1
Q
Derivative - Definition
A
A derivative is a security that derives its value from the value or return of another asset or security (the so called underlying)
2
Q
Derivative markets
A
- Marked by high leverage -> risky
- Provide price information
- Allow for management of risk -> hedging
- Reduce transaction costs
3
Q
Exchange Traded Derivatives
A
- Standardized
- Backed by a clearinghouse
- Options and futures
4
Q
Over-the-counter derivatives
A
- Unregulated
- No clearinghouse (-> default risk)
- Custom instruments created and traded between two counterparties
- Options, forwards, and swaps
5
Q
Forward Commitment
A
Legally binding promise to perform some action in the future
Can be written on equities, indices, bonds, physical assets or interest rates
- Forward Contracts
- Future Contracts
- Swaps
6
Q
Forward Commitment - Forward Contracts
A
One party agrees to buy, and the counterparty to sell, a physical asset or a security at a specific price on a specific point in time in the future
7
Q
Forward Commitment - Future Contracts
A
A forward contract that is standardized and exchange traded, regulated, backed by a clearinghouse and requires daily settlement of gains and losses
8
Q
Forward Commitment - Swaps
A
A series of forward contracts, mainly on interest rates, different currencies, or equity returns
9
Q
Contingent Claims
A
- A claim to payoff that depends on a particular event
- Options are contingent claims that depend on a stock price at some future date
- In contrast to forwards, futures and swaps, where payments are made in both cases, upward and downward movements, contingent claims only require a payment if a certain threshold price is broken
- It takes two options to build a forward or a future
10
Q
Concept of Arbitrage
A
- Arbitrage is a very important concept in valuing/pricing derivative securities
- If a return greater than the risk-free rate can be earned by holding a portfolio of assets that produces a certain riskless return, an arbitrage opportunity arises
- Arbitrage opportunity: A situation where a return greater than the risk-free rate can be generated without incurring any risk (riskless return)
- Arbitrage is based on the law of one price
11
Q
Arbitrage - Law Of Price
A
Arbitrage is based on the law of one price
- Two securities or portfolios that have identical cash flows in the future, regardless of future events, should have the same price
- Example: If securities A and B have identical future payoffs, and A is priced lower than B, buy A and sell B short
12
Q
No-Arbitrage Principle
A
- There should not be a riskless profit to be gained by a combination of the analyzed contract with positions in other assets
- If there were any arbitrage opportunity, market participants would exploit them and therewith bring the market back to an equilibrium without arbitrage opportunities
- No-arbitrage pricing is crucial to the determination of the value of all derivative instruments
13
Q
No Arbitrage Principle - Assumptions
A
- No transaction costs
- Short sales are possible without restrictions
- Borrowing and lending without restrictions at risk-free rate
14
Q
Forwards - Definition
A
A bilateral contract that obligates one party to buy and the other party to sell a specific quantity of an asset at a set price on a specific point in time in the future
- Forwards exist on physical assets and on financial assets
15
Q
Why do parties enter a forward contract?
A
- Speculate on the future price (betting)
- Hedge the risk they already have and eliminate uncertainty about the future price
16
Q
Forwards - Long and Short Position
A
- The party that agrees to buy the asset has a long position (called the long)
- The party that agrees to sell the asset has a short position (called the short)
- Both parties are exposed to default risk (i.e. probability that the counterparty will not perform as promised)
- Normally, no cash is paid to enter into the contract at its inception
- At any time, one party will have a negative contract value (“owe money”) and the other side a positive contract value of an equal amount
- Example: Party A agrees to buy a $1.000 face value, 90-day treasury bill from party B in 30 days from now at a price of $990
17
Q
Settlement Options of a Forward Contract
A
- Delivery
- Cash Settlement
- Termination
18
Q
Settlement Options of a Forward Contract - Delivery
A
The asset is delivered at the settlement date to the specified price
19
Q
Settlement Options of a Forward Contract - Cash Settlement
A
- The party that has the position with the negative value is obligated to pay this amount to the other party
- The long (short) receives a payment if the price of the asset is above (below) the agreed upon price
- Ignoring transaction costs, the method yields the same results as asset delivery
20
Q
Settlement Options of a Forward Contract - Termination
A
A party can exit the contract prior to expiration by entering into an opposite forward contract (with the same or a third party) with an expiration date equal to the time remaining on the original contract
21
Q
Equity Forward
A
- Forward contract where the underlying asset is a single stock or a portfolio of stocks, e.g. an index
- The stock seller can lock in the selling price of the shares
22
Q
Bond Forward
A
- Forward contracts on bonds are quite similar to bonds
