L1 flash cards derivatives (ss17)

Exchange Traded Derivatives
 Involves a Clearing House
 Physical Market
 Low Default Risk
 Contains standard terms and features
 Markets can be called futures market or options exchange
Study Session 17, Reading 60

Over-the-Counter Derivatives
 No Physical Market (Not listed on the market)
 Transaction Created by Two Parties
 Decentralized Market and Exchange

Exchange-Traded vs Over-the-Counter
Exchange-Traded
 Physical Market
 Have Standard Terms and
Features
 Organized Facility
Over-the-Counter
 No Physical Market
 Transaction created by two
parties
 Decentralized Market and
Exchange

Forwards
 Forward contract is an agreement between two parties to
buy/sell an asset at some specific future date at a specific
price determined at the initiation of the contract

Futures
 Futures contracts are exchange traded, give the
buyer/ seller a right to buy/sell a security in the
future at a specific price

Forwards vs Futures
Forwards Contract
 Non-Exchange Traded
 No Clearing House
 Between Two Parties
 Customized Contract
 Higher Default Risk
Futures Contract
 Exchange Traded
 Involve Clearing House
 Market to Market
 Standardized Contract
 Lower/Minimal Default Risk

Options
 A Contingent Claim
 An option/right, not an obligation to buy/sell an asset if a
certain threshold is reached
 Option premium must be paid to acquire the right

Swaps
 Swap is equal to a series of forward contracts
 Private transactions that are not directly regulated
 Payments payments can be fixed and floating
 Swaps can be on interest rates, exchange rates, stock
prices, commodity prices etc.

Purpose of Derivative Markets
 Improve market efficiency for the underlying asset
 Provide price discovery
 Mechanism for hedging against risk
 Reduce market transaction cost
 Require a high degree of transparency

Purpose of Derivative Markets
 The price of the contract with the shortest time to expiration
often serves as a proxy for the underlying asset
 The price of all future contracts serve as prices that can be
accepted by those who trade the contracts
 Options also aid in price discovery in the way the market
participants view the volatility of the markets

Criticism of Derivative Markets
 Very complex instruments
 Most investors fail to understand
 Mistakenly characterized as legal gambling

Role of Arbitrage in Prices
 The market will cause the prices of two equivalent assets to be
equal (i.e. eliminate the arbitrage opportunity)
 Risk free profit can be made if an arbitrage opportunity exists
 If the calculated forward price is different from the quoted
price, then an arbitrage opportunity exists

Role of Arbitrage in Prices
 Law of one price suggests that there should be one price for
identical assets
 Forward price is the spot price adjusted for interest rate
 If the calculated forward price is different from the quoted
price, then an arbitrage opportunity exists

Role of Arbitrage in Market Efficiency
 Efficient markets have less arbitrage opportunities
 Fully efficient markets have no arbitrage opportunities

Delivery Settled vs Cash Settled Contracts
 Underlying asset can be delivered at the expiration date in
delivery settled contract
 Long will pay the specified price (the forward price)
 Short will deliver the asset

Delivery Settled vs Cash Settled Contracts
 Only the owed difference will be paid by the party in a cash
settled contract
 If the price has gone up the long the short will make a cash
payment to long or vice versa

Default Risk
Long
 If the price of the asset
increases, the long will
receive a payment
 Long faces the default risk
that the short will not be
able to meet the
commitment
Short
 If the price of the asset
declines, the long will make a
payment to short
 Short faces default risk that
long will not be able to make
the payment

Settling a Forward Contract
at Expiration
 Payment made by the long at delivery, and delivery of asset is made
by the short.
 Long gets payment if the price has gone up
 Short gets a payment if the price has gone down

Termination Before Expiration And Effect On
Credit Risk
 New contract can be entered by either party in order to cancel
the existing position
 Eg. If long, can take a short position in an identical forward
contract to cancel position

Termination Before Expiration And Effect On
Credit Risk
 Credit risk can arise from entering into new contract with a
different counterparty
 Credit risk can be minimized by re-entering in the contract
with the same party
 Both parties can agree to cancel the both contracts to cancel
the position

Dealers
 Facilitate contracts for end users
 A big network of financial (banking and non-banking)
institutions act as dealers

