MANG 6020
Financial Risk Management
Lecture 3: Financial Markets and Products II
Dr Yue Zhou, Lecturer in Finance
Southampton Business School
University of Southampton
Yue.Zhou@soton.ac.uk
Academic year 24/25
Learning outcomes
At the end of this lecture, you should be able to:
• Understand the Types of Traders and Market Structure
• Analyze Key Derivative Instruments – Learn the characteristics, pricing, and
applications of futures, forwards, swaps, and options in financial markets.
• Evaluate Forward and Futures Pricing – Apply pricing models to determine the value of
forward and futures contracts, considering arbitrage opportunities.
• Explore Interest Rate Swaps and Their Applications – Understand how interest rate
swaps function and how they can be used to manage financial risk.
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Part I The Markets
Type of Traders
•
Hedgers
–
•
Using derivatives markets to offset the risk of prices moving unfavorable for their ongoing business → reduce risk
Speculators
–
Use derivatives to seek profit by betting on the future direct of market prices of the underlying asset → taking risk
• Scalpers: watching for very short-term trends (e.g. few minutes) and attempt to profit from small changes in the
contract price
• Day traders: holding positions for less than one trading day
• Position traders: holding for much longer periods of time, intent to make significant profits from major movements in
the markets
•
Arbitrageurs
–
•
Using derivatives to take offsetting position in two or more instruments to lock in a profit
Market Maker
–
A market maker is a firm facilitate or individuals the trading of a particular security to keep the financial market liquid by
providing buy and sell quotations simultaneously.
–
The most common type of market maker is a brokerage house that provides purchase and sale solutions for investors in an
effort to keep financial markets liquid
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Short Selling
• Selling an asset that is not owned. Possible in some cases, but not all investment assets.
• Example：The stock price is $120 in April, and expected to decreased to 100 in July
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Exchange-traded Market
• An exchange market is a market where investors trade standardized contracts made by
exchanges
• Have been used to trade financial products, e.g., stocks or derivatives
• US
– New York Stock Exchange: stocks
– Chicago Board Option Exchange: derivatives, e.g., futures and options
• UK: London Stock Exchange: equity, fixed income, exchange-traded funds/exchangetraded products and foreign exchange markets.
• EU: Euronext: operates Securities Markets (in Amsterdam, Brussels, Dublin Lisbon, Oslo
and Paris) and Derivatives Markets (in Amsterdam, Brussels, Lisbon, Oslo and Paris)
• China: Shanghai Stock Exchange and Shenzhen Stock Exchange
• The role of exchange is to define the contacts that trade and organize trading so that
market participants can be sure that the trades they agree to will be honored.
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Clearing Houses
•
Exchange-traded derivatives contracts are administered by a clearing house: stand between traders
in the exchange-traded market, guarantees the performance of the parties to each transaction
•
The clearing house has a number of members, and trades by non-members have to be channeled
through members for clearing.
•
The members of clearing house contribute to a guaranty fund that is managed by the clearing
house.
•
Clearing houses require traders to post cash or marketable securities as collateral, which is referred
to as margin
•
Margin refers to cash or assets transferred from one trader to another for protection against
counterparty default
•
The margin is set to be sufficiently high that exchange is unlikely to lose money if it has to close
out a trader
•
This combined with the guaranty fund means that traders are subject to virtually no credit risk
•
It reduces counterparty, operational, settlement, market, legal, and default risk for traders.
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Over-the-Counter (OTC) Market
•
A network of dealers at financial institutions, corporations, and fund managers who trade directly with each
other, without involving an exchange.
•
OTC market participants can be divided into end users and dealers. End-users include companies, fund
managers and other financial institutions that use derivatives to manage risk or gain specific exposures. Dealers
are large financial institutions that provide bid and ask quotes for common derivatives trades.
•
Interest rate derivatives are the most popular derivatives in the OTC market. Most interest rate derivatives are
interest rate swaps.
•
The attraction of the OTC market is that derivatives do not need to be standardized, so they can be tailored to
the needs of the end user.
•
Prior to the credit crisis that started in 2007, most OTC trades were handled by bilateral agreements between
market participants. The agreements often involved collateral being posted, but the amount of collateral
required was not usually as great as the amount of margin that would be required for similar transactions in the
exchange-traded market.
