – non-linear – vanilla
Cap – non-linear – vanilla
Chooser option – non-linear – exotic
Compound option – non-linear – exotic
Contingent premium option – non-linear – exotic
Credit derivative – non-linear – exotic
Floor – non-linear – vanilla
Forward – linear – vanilla
Future – linear – vanilla
Lookback option – non-linear – exotic
Put option – non-linear – vanilla
Quanto – non-linear – exotic
Rainbow option – non-linear – exotic
Ratchet option – non-linear – exotic
Swap – linear – vanilla
Swaption – non-linear – vanilla
Strangle – non-linear – exotic
Straddle – non-linear – exotic
Condor – non-linear – exotic
Bermudean option – non-linear - exotic
Asian – Average (some form)
Chooser – non – path dependent (some are path-dependent) also called “as-you-like-it” options – used solving with Black-Scholes. A regular choose options gives its owner the right to purchase, for an amount Ei at time Ti, either a call or put with exercise price E2 at time T2. Thus a regular choose algorithm is a “call on a call or put” - max (C (S, Ti) – E1, P(S, Ti) – E, 0)
Black-Scholes assumptions:
- Asset price follows lognormal random walk
- Risk free interest rate and the asset volatility (sigma) are known function of time over the life of the option
- No transaction cost
- No dividends
- No Arbitrage (anything, especially interest rate)
- trading continuously
- short selling permitted and assets are divisible.
. Usage varies with regard to what structures the term encompasses. Basket options and quantos are linked to multiple underliers, but are generally not referred to as rainbows. Some standard forms of rainbow options are:
A maximum option is a bundle of vanilla options with a variety of features—different strikes, different underliers, some may be puts, others calls, but they generally have the same expiration date. Only one of these may be exercised, and this is chosen in the holder's favor at expiration.
A minimum option is a bundle of vanilla options—like a maximum option. Only one of the options can be exercised, and this is chosen in the issuer's favor at expiration.
A better-of option is a bundle of long forwards. All mature on the option's expiration date but have different underliers. At expiration, only one settles, and this is chosen in the holder's favor.
A worst-of option is a bundle of long forwards. All mature on the option's expiration date but have different underliers. At expiration, only one settles, and this is chosen in the issuer's favor.
A two-asset correlation option is linked to two underliers. It pays off like a vanilla option on one underlier if the expiration value of the other underlier is in a specified range. The vanilla option can be either a put or a call.
A spread option is a derivative with a spread as an underlier. The spread might be a price spread, credit spread, calendar spread, etc.
Together, maximum options and minimum options are referred to as min-max options. Better-of or worst-of options are referred to collectively as alternative options
An alternative option can result in the holder having to make a payment to the issuer at expiration. Consider a better-of option on three-month USD/EUR and USD/JPY forwards, both with a USD 100MM notional. If both exchange rates move against the holder, he will have to make a payment to the issue to settle whichever forward has declined least in value.
    Worst-of options blur the distinction between option issuers and option holders. Certainly, someone would require a premium or other compensation for holding a worst-of option. Worst-of options arise with bond futures that grant the short party the right to deliver any of several qualifying bonds.
An outperformance option (or Margrabe option) is an option that grants the right to exchange one asset for another. Essentially, it is a spread option with a strike price equal to zero.
Pricing of rainbow options depends upon the particular structure, but it is generally sensitive to correlations between the underliers. The classic paper on analytic solutions for pricing two-factor min-max options is Stulz (1982). Johnson (1987) extends these results to more than two factors. For numerical solutions, see Boyle and Tse (1990). See Margrabe (1978) for outperformance options. Kirk (1995) and Pearson (1995) provide approximate solutions for pricing spread options. Haug (1997) covers many of the above formulas.
Strangle: An options spread comprising a long put and a long call, both with out-of-the-money strike prices.
Straddle: An options spread comprising a long put and a long call both with the same strike price.
Ratchet Option: A ratchet option (also called a reset option or cliquet option) is a series of consecutive forward start options. The first is active immediately. The second becomes active when the first expires, etc. Each option is struck at-the-money when it becomes active. The effect of the entire instrument is of an option that periodically "locks in" profits in a manner somewhat analogues to a mechanical ratchet. Ratchet features can be incorporated into other structures. For example, there are ratchet caps or ratchet floors.
Quanto: A cash settled derivative that has an underlier denominated in one currency, but settles in another currency based on a fixed exchange rate.
Rainbow options – are derivatives linked to two or more underliers