Dealers
 Each dealer has a quote desk.
 Dealers are ready to take either side of the transaction, which
is usually completed over the phone.
-shift risk from parties as they take on transaction
-lay off risk by dealing with other dealers
-make profit from offloading risk to other dealers

End Users
 End users usually want to manage the risk
 End users include corporations, non-profit organizations and
governments
-Eg. A corn producer can buy/sell a forwards contract if he is
unsure about future corn prices

Equity Forward Contracts
 A contract to buy one stock, a portfolio of stocks, or a stock
index at a specific price in the future
 A single stock or a portfolio can be sold or bought at a future
date by locking in the price today

Equity Forward Contracts
 Index forward contracts behave identically to a single or a
portfolio of forwards contracts
 When underlying stocks pay dividends, forward price
adjustments will be needed

Bond Forward Contracts
 Similar to forwards contracts on equities
 Different than forwards contracts on interest rates
 Forward price needs to be adjusted for coupon paying bonds
 Zero coupon bonds act similar to non-dividend paying stocks

Bond Forward Contracts
 Forward contract on a bond must expire before the maturity of
the bond
 Forward contract should clearly define default risk.
-Eg. how default will affect the parties, should be
clearly mentioned in the contract.

Eurodollar Time Deposits
 Any deposit in US dollars outside the US
 Banks borrow funds by issuing Eurodollar time deposits
 Eurodollar time deposits are short term unsecured loans.
 The Eurodollar time deposits market, primarily centred in
London, is relatively less regulated.

LIBOR
 Lending rate between financial institutions
 Used for derivative pricing
 Rate at which London banks issue dollar loans to other
banks, the best rate on the dollars loaned by a bank
 an add-on interest rate, it is added to the face value

EURIBOR
 Interbank borrowing rate
 Issued by European Central Bank
 Used for borrowing between financial institutions

Forward Rate Agreement
 A Forward Rate Agreement is a forward contract on interest
rates
 FRA is different from a forward contract on a bond
 Only the interest differential on the notional amount of the
contract is paid

Forward Rate Agreement
 The parties to the contract will exchange a fixed rate for a
variable rate
 If rates rise then the long will get a differential payment (ie
long interest rates). If the interest rates decline then the short
will get a differential payment (ie short interest rates). At
expiration the present value of interest rate differential is paid.
The rate is called a forward contract rate.

Calculation
 Payment is the difference between the rate at expiration and
forward rate
Company X enters into an FRA with Company Y. Company X will receive a
fixed rate of 5% for one year on a principal of $1 million in three years.
Company Y will receive the one-year LIBOR rate, determined in three years'
time, on the principal amount. The agreement will be settled in cash in
three years. After three years' time, the LIBOR is at 5.5%. Company X will
pay Company Y, as the LIBOR is higher than the fixed rate.

Calculation
Mathematically, $1 million at 5% generates $50,000 of interest
for Company X while $1 million at 5.5% generates $55,000 in
interest for Company Y.

Calculating The Payoff
 Difference in the interest rates is paid
 The payoff is adjusted for the present value in the case of a
cash settled FRA
 Payoff made at maturity in the instance of a cash settled
contract
- Long gets a payoff if the interest rates go up.
- Short gets a payoff if the rates go down

Formula and Component Terms
 Notional principal is agreed upon at the initiation of the
contract
 Underlying rate is the rate at expiration, usually LIBOR
 Forward contract rate is the agreed rate
 Days in underlying rate are the days to maturity of the
instrument

Currency Forward Contracts
 Used by banks and corporations to manage foreign exchange
risk
 Eliminates uncertainty about future exchange rates
 Forward rate can be locked in without any upfront cost

Futures Contracts
 Standardized contracts
 Traded on exchanges
 Marked to market
 Limited default risk

Futures vs Forwards
Futures Contract
 Standardized
 Settled daily
 Involves Clearing House
 No/Minimal Default Risk
 Terms set by Exchange
(Market to Market)
Forwards Contract
 Non-standardized
 Not settled daily
 No Clearing House
 Considerable Default Risk
 Terms set by the parties

Margin and its Role
 A percentage of the contract value is initially deposited into
the margin account by each party.
 The margin allows each party to avoid paying the full amount
of the contract value at the initiation of the contract

Margin in Stock and Future Market
 Margin in stock market means a loan is made but a margin in
futures market means a percentage of the contract value has
been paid

Initial Margin
 It is the margin required to set up an account and buy the
contract
 Investor deposits the initial margin into her account before
starting futures trading. The deposit can be likened to a down
payment.