–
•
The most common such agreement was an International Swaps and Derivatives Association (ISDA) Master Agreement.
As a result, whereas exchange-traded markets were almost completely free of credit risk, OTC markets were not.
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MANG 6020 Financial Risk Management
OTC market
•
Following the credit crisis that started in 2007, regulators have become more concerned about
systemic risk → reducing credit risk by making the OTC markets more like exchange-traded
markets.
•
Standard OTC transactions be handled by what are known as central clearing parties (CCP)
•
CCP takes the credit risk of dealers, and it manage this risk by requiring an initial marking and a
daily variation margin from them.
•
Before the 2007-08 credit crisis, over-the-counter markets were largely unregulated. Several new
rules have been introduced since the financial crisis. E.g. Central counterparties (CCPS) must be
used for standardized trading between dealers.
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MANG 6020 Financial Risk Management
Part II Plain Vanilla Derivatives
Size of OTC and Exchange-Traded Derivatives Markets
Between 1998 and 2016
800
Size of
Market
700
($ trillion)
600
OTC
500
Exchange
400
300
200
100
0
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MANG 6020 Financial Risk Management
Introduction of Derivatives
An instrument whose value depends on the values of other basic underlying assets
They are useful because they precisely capture and isolate particular risks, so that they can
be transferred. This makes them very helpful in risk management
Basic types of derivatives
• Futures and Forward: an agreement to buy or sell an asset at a certain price at a certain
future time
– Futures: standardized and trades on the exchange
– Forward: traded in the OTC market, particularly popular on currencies and interest rates
• Swap
– A swap is an agreement to exchange cash flows at specified future times according to certain
specified rules
• Option
– Gives holders the rights (but not obligations) to buy/sell at a certain price
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MANG 6020 Financial Risk Management
Futures & Forward
•
Futures: an agreement (obligation) to buy/sell an asset at some future date T for some price K
fixed now.
–
Financial Asset: Underlying asset is financial asset, e.g., stocks and bonds
–
Commodity Asset:
•
Agricultural commodities
• cultivated products: corn, wheat, soybeans, cocoa and sugar
• Livestock: cattle and hogs
•
Mentals: gold, silver, platinum, copper, lead, etc..
•
Energy
• Crude oil: which is the world’s largest commodity market.
• Natural Gas
• Electricity
•
Weather: the most popular contracts are those based on temperature
• Forward: Similar to futures contracts but trade in the OTC market, particularly popular on
currencies and interest rates.
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MANG 6020 Financial Risk Management
Futures & Forward
•
•
•
•
•
Long position: agrees to buy the asset on a certain specified data for a certain price
Short position: agrees to sell the asset on the same date for the same price
The contract delivery date can be any data mutually convenient to the two parties. Usually, in forward
contracts a single delivery date is specifies, while in futures contracts there is a range of possible delivery
dates.
Futures are settled daily while forward are not.
Most futures contracts are closed out prior to delivery while forward contracts do lead to delivery of the
physical assets or the final settlement in cash.
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Comparison of Forward and Future contracts
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Example 3.1: Forward vs Futures
• Investor A takes a long position in a 90-day forward contract on £1 million. The forward
price is 1.6000 dollars per pound. Investor B takes a long position in 90-day futures
contracts on £1 million. The futures price is also 1.6000 dollars per pound. At the end of
the 90 days, the exchange rate proves to be 1.7000. The result of this is that investors A
and B each make a total gain equal to
(1.7000 – 1.6000) x1,000,000=$100,000
• Investor A’s gain is made entirely on the 90th day. Investor B’s gain is realized day by day
over the 90-day period. On some days investor B may realize a loss, whereas on other
days he or she will realize a gain.
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Assumptions and Notations will be used for Pricing
Future/Forward
•
Assumptions
– 1. They are subject to no transactions costs when they trade.
– 2. They are subject to the same tax rate on all net trading profits.
– 3. They can borrow money at the same risk-free rate of interest as they can lend money.
– 4. They take advantage of arbitrage opportunities as they occur.
•
Notations
S0: Price of the asset underlying the forward or future contract today
F0: Futures or forward price today
T: Time until delivery date in a forward or future contract
r: Continuously compounded Risk-free interest rate for maturing at the delivery date (i.e. in T
years)
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MANG 6020 Financial Risk Management
Example 3.2: Forward price for an investment assets
• Consider a long forward contract to purchase a non-dividend-paying stock in three
months.
