Level I Study Session 16 Analysis of Derivatives

1
Level IStudy Session 16Analysis of Derivatives

• Dr. Enzo Mondello

2
Overview
Content Introduction Futures Market The Options
Market Option Payoffs Strategies The Swap
Market Introduction
3
Introduction

• LOS A.a Define derivative instruments, arbitrage
  opportunity, forward
• contract, futures contract, options (calls and
  puts) and swaps
• Financial Derivatives are instruments which are
  derived from
• other financial instruments or assets. The
  payoff of financial
• derivatives depends on their underlying.
• Forwards A forward contract negotiated today
  gives the
• holder of the contract the full obligation to
  conduct a transaction
• at a specific time in the future involving a
  certain quantity and
• type of asset at a predetermined price. With
  such an instrument
• the uncertainty of the price movement of an
  underlying can be
• reduced.

4
Introduction

• Futures Such a contract is the same as a
  forward. The difference
• lies in the standardisation. In contrast to a
  forward a future
• contract is highly standardised. The
  standardisation concerns
• the life time of the contract, the price, the
  underlying (stock,
• index, bond, interest rate, exchange rate, raw
  material).
• Purchaser of the contract
• receives delivery of the underlying and pays for
  it
• Seller of the contract
• delivers the underlying and receives payment

5
Introduction

• Options The buyer of the option has the right
  but not the legal
• obligation to enter into a transaction
  involving an underlying asset
• at a predetermined future date and at a
  predetermined price
• (exercise or strike price). The seller of the
  option contract has the
• obligation to perform.
• Option long
• Its always the buyer of the contract who can
  decide
• whether or not to buy or sell the underlying
  asset. He will
• use his right (option) only if he can earn
  money.
• Option short
• Its always the seller (writer) of the contract
  who has the
• obligation to fulfil the contract when the buyer
  exercises his
• option.

6
Introduction

• Options on Futures This is an option that uses
  a futures contract
• as the underlying asset. When the option is
  exercised, the buyer will
• receive the underlying (i.e. the futures
  contract). The option writer
• delivers the futures contract.
• By exercising the call option
• Buyer receives a long position in the underlying
  futures con-
• tract having the settlement price prevailing at
  the time the
• option is exercised. In addition to the contract
  he receives
• a cash payment as a difference between the
  settlement price
• and the price of the option

7
Introduction
Writer (seller) Receives a short position in
the underlying futures contract having
settlement price prevailing (at the time the
option is exercised). In addition to that
position he has to pay the difference between
the futures settlement price and the
exercise price to the buyer. The buyer of the
option (owner of the contract) will not
exercise the contract if the futures settlement
price is below the strike price. If the option
on a futures contract is a put the buyer has a
short position while the seller is long.
8
Introduction

• Swaps These are agreements between two or more
  parties to
• exchange sets of cash flows over a
  predetermined period of time in
• the future. Its also a forward contract but
  the underlying asset will
• be swapped at the opening time of the contract
  for a certain time
• period.
• The cash flows are tied to the value of debt
  instruments or
• the value of foreign currencies.
• ?Interest Rate Swaps
• ?Currency Swaps
• Swaps are tailored-made and meet the specific
  needs of the
• counterparties. Swaps are not exchange-traded and
  therefore not
• very regulated.

9
Introduction
LOS A.b Discuss the no-arbitrage principle
Pricing errors will be instantaneously
corrected so that all quoted prices have to be
free of all known errors. ? No-Arbitrage
Principle Any rational price for a financial
instru- ment must exclude arbitrage
opportunities. This principle in combination
with the thesis of market efficiency is
fundamental for the pricing of financial
derivatives.
10
Introduction
Los A.c Distinguish between a futures and a
forward contract Forwards Futures Privat
e contracts Exchange-traded contracts Unique
contracts Structured contracts Default
risk Guaranteed by the clearinghouse No
up-front cash Margin account deposits Low or no
regulation Regulated Apart from these
differences, forwards and futures are
very similar and are especially priced by the
same economic principles.
11
Introduction

• LOS A.d Distinguish between an option buyer and
  an option writer
• Call The buyer of the option has the right to
  purchase a certain
• amount of the underlying asset at a specific
  price (exercise or strike
• price) during a specified time period.
• Put The buyer of the option has the right to
  sell a certain
• amount of the underlying asset at a specific
  price during a
• specified time period.
• To obtain this right the buyer of the options
  (calls and puts) has
• to pay a price called the premium to the
  seller (writer) of the
• option.
• The seller of the option is called the option
  writer and he receives
• for his obligation to deliver (call) or buy (put)
  the premium from the
• buyer of the contract.