Maintenance Margin
 The minimum balance required to be maintained in the
margin account
 The maintenance margin requirement is lower than the initial
margin.

Variation Margin
 When the account balance falls below the maintenance
margin requirement, the investor need to deposit money in
the account to bring it back to initial margin.
 The amount deposited in the account to bring it back to the
initial margin

Settlement Price
 The official price of the futures contract, designated by the
clearing house, which usually represents the average of the
final few trades of the day
 eliminates the biases from the pricing of the futures

Price Limits
 Price limits are imposed on some futures where the price
cannot move beyond those limits.

Limit Move
 If the transaction is made at a price beyond the price limit
then the price freezes and it is called a limit move
 In case of price being stuck at upper limit it is called “limit up”
and “limit down” in case of price being stuck at the lower limit

Locked Limit
 If the price is beyond limit such that the transaction cannot
take place, then it is called a locked limit.
 The settlement price is one of the limits if the price has not
moved back within the limits by the end of the day

Margin: Example
The prices of a futures contract for five
consecutive trading days is provided in
the table. The initial margin
requirement is set at $4.00 per contract
and the maintenance margin is $3.60
per contract.

Margin: Example
 On day 0, a trader enters into a short position for 15 contracts.

Margin: Example
On day 0, the trader must
deposit an initial margin of
$60 (= $4 x 15).
Subsequent gains and
losses on the short position
are reflected in the ending
margin balance for the day.
The ending balance on day
4 is $45, which is below the
maintenance margin of
$54 (= $3.60 x 15).

Margin: Example
 On any day in which the
amount of money in the
margin account at the
end of the day falls below
the maintenance margin
requirement, the trader m
must deposit sufficient
funds to bring the
balance back up to the
initial margin.
requirement.

Margin: Example
 Therefore, the trader
must deposit $45 on day 5
to bring the margin
balance up to $90. After
reflecting a gain of $15,
the ending balance on
day 5 is $105.
 requirement.

Terminating Futures Contract
 Futures contracts can be settled either during or before
expiration. Termination terms are determined when the
contract is initiated. They specify whether the contract is
settled by physical delivery or cash.
 Most futures contracts are exited before expiration. An
offsetting contract needs to be entered for an investor to close
a position before expiration.

Delivery and Cash Settlements
Delivery-Settled Contracts
 Clearing house matches
the long position party
with the short position
party in the same asset
 Long gets the delivery
from the short and pays
the contract price to
the short
Cash-Settled Contracts
 The investor’s account will
be marked to the market
on the final day and the
position is closed
 Cash settlement contracts
have lower transaction
costs

Treasury Bill Futures
 Short term interest rate futures
 While the contract is trading, the price is quoted as 100 minus
the rate quoted as a percentage into the contract by the
futures market
 Expiry may be the current month, next month, or the next
quarter (eg March, June, September and December)
 For treasury futures, the contract with the nearest expiration
tends to have the highest trading volume Study Session 17, Reading 62

Eurodollar Futures
 Eurodollars futures are based on the LIBOR
 Final settlement is made on the final day based on the
Eurodollar rate determined by British Bankers Association
 Contracts do not permit the actual delivery of Eurodollar time
deposits

Treasury Bond Futures
 Medium or long term interest rate futures
 Very actively traded futures contracts
 A vast universe of bonds with differing maturities makes the
futures on bonds very complex
 A conversion factor is used to determine the health of the
deliverable bonds and which bonds can be delivered by the
short
 Cheapest to deliver bonds are identified by the short

Stock Index Futures
 Futures on stock indices have a multiplier which is multiplied
by the quoted futures price
 typically expire in March, June, September or December, but
the trading volumes are highest in the nearest two or three
expiration futures

Currency Futures
 Market is not as active as the currency forwards market
 Each contract has a designated size and quotation unit
 Typically expire in March, June, September and December
 Currency futures contracts call for actual delivery of the
underlying currency

Call and Put Options
 An option is a derivative contract which gives the owner a right but
not the obligation to exercise it in future. It is a right, not an
obligation.
Call Option
 right to buy an asset in the
 buyer expects the prices to go
up
 option is exercised if the price
of the asset is greater than the
strike price
Put Option
 right to sell an asset in the
 buyer expects the price to
decline
 option is exercised if the price
of the asset is below the strike
price