5. Derivatives - Categorization
Standard derivatives are listed
Categorization is not firm
Usually rainbows are considered exotic
Generally spreads and swaps are considered vanilla
Listed derivatives are categorized either as linear/non-linear and as vanilla or exotic

6. Swap A swap is a cash-settled simple form of OTC derivative
A swap is an agreement between two counterparties to exchange two stream of cash flows
The present values are equal
Primary reason – hedging and/or speculation
Change the character of asset without liquidation
The parties swap the cash flow streams
All that matters is that their present values be equal ( except for a bid-ask spread, if one party to the swap is a dealer)
The fundamental purpose is to change the character of an asset or liability without liquidation that asset or liability
For example, an investor realizing returns from an equity investment can swap those returns into less risky fixed income cash flows without having to liquidate the equities. A corporation with floating rate debt can swap that debt into a fixed rate obligation without having to reture and reissue the debt

7. With a Swap, You can change the Character of an Asset without having to liquidate the asset
Cash Flow
Stream A
Original
Counterparty
You
Cash Flow
Stream B
Cash Flow
Stream A
You have the same assets but the character of the assets are changed as the cash flow streams are changed
If you reversed all the arrows it would illustrate how a swap can change the character of a liability
Swap
Counterparty
Cash flow from Stream from a counterparty is exchanged for Cash flow from a swap counterparty

8. Characteristics of a Swap
When first entered it has zero market value
Swap gains positive or negative value over time
Market variables that affect the cash flow streams
Payment conditions
Risks associated with swaps
Market Risk
Settlement Risk
Liquidity Risk
Pre-settlement Risk
When a swap is first entered into it has zero market value ( except possibly for a small bid-ask spread) This is because both cash flow streams have identical offsetting market values. As time goes by, the swap is likely to take on a positive or negative market values.
Market variables that affect the market values of one or both cash flow stream will fluctuate causing the values of the cash flow streams to change
The swap’s market values which is simply the difference between the two cash flows streams market values, will then also change
One cash flow stream may have more accelerate payments than the other, so the swap takes on a positive market values for the party making the more accelerate payments. An extreme case of this is some customized swaps that require one party to make a substantial payment right at the outset
For the first two reasons, swaps entail market risk. For both reason, they entail pre-settlement risk. Collateralization is a common way of addressing pres-settlement risk of one or both of the counterparties. Settlement risk can be a problem for some swaps. However, cash flow streams are often structured so that payments for one occur on the same dates as payments for the other. This allows cash flows to be netted against each other ( so long as the cash flows are in the same currency)

9. Swaps – Types
Vanilla Swaps – any swap with standardized provisions for example
Vanilla interest rate swaps
Vanilla currency swaps
Asset Swaps
Liability Swaps
Interest Rate Swaps
Currency Swaps
Total Return Swaps
Vanilla swaps are appealing because pricing tends to be transparent and transaction costs are small. Vanilla swaps can be used to speculate or to quickly hedge the market risk of a position without necessarily offsetting the specific cash flows of that position. Swaps can be customized to offset the specific cash flows of a position Dealers often structure such non-vanilla swaps for clients. They may charge a fee for doing so, and pricing may reflect a large bid-ask spread. An asset swap is a non-vanilla swap customized to change the character of a specific asset. A liability swap is sucha swap customized to change the character of a specific liability

10. Swaps - Categories Equity Swap Credit Default Swap Forex Swap
Currency Swap
Constant Maturity Swap
Volatility Swap
Basis Swap
Variance Swap

11. Interest Rate Swap
Floating Rate
Cash Flows
Lender
Corporation
Fixed Rate
Cash Flows
Floating Rate
Cash Flows
If a corporation has borrowed money at a floating rate of interest but would prefer to lock in a fixed rate, it can swap its floating rate payments into fixed rate payments.
Swap
Counterparty
By entering into a swap with a third party, a corporation can convert floating rate payments into fixed rate payments