12
Introduction
Position of
Buyer of the Option
Seller of the option
the contract
Pays the premium and
Receives the premium
Type of
receives the right to enter in the underlying
contract
and has an obligation
option
to fulfil the contract
The buyer of the option
The writer of the option
Call
receives the right to
has an obligation to
buy the underlying asset
deliver the underlying asset
The buyer of the option
The writer of the option
Put
owns the right to deliver
has an obligation to
the underlying asset
buy the underlying asset
13
Introduction

• LOS A.f Explain the major application of
  financial derivatives
• Market Completeness All identifiable payoffs
  can be traded
• in the securities markets.
• Speculation High risk position
• Risk Management Hedging the positions in the
  markets. The risks
• of own positions will be shifted to other
  market participants.
• Concept of Arbitrage Derivatives can be used to
  arbitrage away
• mispricing in the markets
• Trading Efficiency Derivatives markets are
  often more liquid and
• offer lower transaction costs than the
  underlying markets.

14
Futures Markets

• LOS B.h Types of futures contracts
• Agricultural and metallurgical contracts i.e.
  agricultural goods,
• oil, livestock, forest product, textiles,
  foodstuffs, and
• minerals.
• Interest earning assets i.e. interest rate
  futures (existing contracts
• span almost the entire yield curve)
• Foreign currencies
• Indexes i.e. stock indexes (there is no physical
  delivery of the index
• but there are two possibilities to close the
  position 1) reversing
• the trade or 2) cash settlement at the end of
  trading)

15
Futures Markets
LOS B.a Distinguish between speculator and
hedger Speculators (or traders) accept their
market risks in their portfolios whereas hedgers
trade financial futures to reduce their
market risks in their portfolio. Short
Hedgers own assets which they must deliver in the
future and so want to reduce their risk by
selling the asset now in the futures market (for
the spot price) Long Hedgers dont own the asset
today which they must have in the future and
so buy the asset now in the futures market to
reduce their risk (for the spot price)
16
Futures Markets
Account Executives take orders from the general
public (clients) Floor Brokers execute the
orders from the account executives
17
Futures Markets
LOS B.b Distinguish between volume and open
interest Long Position Purchaser of a futures
contract Short Position Seller of a futures
contract ? For each contract there is a buyer
and a seller
18
Futures Markets
Futures
Seller Short Futures
Buyer Long Futures
Buy to open
Sell to open
Open a position
Buy to close
Close a position
Sell to close
19
Futures Markets
Open interest Is the number of contracts that
currently exist in the futures markets. For
instance, an open interest of 200 means that
there are 200 short and long positions
each. Trading volume Is a measure for the
activity in the futures markets. Is either a new
contract created by a buyer and a seller or an
existing contract being traded. Organized
exchange Is a non-profit association of members.
Securities can only be traded by members. Trades
take place in designated locations. It is an open
outcry market.
20
Futures Markets

• LOS B.c Discuss how the standardisation of
  futures contracts promotes liquidity
• The standardisation concerns
• the quality and quantity of goods that can be
  delivered
• the delivery time and
• the manner of delivery
• minimum price fluctuation (tick size)
• daily price limit (maximum price movement
  allowed in a single trading day)
• ? Uniformity promotes market liquidity.

21
Futures Markets

• LOS B.d Discuss the role of the clearinghouse in
  trading futures contracts
• Each exchange has a clearinghouse
• The clearinghouse acts as an intermediary
  between buyers and
• sellers of contracts ? It buys contracts from
  sellers, and then sells
• them to buyers.
• The clearinghouse thus becomes the guarantor
  that all traders
• will honor their obligations. Traders do not
  have to rely on the
• creditworthiness of the party on the other
  side of the transaction.