Call and Put Option: Terms
 Exercise price is a price at which the option can be exercised
(also called the strike price)
 The option premium is the amount paid to buy the right
 Payoff is the amount which option buyer receives upon
exercise of the option (it may be negative)

European and American Options
European Options
 Can only be exercised
at expiry
 Easier to value
 Trade at a discount
American Options
 can be exercised at any time
during the life of the option
 Difficult to value due to optimal
exercise time consideration
 Trade at a premium due to
flexibility on exercise dates

Moneyness of an Option
 Moneyness is the relationship between the price of the
underlying asset and the strike price
 An option can be characterised as: in the money, at the money
and out of the money
 An option is in the money, when it has a positive payoff (eg
long call = price > strike)

In the Money
 “In the money” Options: cash inflow s > cash outflow
For Call Options:
 price of the asset > option's
strike price
For Put Options:
 price of the asset < option's
strike price

At the Money
 An option is “at the money” when the exercise price is equal
to the market price of the underlying asset
 The definition for an at the money option is the same for both
put options and call options
 At the money options are usually not exercised because they
result in neutral cash flow at maturity (but a loss to option
holder given the option premium already paid)

Out of the Money
 Outflow > Inflow
 Option results in a loss and is allowed to expire worthless.
For Call Options:
 option's strike price > market
price of the underlying asset.
For Put Options:
 option's strike price <
market price of the
underlying asset.

Exchange-Traded vs Over-the-Counter
Options
Exchange-Traded
 Undertaken by both
institutional and individual
investors
 Credit risk does not exist
 Options exchange fixes all
the terms of the options
contract
 Public contracts
Over-the-Counter
 Undertaken by large
institutions, not individual
investors
 Credit risk exist
 Participants choose and
agree on the terms of the
option
 Private party contracts

Over the Counter Options
 Over the counter market is much like a forwards market
 There are no guarantees in the over the counter markets
 More flexible
 Dealers market

Exchange Traded Options
 The options exchange fixes all the terms of the options
contract, whether the option is European/American or delivery
settled/cash settled
 Fairly short term expirations for exchange traded options
 LEAPS (Long Term Equity Anticipatory Securities) are long term
options

Types of Options by Underlying
Instruments
 Financial Option – Option when the underlying asset is a
financial asset
(i.e. stock options, interest rate options, bond options)
 Commodity Option – Option when the underlying asset is a
commodity,

Financial Options: Stock Options
 The most popular form of option contract
 Typically exchange traded and available on most widely traded
stocks.
 Can also be created in the over the counter market
 Equity Options - options on individual stocks
 Index Options - options on a stock market index

Financial Options: Bond Options
 Options on bonds
 Primarily traded in over the counter markets
 Can be delivery settled or cash settled
 Exchanges have not been successful with bond options
 Bond options are mostly on government bonds

Interest Rate Options
 Underlying is an interest rate
 Option to borrow/lend in the future
 Effective tool to hedge against interest rate uncertainty
 When the contract expires, the payoff is made immediately

Out of the Money
 Exercise rate is used for interest rate options, instead of exercise
price
 Payoff is the differential between the underlying rate and the strike
rate
Call holder: right to make a fixed
rate payment and receive a
variable rate payment
-“In the money”: unknown rate >
strike rate
-“Out of the money”: unknown
rate < strike rate
Put holder: right to make a variable
rate payment and receive a fixed
rate payment
-“In the money”: unknown rate <
strike rate
-“Out of the money”: unknown rate
> strike rate

Interest Rate Cap
 A limit on the upward movement of interest rates
 A set of interest rate call options
 Each option is independent of the other option
 Each call option is called a caplet

Interest Rate Floor
 A limit on the downward movement of interest rates
 A series of interest rate put options
 Options are independent of each other
 Each option is called a floorlet

Interest Rate Floor and Interest Rate Cap
Interest Rate Cap
 A limit on the upward movement of
interest rates
 A set of interest rate call options
 Each option is independent of the
other option
 Each call option is called a caplet
Interest Rate Floor
 A limit on the downward movement of
interest rates
 A series of interest rate put options
 Options are independent of each other
 Each option is called a floorlet