• Assume the current stock price is $40 and the three-month risk-free interest rate is 5%
per annum. The stock price will be stable in the following three-month.
• Suppose first that the forward price is relatively high at $43.
• An arbitrageur can borrow $40 at the risk-free interest rate of 5% per annum, buy one
share, and short a forward contract to sell one share in three months.
• At the end of the three months, the arbitrageur delivers the share and receives $43.
• The sum of money required to pay off the loan is 40e0.05*0.25=$40.50
• By following this strategy, the arbitrageur locks in a profit of $43 - $40.50 = $2.50
• If there is no arbitrage, the forward price must be exactly $40.50
• Homework: What if the forward price today is $39, what arbitrage opportunity you have?
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Example 3.3 : Forward price for an investment assets with knowing income
•
Consider a long forward contract to purchase a coupon-bearing bond whose current price is $900.
The forward contract matures in 9 months. A coupon payment of $40 is expected after 4 months,
•
Four months and nine months risk-free interest rates continuously compounded are 3% and 4% per
annum.
•
Suppose the current forward price is $910.
•
The present value of the coupon is 40e-0.03*4/12=$39.60
•
The present value of last payment in 9 months is $900-$39.60=$860.40, with a future value
860.40e0.04*9/12=886.60
•
Strategy?
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MANG 6020 Financial Risk Management
Example 3.3: Continued
•
Strategy:
– borrow $900 and by one unit of the bond: where one loan $39.60 for the coupon payment in four-month,
and the other loan860.40 for 9 months
– Enter into forward contract to sell asset in 9 months for $910
– In 4 months, receive $40 to repay the first loan
– In 9 months, sell the bond at $910, and repay the second loan
– Profit is $910 – $886.60=$23.40
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MANG 6020 Financial Risk Management
Valuation Forward and Futures Contracts: A Generalization
•
The forward or futures price of an investment asset that provides no income is given by
F0 = S0erT
If F0 > S0erT,,arbitrageurs can buy the asset and short forward contracts on the assets.
If, F0 <S0erT ,they can short the asset and enter into long forward contracts on it.
When, F0 = S0erT, there is no arbitrage opportunities.
•
This equation relates the forward price and the spot price for any investment asset that provides no income and has no
storage costs
•
When the asset provides income during the life of the contract that has a present value I
F0 = (S0 – I )erT
•
When it provides a yield at rate q
F0 = S0 e(r–q )T
•
A foreign currency can be regarded as an investment asset that provides a yield equal to the foreign risk-free rate rf, so
the forward/futures price for a foreign currency is
F0 = S0 e(r– rf )T
q
the average yield during the life of the contract (expressed with continuous compounding)
rf
The foreign risk-free rate (continuously compounding)
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MANG 6020 Financial Risk Management
Valuing Forward and Futures Contracts
• With the following definitions:
• F0: the current forward price for a contract that was negotiated some time ago
• T: years from today to delivery date
• r: T-year risk free interest rate
• K: Delivery price in the contract
• f: value of forward contract today
– The value, f, of a long forward contract, the payoff at time T is F0−K, and the value of the
forward is
f= (F0−K)e−rT
At the beginning of the life of the forward contract, the delivery price is set equal to the forward
price and f=0
– the value , f, of a short forward contract is
f = (K – F0 )e–rT
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Example 3.4: Valuing a forward contract
• A long forward contract on a non-dividend-paying stock was entered into some time ago.
It currently has six months to maturity.
• The risk-free rate of interest (with continuous compounding) is 10% per annum, the stock
price is $25, and the delivery price is $24.
• In this case S0 = 25, r=0.10, T=0.5, and K=24
• The six-month forward price, F0 is given by
F0 = S0erT=25e0.1*0.5=$26.28
• The value of the forward contract is
f = (26.28 – 24 )e-0.1*0.5=$2.17
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MANG 6020 Financial Risk Management
Valuing Forward and Futures Contracts
• From previous examples and equations, we can value a long forward contract on an asset
by making the assumption that the price of assets at maturity of the forward contract
equals the forward price F0
• The forward or futures price of an investment asset that provides no income is given by
F0 = S0erT
• The payoff at time T is F0-K with a present value (F0−K)e−rT which is the value of the
forward contract
• We can have the following expression for the value of a long forward contract on an
investment assets that provide no income
• f= S0−Ke−rT
• Same method can be applied for assets with income during the life of the contract
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MANG 6020 Financial Risk Management
Part III Swap
Swaps
•
A swap is an over-the-counter derivatives agreement between two companies to exchange cash
flows in the future.