22
Futures Markets

• LOS B.e Define initial margin, maintenance
  margin, variation margin,
• daily settlement, margin call and marking to
  market
• Initial margin is the amount deposited before
  trading in futures.
• Its usually equal to the daily allowed price
  fluctuation of the
• contract.
• Maintenance margin is the point at which an
  investor who has
• lost money must bring it back up to the
  original level (initial
• margin).
• Variation margin is the amount required to
  replenish the account
• to the initial margin when the traders
  account falls under Maint. M.
• Daily settlement refers to the practice in the
  futures market
• of requiring traders to realize any losses and
  gains they incur on a
• daily basis. This is also called marking to
  market.
• Margin call is a demand for more margin, to
  bring account up to
• its initial level.

23
Futures Markets
margin
post margin
Clearing- house
Trader
Broker
Broker has to post mar- gin withclearinghouse
Before trading the trader must deposit
funds (margin)
24
Futures Markets

• LOS B.f Calculate the price at which a trader
  will receive a mainte-
• nance margin call
• Example
• Short position in agricultural futures (corn)
• 1 contract of corn at 2.20 per bushel (1
  contract 5000 bushels)
• Initial margin 1200
• Maintenance margin level is 75
• Calculate the margin call if the price of corn
  goes up by 0.10 a bushel
• respectively 0.04 a bushel?

25
Futures Markets

• Variation margin must always be paid in cash or
  cash equivalents
• (i.e. bank letters of credit or T-Bills)
• If the balance in the margin account exceeds the
  initial margin, the
• trader can remove these funds from the
  account. If not (that means
• the balance of the account falls below the
  initial margin) the trader
• cant remove the cash.

26
Futures Markets
LOS B.g Describe the three ways to close a
futures position 1. Delivery - almost never
used -, the actual physical delivery of a
specific amount of goods 2. Offset - the normal
way to close a position - if you bought a
futures contract, you simply enter a reversing
transaction and sell the exact same
contract. 3. Exchange for physicals - an
agreement between two parties to cancel their
contracts and exchange actual goods.
27
Futures Markets

• LOS B.h Explain the purposes of futures markets
  
• Price discovery Futures give us an idea what
  the market thinks
• the price of some goods will be in the future,
  this can assist in
• planning and forecasting.
• Hedging Futures allow investors to limit and
  control risk in a
• variety of creative ways.
• Exam Tips
• In the past, questions have focused more on
  valuation and pricing,
• rather than on definitions and procedures. So be
  prepared for a
• question on margins, and calculating the point at
  which a margin
• call would occur.

28
The Options Market
LOS C.a Distinguish between the rights and
obligations of put and call buyers and writers
See slide 5. LOS C.b Define in
-the-money, out-of-the-money, and
at-the- money for both puts and calls, and
calculate the amount which an option is in or out
of the money A call option is
in-the-money when the price of the
underlying stock (S) is greater than the strike
price (X). ? S gt X When the price of the
underlying stock (S) is less than the
strike price (X), the option is
out-of-the-money. ? S lt X
29
The Options Market
When the strike price (X) and the underlying
stock price (S) are exactly the same, the call
option is at-the-money. ? S X For put
options this is reversed
In-the-money
S lt X S X S gt X
At-the-money
Out-of-the-money
Moneyness is related to whether it would make
sense to exercise the option.
30
The Options Market

• LOS C.c Distinguish between a European and an
  American call or
• put option
• An American option can be exercised anytime
  prior to expiration
• A European option can only be exercised at
  maturity
• Since the owner of the American option has more
  rights, the
• American option is always worth more than the
  European
• option before maturity.

31
The Options Market
LOS C.d Explain why an American option must be
worth at least as much as a European option
The holder of an American option has all of
the rights of a holder of a European option, plus
the holder of the American option can exercise
those rights at any time prior to expiration,
rather than only at expiration as with the
European option.
32
The Options Market

• LOS C.e Describe the ways in which an order can
  open or close a
• position
• An order can open a position by either buying or
  writing an
• option
• An order can close a position by either buying
  or writing
• an option
• ? If a position is opened by selling a call, that
  position could be
• closed by buying a call. The order that
  closes an existing position
• is called an offsetting order.
• A market order instructs the floor broker to
  transact the trade at
• whatever price is currently available. Limit
  order has to meet cer-
• tain conditions, e.g. price.