Collars
 A combination of caps and floors
-Long cap and short floor
-Short cap and long floor
 Hedging can be undertaken at zero cost by matching the long
call and short floor
 Underlying can be any interest rate

Option Payoff
 The option value at expiration is called an option’s “payoff”
Payoff For Calls
 Payoff is the maximum of 0 or
“spot price minus strike price”
 Max (0, (Underlying Price -
Strike Price))
 Upside potential is unlimited
 Loss is limited to option
premium.
Payoff For Puts
 Payoff is the maximum of
either 0 or the “strike price
minus the underlying price”
 Max (0, (Strike Price -
Underlying Price))
 Downside potential is limited
 For a long put position, the
loss is limited to option
premium

Payoff for Calls: Long Position

Payoff for Calls: Short Position

Payoff for Puts: Long Position

Payoff for Puts: Short Position

Components of Option Price
 Option price have two components:
-Intrinsic value: Difference between the actual price and the
strike price
-Time value: Depends on the remaining time in option
expiration and volatility
 Option value = Intrinsic value + Time value
 Prior to expiry, Option value exceeds its Intrinsic value. The
difference is Time value.
 As the option reaches expiry, Time value decreases and
Intrinsic value increases.
 At expiry, Time value is 0 and Intrinsic value is at maximum.

Intrinsic Value
 For a Call: 0 or “spot price minus strike price”
 For a Put: 0 or “strike piece minus spot price”
 Before expiration, an option will normally sell for more than its
intrinsic value
 “At the Money” or “Out of the Money” Option: Intrinsic Value
= 0
 “In the Money” Option: Intrinsic Value > 0

Time Value
 The difference between the market price and intrinsic value
 At expiration, Time value = 0
 Given European options cannot be exercised early, all the
option value is “time value”

European and American Options:
Minimum and Maximum Values
 All options have a floor value of zero
 American options are more valuable than European options given
the flexible exercise regime
European Option:
Call Option:
 0≤co≤ So, min. value for call
option is 0 and the max. value is
the spot price of the underlying
Put Option:
 po≥0, min. value
 po≤ X/(1+r)t, max. Value
American Option:
Call Option:
 0≤Co≤ So, min. value for
American call will be zero and
max. value can be spot price
Put Option:
 Po≥0, min. value
 Po≤ X, max. value

European Options
 Given the lack of exercise option, the European put option needs to
be discounted
Example
Given: So= 28, X=25, r= 5% t=1/2 years
Since, 0≤co≤ So
0≤co≤28, minimum and maximum values for a European call option
Since, po≥0, min. value po≤ X/(1+r)t, max. value
0≤po≤24.4~ (25/(1.05).5), minimum and maximum value for European
put option

American Options
 Given the option of early exercise, the American put option does not
need to be discounted.
Example
Given: So= 28, X=25
Since, 0≤Co≤ So
0≤Co≤28, minimum and maximum values for a American call option
Since, Po≥0, min. value Po≤ X, max. Value
0≤Po≤25, minimum and maximum value for American put option

Lowest Prices of European Options
 Option Price is between 0 and the maximum
 Lower bound = 0 or current price [of underlying]- exercise
price (present value), whichever is higher
 To get a lower bound, options can be combined with risk free
bonds. An investor needs to buy a bond with a Face value =
Exercise price & a Current value = Exercise price (Present
value). This involves borrowing and lending money equal to
the present value of exercise price

European Call
 Lower bound combination for European calls.
 co ≥ Max*0,So-X/(1+r)T]
Transaction Current Value Value at Expiration
ST ≤ X ST > X
Buy Call C0 0 ST - X
Sell Short Underlying -S0 -ST -ST
Buy Bond X/(1+r)^T X X
Total C0 - S0 + X/(1+r)^T X-St≥0 0

European Put
 Lower bound combination for European Puts.
 Lower bound = 0 or exercise price (present value) - price of the
underlying
 po≥ Max*0,X/(1+r)T-So]
Transaction Current Value Value at Expiration
ST ≤ X ST > X
Buy Put P0 X - ST 0
Sell Short Underlying S0 ST ≤ X ST
Buy Bond -X/(1+r)^T -X0 -X
Total P0 - S0 + X/(1+r)^T 0 ST - X ≥ 0