• The agreement defines the dates when the cash flows are to be paid and the way in which
they are to be calculated.
•
Usually, the calculation of the cash flows involves the future value of an interest rate, an exchange
rate, or other market variable.
•
Suppose it is March 1, 2014, and a company enters into a forward contract to buy 100 ounces of
gold for $1,800 per ounce in one year. The company can sell the gold in one year as soon as it is
received. The forward contract is therefore equivalent to a swap where the company agrees that on
March 1, 2015, it will pay $180,000 and receive 100 x S , where S is the market price of one ounce
of gold on that date.
– forward contract is equivalent to the exchange of cash flows on just one future date
– swaps typically lead to cash-flow exchanges taking place on several future dates
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MANG 6020 Financial Risk Management
Interest Rate Swap
• The most common swap is a “plain vanilla” interest rate swap where a fixed rate of
interest is changed for a floating rate, e.g. LIBOR
• In this a company agrees to pay cash flows equal to interest at a predetermined fixed rate
on a notional principal for a predetermined number of years.
• In turn, it receives interest at a floating rate on the same notional principal for the same
period of time.
• The floating rate in most interest rate swap agreements is the LIBOR
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Example 3.5
• An agreement to receive 6-month LIBOR and pay a fixed rate of 5% per annum every 6
months for 3 years on a notional principal of $100 million
---------Millions of Dollars--------Date
LIBOR
FLOATING
FIXED
Net
Rate
Cash Flow
Cash Flow
Cash Flow
Mar. 8, 2016
4.2%
Sept. 8, 2016
4.8%
+2.10
–2.50
–0.40
Mar. 8, 2017
5.3%
+2.40
–2.50
–0.10
Sept. 8, 2017
5.5%
+2.65
–2.50
+0.15
Mar. 8, 2018
5.6%
+2.75
–2.50
+0.25
Sept. 8, 2018
5.9%
+2.80
–2.50
+0.30
Mar. 8, 2019
6.4%
+2.95
–2.50
+0.45
•
Swap can be regarded as the exchange of a fixed-rate bond for a floating-rate bond
•
On a floating-rate, interest is generally set at the beginning of the period to which it will apply and is
paid at the end of the period. E.g. prevailing six months before the payment date in the example. 28
MANG 6020 Financial Risk Management
Using the Swap to Transform a Liability
• Converting a liability from
– floating rate to fixed rate: Suppose that Microsoft has arranged to borrow $100 million at LIBOR plus 10
basis points. (One basis point is one-hundredth of 1%, so the rate is LIBOR plus 0.1%.) After Microsoft has
entered into the swap, it has three sets of cash flows:
• 1. It pays LIBOR plus 0.1% to its outside lenders.
• 2. It receives LIBOR under the terms of the swap.
• 3. It pays 5% under the terms of the swap.
– fixed rate to floating rate: Suppose that Intel has a three-year $100 million loan outstanding on which it
pays 5.2%. After it has entered into the swap, it has three sets of cash flows:
• 1. It pays 5.2% to its outside lenders.
• 2. It pays LIBOR under the terms of the swap.
• 3. It receives 5% under the terms of the swap.
– for Intel the swap could have the effect of transforming borrowings at a fixed rate of 5.2% into borrowings
at a floating rate of LIBOR plus 20 basis points.
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Using the Swap to Transform an Asset
• Converting an asset from
– fixed rate to floating rate: Suppose that Microsoft owns $100 million in bonds that will provide interest at
4.7% per annum over the next three years. After Microsoft has entered into the swap, it has three sets of
cash flows:
• 1. It receives 4.7% on the bonds.
• 2. It receives LIBOR under the terms of the swap.
• 3. It pays 5% under the terms of the swap.