33
The Options Market
LOS C.f Discuss the role of the clearinghouse
when trading listed options Just as with
futures contracts, the clearinghouse for options
trades acts as an intermediary between buyers and
sellers of contracts. All purchases and sales
are executed with the clearinghouse as the party
on one side or the other of the transaction ? The
clearinghouse thus becomes the guarantor that all
traders will honor their obli- gations. So there
is no credit risk for traders. Open interest is
the number of contracts that are outstanding at
any given time. To determine the open interest
(number of contracts) you would sum up the open
positions and divide by two.
34
The Options Market

• LOS C.g Define margin and discuss why writers of
  naked options
• must deposit initial margin when initiating
  their positions
• Margin in options trading is an amount that must
  be deposited in
• a traders account to cover the riskiness of
  the option position.
• A covered short call requires no margin because
  the positions
• are covered by holding the underlying asset in
  the account and so
• poses no risk to the system.
• When writing a naked option, where there is no
  offsetting
• position in the traders account, there is a
  risk of default.To cover
• the potential losses, margin is required upon
  initiating the
• position.

35
The Options Market
Exam Tips Its important that you can evaluate
whether the prices of puts or calls make sense
relative to the current stock price.
Moneyness is an important concept that is often
tested.
36
Options Payoffs Strategies

• LOS D.a Calculate the intrinsic value of a put
  or call option and
• explain the relationship between intrinsic
  value and whether the
• option is in or out of the money
• A call has an intrinsic value if the stock price
  is above the strike
• price, it is therefore in-the-money (S gt X).
• Example
• If you own a call option with a strike price of
  100, and the
• stock is trading at 110, the option has value
  because you
• own the right to buy the stock (X) below its
  current price (S).
• The intrinsic value of the call is 110 100
  10
• A put has an intrinsic value if the stock price
  is below the strike
• price, it is therefore in-the-money (S lt X).

37
Options Payoffs Strategies
LOS D.b Calculate the expiration-day value of a
put or a call Expiration day value of a call
option, CT CT Max (0, ST X) where ST
underlying stock price X option exercise
price Expiration day value of a put option,
PT PT Max (0, X ST)
38
Options Payoffs Strategies
Example Calculate the intrinsic value of a put
(expiration date) by considering the following
information a) S 300, X 290 b) S 280,
X 250
39
Options Payoffs Strategies

• LOS D.c Explain short and long option positions
  
• A short position is the position of the option
  writer, regardless
• of whether the option is a put or a call.
• A long position is the position of the option
  buyer, or owner,
• regardless of whether the option is a put or
  call.

40
Options Payoffs Strategies
LOS D.d. / g Draw, interpret and compute the
expiration profit / loss diagrams for the long
call, short call, long put, and short put
strategies
Profit / losses to the buyer of the call
Profit graph of a Call
10
0
Profit / losses to the writer of the call
-10
100
110
41
Options Payoffs Strategies

• Interpretation of the graph
• The worst situation facing the buyer of a call
  is the loss of 10
• Breakeven for buyer and seller is the strike
  price plus premium
• The potential profit for the buyer is unlimited
• The potential loss for the writer is unlimited
• The buyer will exercise the option whenever the
  stocks price
• exceeds the strike price of 100
• The greatest profit the writer can make is the
  10 premium
• Options trading is a zero-sum game because the
  sum of the gains
• and losses between buyer and seller is always
  zero

42
Options Payoffs Strategies
Profit graph of a Put
Profit / losses to the writer of the put
10
0
-10
Profit / losses to the buyer of the put
90
100
43
Options Payoffs Strategies

• Interpretation of the graph
• Worst situation facing the buyer of a put is the
  loss of 10 (premium)
• Maximum gain to the buyer is limited to the
  strike price minus
• premium
• Potential loss to the writer is limited to the
  strike price less the
• premium
• The buyer will exercise the option at expiration
  whenever the stock
• price is less than the strike price
• The greatest profit the writer can make is 10
  premium
• Trading put options is a zero-sum game