- In contrast to equities, bonds do have a maturity -> Forward contract must settle before the bond matures
- Risk free bonds are often quoted as a percentage discount from face value
- Because of the possibility of default and embedded options special provisions must be included
23
Q
Forward Rate Agreement
A
- Forward rate agreement can be viewed as a forward contract to borrow/lend money at a certain rate at some future date
- In practice, settled in cash and no actual loan is made at settlement date
-> The creditworthiness of the parties to the contract need not to be considered in the forward interest rate, and a riskless rate as the LIBOR can be specified as floating market rate in the contract - The long position is the party that would borrow money (positive value when specified rate < market rate)
- The short position is the party that would lend money (positive value when specified rate > market rate)
24
Q
Currency Forward
A
- One party agrees to exchange a certain amount of one currency for a certain amount of another currency at a future date
- In practice, an exchange rate will be specified at which one party can buy a fixed amount of the currency underlying the contract
- Currency forward can be delivered or settled in cash
25
Futures vs. Forwards - Similarities
- Deliverable contracts that obligate the long to buy and the short to sell a certain quantity of an asset for a certain price on specified future point in time
- Possible pure cash settlement contracts
- Priced to zero value at the time an investor enters into the contract
26
Futures vs. Forwards - Differences
- Futures are exchange traded while forwards are private contracts and not traded
- Futures are highly standardized, while forwards are customized satisfying the needs from the parties involved
- Futures have a single clearinghouse as counterparty, while forwards are with the originating counterparty
27
Characteristics of Futures - **Standardization**
- Concerning **quality and quantity of the goods that can be delivered**, concerning **delivery time** (settlement date) and the **manner of delivery**
- Concerning a **daily price limit**, which sets the maximum price movement allowed in a single day (not in effect during the delivery month), e.g. wheat cannot move more than $0,20 from its closing price of the preceding day
- **Uniformity** stimulates trading and promotes market liquidity, as clear conditions are set up
28
Characteristics of Futures - **Clearinghouse**
- Each exchange has a clearinghouse
- Clearinghouse **guarantees that traders in the future market will honor their obligations**
- It **acts as buyer to every seller** and **as seller to every buyer** -> Allows either side to reverse positions at any time without having to contact the other side of the initial trade
- Traders are **freed from default risk** of the original counterparty
29
Characteristics of Futures - **Margins**
- Serve as **performance guarantee**
- Deposit by both the long and the short position in the clearinghouse
- **Margin payment** (settlement of accounts) is **required daily** by the exchange to **safeguard its clearinghouse** (so called marking to market)
- **Initial and maintenance margins** (daily) are set by the clearinghouse and are based on **historical daily price volatility** of the underlying asset
- **No loan** involved, **no interest change**
30
Characteristics of Futures - **Futures Trading**
- **Future exchange selects contracts that will trade** -> standardization of asset, amount and delivery date
- **Delivery price** for the contract is the **equilibrium price at this point in time** and **depends on supply and demand**
- **Mechanism of open outcry** on exchange floor (“pits”) -> All traders know the current equilibrium price
31
Characteristics of Futures - **Closing a future**
- Same functionality as explained for forwards
- By incurring an opposite trade, the clearinghouse will net the position
- Losses incurred due to netting of position are deducted from margin deposit
- Most futures are settled in this way
32
Margins
- Initial margin
- Maintenance margin
- Variation margin
- Settlement price
33
Margins - **Initial Margin**
- Must be deposited before any trading takes place
- Set for each type underlying asset
- About one day’s maximum price fluctuation of the underlying asset (relatively low)
34
Margins - **Maintenance Margin**
- Amount of margin that must be maintained in a futures account
- If margin balance falls below this margin due to a change in the contract price, additional funds must be deposited to bring the margin back to the **initial margin requirement**
35
Margins - **Variation Margin**
- Funds that must be deposited into the accounts to bring it back to the initial margin account
- If accounts exceed initial margin requirements, funds can be withdrawn or used for other trades
36
Margins - **Settlement Price**
- Price used to make margin calculations at the end of each trading day
- Average of the prices of the trades during the last period of trading (an average closing price)
37
Ways of Terminating Future Contracts (4)
- Delivery
- Cash Settlement
- Closing
- Exchange for Physicals (EFP)
38
Ways of Terminating Future Contracts - **Delivery**
- Presents less than one percent of all settlements