– floating rate to fixed rate: Suppose that Intel has an investment of $100 million that yields LIBOR minus 20
basis points. After it has entered into the swap, it has three sets of cash flows:
• 1. It receives LIBOR minus 20 basis points on its investment.
• 2. It pays LIBOR under the terms of the swap.
• 3. It receives 5% under the terms of the swap.
– one possible use of the swap for Intel is to transform an asset earning LIBOR minus 20 basis points into
an asset earning 4.8%.
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With the Financial Intermediary
• Usually, two nonfinancial companies such as Intel and Microsoft do not get in touch
directly to arrange a swap in the way indicated before
• ‘‘Plain vanilla’’ fixed-for-floating swaps on U.S. interest rates are usually structured so that
the financial institution earns about 3 or 4 basis points (0.03% or 0.04%) on a pair of
offsetting transactions.
• The financial institution enters into two offsetting swap transactions with Intel and
Microsoft. Assuming that both companies honor their obligations, the financial institution
is certain to make a profit of 0.03% (3 basis points) per year multiplied by the notional
principal of $100 million. (This amounts to $30,000 per year for the three-year period.)
Microsoft ends up borrowing at 5.115% (instead of 5.1%). Intel ends up borrowing at
LIBOR plus 21.5 basis points (instead of at LIBOR plus 20 basis points).
• Similar logic can be applied in the case of using the swap to transform an asset
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Market Marker
•
In practice, it is unlikely that two companies will contact a financial institution at the same time and
want to take opposite positions in exactly the same swap. For this reason, many large financial
institutions act as market makers for swaps.
•
The bid-offer spread in the table is 3 or 4 basis points.
•
The average of the bid and offered fixed rates is know as the swap rate, as shown in the last
column in the table.
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Valuation of Plain Vanilla Interest Rate Swaps
• A plain vanilla interest rate swap can be valued by assuming that the interest rates that
are realized in the future equal today’s forward interest rates.
• Each exchange of payments in an interest rate swap is a forward rate agreement (FRA)
where interest at a predetermined fixed rate is exchanged for interest at the LIBOR floating
rate.
• FRA can be valued by assuming that forward rates are realized. Because it is nothing more
than a portfolio of FRAs, an interest rate swap can also be valued by assuming that
forward rates are realized.
•
The procedure is as follows:
– 1. Calculate forward rates for each of the LIBOR rates that will determine swap cash flows.
– 2. Calculate the swap cash flows on the assumption that LIBOR rates will equal forward rates.
– 3. Discount the swap cash flows at the risk-free rate.
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Example 3.6
• Consider an interest rate swap that has 14 months remaining and a notional principal of
$100 million. A fixed rate of 5% per annum is received and LIBOR is paid, with exchanges
taking place every six months.
• Assume that
– (a) four months ago, the six-month LIBOR rate was 4%,
– (b) the forward LIBOR interest rate for a six-month period starting in two months is 4.6%,
– (c) the forward LIBOR for a six-month period starting in eight months is 5.2%.
– All rates are expressed with semiannual compounding.
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Example
• Assuming that forward rates are realized, the cash flows on the swap are as shown in
Table. For example, in eight months
– the fixed-rate cash flow received is 0.5 × 0.05 × 100, or $2.5 million;
– the floating-rate cash flow paid is 0.5 × 0.046 × 100, or $2.3 million.
• The value of the swap is the present value of the net cash flows in the final column. The
discount rates used to discount the cash flows are usually OIS zero rates.
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MANG 6020 Financial Risk Management
Part IV Options （self-study)
Basics of Options
Options are traded both on exchanges and in the over‐the‐counter market.
• Type of options:
– call option: gives the holder the right to buy the underlying asset by a certain date for a certain price.
– put option: gives the holder the right to sell the underlying asset by a certain date for a certain price.
• Terminology
– The price in the contract is known as the exercise price or strike price
– The date in the contract is known as the expiration date or maturity
– An at‐the‐money option is an option where the strike price equals the price of the underlying asset.
– An out‐of‐the‐money option is a call option where the strike price is above the price of the underlying asset
or a put option where the strike price is below this price.
– An in‐the‐money option is a call option where the strike price is below the price of the underlying asset or
a put option where the strike price is above this price.
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Basics of Options
• American vs. European Options
– An American option can be exercised at any time during its life
– A European option can be exercised only at maturity
• Most of the options that are traded on exchanges are American.