44
Options Payoffs Strategies

• LOS D.i Explain and interpret the profit / loss
  diagram for a covered
• call strategy
• Writing a covered call is a strategy designed to
  generate income
• from a stock already held that the investor
  believes will not appre-
• ciate in value in the short term.
• ? The risk to this strategy is that if the stock
  does rise, any gain will
• be nullified by the call option
• When a call is written, the extra income
  increases the investor profit
• if the stock price closes below the strike
  price, while if the
• stock rises above the strike price, the amount
  of gain is
• limited

45
Options Payoffs Strategies
(Profit / loss)
10 premium
20
The covered calls profit line
10
0
The stocks profit line
(Stocks Price)
100 110
Spot price
Strike price
46
Options Payoffs Strategies

• Interpretation of the graph
• If the stock closes below 100, the option will
  expire, and the
• option writers loss is offset by the premium
  income of 10
• If the stock closes between 100 and 110, the
  option will expire
• worthless. Since the option was an
  out-of-the-money-call,
• the option writer will get any stock
  appreciation above the original
• stock price and the strike price. So the gain
  (premium plus stock
• appreciation) will be between 10 and 20.
• If stock closes above 110, the strike price,
  the writer will get
• nothing more. The maximum gain is 20 on the
  covered out-
• of-the-money-call.

47
Options Payoffs Strategies
LOS D.j Compute the profit or loss for a covered
call strategy, given any expiration value of
the underlying asset Example A trader owns a
stock of company B Stock of company B is
currently trading at 30 Strike price for a call
option is 35 Call premium is 4 Calculate the
profit or loss when the stock goes up to 33
resp. to 37 or falls to 28 for the owner of
this covered call strategy!
48
Options Payoffs Strategies

• LOS D.k Explain a portfolio hedging (insurance)
  strategy that uses
• puts options, and interpret the expiration
  profit / loss diagram for this strategy
• Portfolio insurance is a strategy of buying a
  put option to hedge
• a long equity portfolio you already own.
• The strategy sets a floor under your losses. The
  size depends
• on the strike price of the put.
• The cost of the strategy is the amount of the
  put premium to pay
• If the market does not decline in value, the
  put expires worthless.

49
Options Payoffs Strategies
LOS D.l Compute the profit or loss for an
insured portfolio, given any expiration value
of the underlying asset
Profit/ loss
Profit/ loss
Profit on long put
Profit on portfolio
Premium put 2
0
0
Portfolio Price
Portfolio Price
St25
X25
Profit on portfolio
Profit on portfolio plus put
0
Profit on the long put
X25
50
Options Payoffs Strategies
Interpretation of the graph Portfolio insurance
cuts your downside losses but leaves the
upside potential alone. If the stock drops below
25, you will have a gain on your put position
that offsets any additional decline in the stock
price. At a price of 20, for example, you would
have a 5 loss on the stock, plus a 5 gain on
the put and a 2 loss for the premium paid.
Also a net loss of 2 ? The net loss will always
be determined by the strike price of the
put. You pay the put option premium to insure
your portfolio against losses below the
strike.
51
Options Payoffs Strategies

• LOS D.o Describe the effects that portfolio
  hedging (insurance) has
• on the risk and return consequences of a
  portfolio
• On the upside, portfolio insurance using put
  options will reduce
• returns by the amount of the premiums paid for
  the put options.
• If the portfolio does not appreciate enough to
  cover the premium
• there will be a loss overall
• The downside risk is limited. A floor value of
  the portfolio is estab-
• lished, and any decline in the underlying
  asset value will be offset
• by a gain in the put position. The portfolio
  value will not decline
• below this floor value. Of course, returns
  will be reduced by the
• amount of the premium paid.

52
Options Payoffs Strategies
Exam Tips If you can reason out the gain or
loss on the various option questions, you can
probably answer most questions. So you have to
concentrate on the profit and loss diagrams.
53
The Swap Market

• LOS E.a Define swap counterparties, notional
  principal, received
• fixed, and pay fixed
• Notional principal is the amount used to make
  computations in a
• swap. It is not the amount transferred.
• Counterparties are the two main parties to the
  swap that are
• actually at risk.
• In a plain vanilla interest rate swap, on
  counterparty agrees to
• make periodic payments based on a fixed rate
  of interest, and to
• receive periodic payments based on a floating
  rate of interest.
• ? This counterparty is on the pay fixed side
  of the swap!
• The other counterparty who pays floating rates
  and receives fixed
• rates, is referred to as the receive fixed side.