12. Interest Rate Swap - Contd
Vanilla interest rate swaps
Fixed rate loan is exchanged for floating rate loan
Most common are 3-month or 6-month Libor rate (Euribor if the currency is Euro) floating rate
Basis swap is floating-floating interest rate swap
Concurrent cash flows are netted
Both loans have initial payments of principal – also called the notional amount – they net to zero
Final payments net to zero
Generally periodic payments are scheduled on the same date so they can be netted
Interest rate swaps can also be used to speculate on interest rates. A trader who believes that interest rates will rise could incur the expenses of borrowing and then shorting bonds. A simpler and less expensive solution would be to put on a pay-fixed swap.

13. Interest Rate Swap - Contd
Vanilla interest rates are quoted in terms of the fixed rate to be paid against the floating index
For example: 4.3% against a 3-month Libor paid quarterly
In USD markets, vanilla swaps are often quoted, not as an absolute rate, but as the fixed rate’s spread over the corresponding treasury yield
Fixed rates on vanilla swaps are called swap rates
Swap curve is a yield curve comprising swap rates for different maturities of the swap
Due to high liquidity in the USD swap market, the swap curve has emerged as an alternative to treasuries as a benchmark for USD interest rates at maturities exceeding a year

14. Example for Interest Rate Swap
Two Banks enter into a vanilla interest rate swap. The term is four years. They agree to swap fixed rate USD payments at 4.6% in exchange for 6-month USD Libor payments. At the outset, the fixed rate payments are known. The first floating rate payment is also known. But the net would depend on the future of Libor. Let’s calculate the payments for the life of the swap using hypothetical values

15. Cash flows during the life of a hypothetical Swap USD 100MM 4
Cash flows during the life of a hypothetical Swap USD 100MM 4.6% Four year Swap
Time (Years)
6-Month Libor
Fixed Rate Cash Flows
Floating Rate Cash Flows
Swap Net Cash Flows
0.0
2.8%
0.5
3.4%
2.3
1.4
0.9
1.0
4.4%
1.7
0.6
1.5
4.2%
2.2
0.1
2.0
5.0%
2.1
0.2
2.5
5.6%
-0.2
3.0
5.2%
2.8
-0.5
3.5
2.6
-0.3
4.0
3.8%
102.3
102.2
Note: at 4.0, we did not calculate using the 3.8% libor rate

16. Equity Swap
Contractual agreement to exchange cash flows on specific assets for a given period
Based on a specific equity, equity index (Dow Jones, S&P 500 etc), or basket of equities
Notional amounts are not exchanged only cash flows
Benefits: No ownership of underlying, transaction/dividend taxes, limitations of ownership & leverage, exposure to markets
One side will always be an equity, equity index, or basket of equities; the other side can vary in terms of source. Lack of taxation and ownership of the underlier often allows investment in markets that would otherwise be closed.

17. Example of Equity Swap
On December 15 of a given year a money management firm enters into a swap to pay the return on the NASDAQ Composite index and receive the return on the S&P 500 with payments to occur on March 15, June 15, September 15, and December 15 for one year. Payments will be calculated on a notional principal of $20 million.

18. Hypothetical Payments on One-Year Equity Swap with Quarterly Settlement to Pay the NASDAQ Return and Receive the Return on the S&P 500 on Notional Principal of $20 Million
Date
S&P 500 Index
Periodic Return on S&P 500
S&P 500 Cash Flow
NASDAQ Index
Periodic Return on NASDAQ
NASDAQ Cash Flow
Net Cash Flow
December 15
March 15
2.2015%
$440,300
2.6543%
-$530,860
-$90,560
June 15 %
-800,020 %
+702,880
-97,140
September 15 %
-535,100 %
+942,200
407,100
4.1913%
838,260
4.2767%
-855,340
-17,080
The returns on the two assets are compared, and the payments are based on the difference in cash flows. Though this example is index-based on both sides, the analysis for a single-stock equity swap is similar.