Lowest Prices of American Options
 American options are exercisable immediately
 Lower bound = current intrinsic value
-Co ≥ Max(0, So-X)
-Po ≥ Max(0, X-So)
 Option price will be at least intrinsic value, otherwise an
arbitrage opportunity exists.
 The lower bound for American puts is higher than the lower
bound for European puts

Effects of Exercise Price on
Option Values
 Put options with a higher exercise price, have higher option prices
 Call options with a higher exercise price, have lower option prices
 A call option with higher exercise price cannot have a higher value than an
option with lower exercise price
 Call option buyers are willing to pay less for an option with a higher exercise
price
 The value of a put with a higher exercise price must be as much, if not more
than, the lower exercise price option

Effects of Time to Expiration on
Option Values
 Additional time to expiry is an advantage for an American put holders since it can
be exercised at any time, but it can be a disadvantage for a European put holder
due to the loss of interest
 More time to expiry, the more valuable an option
 For the options deep in the money or deep out of money, the time value of the
option may be diluted.
 For a European put, longer or shorter time to expiry can be worth more

Put-Call Parity for European Option
 A premium on the call option corresponds to the fair value of a put option having
the same exercise price and expiration date and vice versa
 Arbitrage opportunity will exist if the prices diverge
 C+X/(1+r)t= So + P

 C+X/(1+r)t= So + P
The left hand side of the equation consists of a European call and risk free bond
-If price of underlying < strike price, then the option is worthless at expiry
and the bond = X
-If price of underlying > strike price, then the call expires as S-X

 C+X/(1+r)t= So + P
The right hand side of the equation comprises of a European put and the
underlying asset
-If price < strike price, the put expires as X-S
-If price > strike price then the put expires worthless and the value of the
underlying is ST

Put-Call Parity Used to Arbitrage
 Right hand side of the equation is called a synthetic call
 An “in the money” synthetic call will give the underlying value minus the payoff of a
bond
 Right(?) hand side of the equation is called the synthetic put
 Prices not conforming to put call parity will result in an arbitrage opportunity

Effects of Cash Flows on
Put-Call Parity
 In the case of stocks, present value of dividends is deducted from the underlying’s
price
 In the case of bonds, present value of coupon payments is deducted from the
underlying asset’s price
co+X/(1+r)T= Po + [So-PV(CF,0,T)]

Effects of Cash Flows on
the Lower bounds
 In the case of stocks, present value of dividends is deducted from the underlying
asset’s price
 In the case of bonds, present value of coupon payments is deducted from the
underlying asset’s price
co ≥Max{0,*So-PV(CF,0,T)]-X/(1+r)T}
po ≥Max{0,X/(1+r)T-[So-PV(CF,0,T)]}

Effects of Interest Rate Change
on an Option’s Price
 Higher interest rates :
-increase the call option price
-decrease the put option price
 When interest rates are high, investors forfeit more interest when interest rates are
higher while waiting to sell the underlying. (i.e. the opportunity cost of waiting to
sell in a higher interest rates is more significant)
 When the underlying asset is an interest rate or bond, the interest rates do not
have a strong effect on the option prices

Effects of Volatility Change
on an Option’s Price
 Higher volatility of the underlying asset value increases the value of both put and
call options
 Higher volatility increases the possible upside value and downside value of the
underlying asset
-Upside advantage helps calls but at the same time does not hurt the puts
-Downside effect helps the puts but does not hurt calls

Swap Contracts
 Swaps are a series of fixed or variable payments, otherwise described as a series of
forward contracts
 No upfront payment and has zero value at the initiation
 Customized contracts and are typically over the counter instruments
 Only the net payments between parties are made. The difference owed by one
party is paid to the other since the payments are made in the same currency.
However, currency swaps are an exception to this rule as full interest payments are
made in currency swaps.

Termination of Swap Contracts
 Termination date is specified
 Usually the final payment is the termination
 Original time to maturity is also called the tenor of the swap

Termination of Swap Contracts
 Termination can be undertaken by paying or receiving the market value from the
counter party. This can only be undertaken if specified by both parties in advance.
 A swap can also be sold to another party in order to terminate the position
 A swaption is also a way to terminate the swap. It is an option to enter into a swap
in the future.

L1 flash cards derivatives (ss17)

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