- Location, terms of delivery, and specification of what is to be delivered are all specified in the contract
39
Ways of Terminating Future Contracts - **Closing**
- Done by a **reverse or also called offsetting trade**, i.e. exact opposite trade with respect to maturity, quantity and good
- Counterparty is again the clearinghouse -> you are left with a **zero balance**
- Most future positions are settled in this way
40
Ways of Terminating Future Contracts - **Exchange for Physicals**
- Finding a trader with an opposite position to yours
- Settlement by delivery off the floor of exchange by privately negotiating the terms of the transaction (-> difference to delivery, where terms are set up in contract)
- Clearinghouse must be informed
41
Types of Future Contracts (5)
- **Treasury Bill** Futures
- **Eurodollar** Futures
- **Treasury Bond** Futures
- **Stock index** Futures
- **Currency** Futures
42
Types of Future Contracts - **Treasury Bill Futures**
- Based on a $ 1 Mio. Face value 90-day T-Bill and settled in cash
- Price quotes are 100 minus the annualized discount in percent on the T-Bills
- Today of less importance due to growing relevance of Eurodollar futures
43
Types of Future Contracts - **Eurodollar Futures**
- Based on 90-day LIBOR and settled in cash
- Price quotes are 100 minus the annualized LIBOR in percent
44
Types of Future Contracts - **Treasury Bond Futures**
- Based on Treasury Bonds with maturities greater than 15 years and are delivered
- Short position has option to deliver any of several bonds which satisfy the delivery terms (CTD = cheapest-to-deliver)
45
Types of Future Contracts - **Stock Index Futures**
- Based on popular stock indices, as for example on the S&P 500 and settled in cash
- Value of the contract is a predefined multiplier times the level of the index
46
Options
An option contract **gives its owner the right, but not the legal obligation**, to **conduct a transaction involving an underlying asset** at a **predetermined future date (exercise date)** and at a **predetermined price (exercise or strike price)**
47
Long and Short Position in Options
- **Long position** is the party with the right to decide whether to exercise the option or not (buyer/owner of the option)
- **Short position** is the party that has the obligation to perform if the long requires (the seller of the option, also referred to as option writer)
48
Options - Call and Put
- **Call Option:** Owner has the **right to purchase** the underlying asset at a specific price for a specified time period (American)/at a specified date (European)
- **Put Option:** Owner has the **right to sell** the underlying asset at a specific price for a specified time period (American)/at a specified date (European)
49
Option Premium
Price paid to the seller of the option
50
Moneyness
Moneyness and intrinsic value are functions of the relationship between the **underlying stock’s price S** and the **exercise/strike price X**
51
Moneyness - Call Option
Call option: S – X (buying a share for X and selling it for S)
- S – X > 0:Call option is said to be **in-the-money**
- S – X < 0: Call option is said to be **out-of-the-money**
- S – X = 0: Call option is said to be **at-the-money**
52
Moneyness - Put Option
Put option: X – S (buying a share for S and selling it for X)
- X – S > 0: Put option is said to be **in-the-money**
- X – S < 0: Put option is said to be **out-of-the money**
- X – S = 0: Put option is said to be **at-the-money**
53
Options - Intrinsic Value
- **Amount by which the option is in the money at payoff**
- An option at-the-money or out-of-the-money has zero intrinsic value (Kann nicht kleiner null sein, sonst würde niemand die Option wählen)
On expiration date of options the following holds
- Intrinsic value of a **call option**: Max(0;S-X)
- Intrinsic value of a **put option**: Max(0;X-S)
54
Time Value of an Option
- Time value is the **amount by which the option price exceeds the intrinsic value**
- **During the life of an option**, the **time value is always positive**, because there is some probability that the stock price will change in an amount that gives the option a positive payoff at expiration greater than the (current) intrinsic value
-> The **value of the option will typically be greater than its intrinsic value**
- **At expiration the time value is zero**, as no time is remaining -> option value = intrinsic value
- For American options and in most cases for European options, the longer the time to expiration, the greater the time value
55
Exchange Traded Options
Regulated and standardized, liquid and backed by a clearinghouse
56
Over-The-Counter Options
- Primarily for institutional investors as retail business is concentrated on organized exchanges
- Mainly options on currencies, swaps and equities
- Market largely unregulated, involves counterparty risk, consists of custom options and is facilitated by dealers, large banks and brokerage firms
57
Types of Options (3)
- Financial Options
- Options on Futures
- Commodity Options
58
Financial Options (5)
- **Stocks**
- **Stock indices**: settled in cash, index level multiplied by contract multiplier to obtain payoff
- **Treasury bonds**: mostly OTC, delivered or settled in cash