54
The Swap Market

• LOS E.b Explain and interpret the cash flow
  diagram for a plain
• vanilla interest rate swap and a plain vanilla
  currency swap
• If in a plain vanilla interest rate swap the
  fixed rates were higher,
• the pay fixed counterparty will make a payment
  to the receive
• fixed income counterparty.
• ? The amount of the payment will be the net
  difference between
• the fixed and floating rate obligations.
• Example
• notional principle is 10 million
• fixed rate for the year is 8
• floating rate is 7
• ? The pay fixed counterparty would owe
• 0.01 10million 100000

55
The Swap Market

• In a currency swap there are three types of cash
  flows
• 1. The initial exchange of currencies at the
  going rate
• 2. The annual payment of the interest owed, made
  by both counter-
• parties in full in the appropriate currency
• 3. The conclusion of the transaction, where the
  original amounts
• exchanged are reversed

56
The Swap Market

• LOS E.c Calculate the net payment that is made
  from one party to
• the other in an interest rate swap and a
  currency swap and identify which of the
  parties pays it
• Each of the two parties takes the interest rate
  that is applied
• to the currency or debt instruments they
  acquired in the swap
• and multiplies by the notional value of the
  transaction
• In an interest rate swap, whoever owes the
  larger amount pays
• the party owing the smaller amount, with the
  payment being
• the difference
• In a currency swap, each counterparty pays every
  payment full.

57
The Swap Market

• LOS E.e Calculate the payments in a currency
  swap and explain why
• netting does not take place
• The payments made each year will depend on the
  interest rates on
• the notional principal in each counterpartys
  currency.
• Example
• Assume a French firm enters into a plain vanilla
  currency
• swap with a US firm whereby the US firm agrees
  to pay a
• fixed rate of 6 in francs, and receive a
  floating rate of LIBOR
• which initially is 5. The notional principal is
  5 million, and
• the initial exchange rate is 5Ffr / 1
• At the end of the 1st year
• the US firm pays 0.0625Ffr million 1.5Ffr
  million
• The French firm pays 0.055million 0.25
  million

58
The Swap Market

• LOS E.f Describe how and why a financial
  institution might be
• motivated to engage in an interest rate swap
• The most common justification for a financial
  institution to engage
• in an interest rate swap is to match asset and
  liabilities.
• ? Example an institution with fixed rate assets
  but floating
• rate liabilities may want to reduce their
  interest rate ex-
• posure by swapping their fixed rate assets
  for floating rate
• assets.

59
The Swap Market

• LOS E.g Describe how and why a party might be
  motivated to engage
• in a currency swap
• Comparative Advantage These are cases in which
  one firm may
• have better access to the capital market than
  another
• Other swap motivations
• reducing transactions costs
• lowering hedging costs
• avoiding regulation
• maintaining privacy

60
The Swap Market
LOS E.h Explain and interpret the box and arrow
diagram for a plain vanilla currency swap
A box and arrow diagram is just a schematic
diagram of a swap transaction, where the boxes
represent (1) the lenders who loan funds to (2)
the counterparties, who exchange the funds.
Box Lender
Box Party A
Box Party B
Box Lender
X
YFfr ? X
YFfr
61
The Swap Market

• LOS E.i Identify which party has a comparative
  advantage in bor-
• rowing a currency, given the interest rates that
  two parties face
• when borrowing either of two currencies
• The party which can borrow at the lower rate in
  a given currency
• has a comparative advantage. This advantage is
  a frequent
• motivation for currencies swaps.
• Two parties with comparative advantages in
  different currencies
• borrow in the low interest rate currencies,
  and exchange loan
• proceeds with one another.

62
The Swap Market
Exam Tips Be prepared for questions that cover
the basic concepts of swaps. Dont get lost in
details. The LOS focus more on the how than the
why of swaps. Try to understand the structure of
such transactions. This will help you to answer
the questions.