- **Interest rates**: Settled in cash, the underlying asset is a reference rate such as 90-day LIBOR -> in contrast to other options payment is not made at expiration date but on the day of the next interest payment of the LIBOR contract hence, in 90 days
- **Currencies**
59
Options on Futures
- **Call option** on futures gives the holder the **right to enter into the long side** of a future contract if the option is exercised
- **Put option** on futures gives the holder the **right to enter into the short side** of a future contract, the writer of the option will take the long position in the future contract if the option is exercised
60
Commodity Options
- Give the holder the right to buy or sell a fixed quantity of some physical asset at a fixed strike price
- Examples: Options on crude oil or wheat
61
Interest Rate Caps
- **Series of interest rate call options**, having **expiration dates** that **correspond to the reset dates** on a **floating rate loan**
- Used to **protect the borrower from an increase in interest rates** and places an **upper limit on interest payment** on the floating rate loan
62
Interest Rate Floors
- **Series of interest rate put options**, having **expiration dates that correspond to the reset dates on a floating rate loan**
- Used to **protect the lender from a decline in interest rates** and places a **lower limit on interest payment** on the floating rate loan
63
Interest Rate Collars
- Combination of a cap and a floor
- A borrower of a floating rate loan may buy a cap for protection against rates above the cap and sell a floor in order to defray some of the cost of the cap
64
Swaps
- **Agreements to exchange a series of cash flows on periodic settlement dates over a certain time period**, e.g. quarterly payments over two years
- Can be decomposed into a **series of forwards** that expire on certain settlement dates
- Generally, no cash is paid to enter into the contract at its inception (no value at initiation)
- **Simplest swap** consists of **one party making fixed-rate interest payments in return for floating-rate payments from the other party**
- The two **payments are netted** -> only one payment is necessary
- Swaps are **custom** (“tailor made”), largely **unregulated, OTC traded** instruments
- Swaps contain **default risk**
- Market facilitated by dealers, large banks and brokerage firms
- Huge market: more than USD 400 trillion notional amounts outstanding
65
Terminating Swaps - **Variants** (4)
- Mutual Termination
- Offsetting Contract
- Resale
- Swaption
66
Terminating Swaps - **Mutual Termination**
- Cash payment by one party that is acceptable to the other party
- Market disadvantaged party makes the payment of the swaps value
- Other counterparty must be willing to accept
67
Terminating Swaps - **Offsetting contract**
- Counterparty who wants to terminate the contract can enter into an offsetting swap (as with forwards)
- Often applied when the other counterparty does not accept the terms of mutual termination
68
Terminating Swaps - **Resale**
- It is possible to sell the swap to another party with the permission of the other counterparty
- Unusual as no functioning secondary market exists
69
Terminating Swaps - **Swaption**
Option to enter into a swap at some date in the future
70
Currency Swaps
- One counterparty makes payments denominated in one currency, while the payments from the other counterparty are made in a second currency
- The **notional amount** of the contract, expressed in both currencies at the current exchange rate, is **exchanged at contract initiation** and **returned at the contract termination date** in the **same amounts**
71
Plain Vanilla Interest Rate Swaps
- Involve **trading fixed-rate payments for floating-rate payments**
- The **floating rate** quoted is generally the **LIBOR**
- Notional principal swapped is the same for both parties and in the same currency -> notional principal is generally not swapped
- **Arrears method**: LIBOR flat interest rate is determined at the beginning of the settlement period and the cash interest payment is made at the end of the settlement period
72
Swaption
- Definition
- Types
- Use Cases
- Option to enter into a swap at some date in the future
- **Payer swaption** gives the right to enter into a specific swap at some date in the future as fixed-rate payer (**valuable when interest rates increase**)
- **Receiver swaption** gives the right to enter into a specific swap at some date in the future as fixed-rate receiver (**valuable when interest rates decrease**)
- Used to **terminate a swap** (option to enter into an offsetting swap at the cost of the swaption premium), for **speculation on interest rate changes** of for the **lock-in of a fixed-rate**, when anticipating an undesired floating-rate exposure in the future (using payer swaption)
73
Covered Call
- A covered call consists of writing a call and buying the underlying stock
- Such a position is reasonable when you think that the stock will not move much in near future, neither upwards nor downwards, but you want to increase your income by collecting some call option premiums
74
Protective Put
- Consists of **buying a stock and a put option on that stock**
- It is an investment management technique designed to **protect a stock from a decline** (hedge against the loss of the stock)
Financial Analysis
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