• In the exchange‐traded equity option market, one contract is usually an agreement to buy
or sell 100 shares.
• European options are generally easier to analyze than American options, and some of the
properties of an American option are frequently deduced from those of its European
counterpart.
• The advantage of the over‐the‐counter market is that maturity dates, strike prices, and
contract sizes can be tailored to meet the precise needs of a client. They do not have to
correspond to those specified by the exchange.
• The sizes of option trades in the over‐the‐counter are usually much greater than those on
exchanges.
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MANG 6020 Financial Risk Management
Options vs. Forwards/Futures
• A futures/forward contract gives the holder the obligation to buy or sell at a certain price
• An option gives the holder the right to buy or sell at a certain price
• Forward contracts lock in a price for a future transaction.
• Options provide insurance. They limit the downside risk while not giving up the upside
potential.
• For this reason, options are more attractive to many corporate treasurers than forward
contracts.
• It should be emphasized that an option gives the holder the right to do something. The
holder does not have to exercise this right. By contrast, in a forward and futures contract,
the holder is obligated to buy or sell the underlying asset.
• Note that whereas it costs nothing to enter into a forward or futures contract, there is a
cost to acquiring an option. This cost is referred to as the option premium.
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Option Positions: for Call Options
• Profit from buying one European call option: option price = $5, strike price = $100.
• Profit from writing one European call option: option price = $5, strike price = $100
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Option Positions: for Put Options
• Profit from buying a European put option: option price = $7, strike price = $70
•
Profit from writing a European put option: option price = $7, strike price = $70
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Payoffs from Options
•
K = Strike price, ST = Price of asset at maturity
a) Long call: max (ST – K, 0) ;
b) Short call: – max (ST – K, 0) = min (K – ST, 0)
c) Long put: max (K – ST, 0) ;
d) Short put: – max (K – ST, 0) = min (ST – K, 0)
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Underlying Assets
• Stocks: Most trading in stock options is on exchanges.
• Foreign Currency: Most currency options trading is now in the over-the-counter market,
but there is some exchange trading.
• Stock Indices: Many different index options currently trade throughout the world in both
the over the-counter market and the exchange-traded market. The most popular
exchange traded contracts in the United States are those on the S&P 500 Index (SPX), the
S&P 100 Index (OEX), the NASDAQ-100 Index (NDX), and the Dow Jones Industrial Index
(DJX).
• Futures: A futures option normally matures just before the delivery period in the futures
contract. When a call option is exercised, the holder gains the excess of the futures price
over the strike price. When a put option is exercised, the holder gains the excess of the
strike price over the futures price.
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Example: Profit from put option
• An investor buys a put option to sell 100 shares.
– Strike price = $70
– Current stock price = $65
– Price of put option to sell one share = $7
• The initial investment is 100 X $7 = $700.
• At the expiration of the option, the stock price is $55. At this time, the investor buys 100
shares and, under the terms of the put option, sells them for $70 per share to realize a
gain of $15 per share, or $1,500 in total. When the initial cost of the option is taken into
account, the net gain is $1,500 – $700 = $800
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Trading strategies with options: single option and a stock
(a) long position in a stock combined with short position in a call; (b) short position in a stock combined with long position in a call; (c)
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long position in a put combined with long position in a stock; (d) short position in a put combined with short position in a stock
MANG 6020 Financial Risk Management
Spreads
• A spread trading strategy involves taking a position in two or more options of the same
type (i.e., two or more calls or two or more puts).
• One of the most popular types of spreads is a bull spread.
• This can be created by buying a European call option on a stock with a certain strike price
and selling a European call option on the same stock with a higher strike price.
• Both options have the same expiration date.
• Suppose that K1 is the strike price of the call option bought, K2 is the strike price of the
call option sold, and ST is the stock price on the expiration date of the options, the payoff
will be released from a bull spread as
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Profit from bull spread created using call options
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Example: Bull spread using call options
• An investor buys for $3 a three-month call with a strike price of $30 and sells for $1 a
three-month call with a strike price of $35. The payoff from this bull spread strategy is $5
if the stock price is above $35 and zero if it is below $30. If the stock price is between
$30 and $35, the payoff is the amount by which the stock price exceeds $30. The cost of
the strategy is $3 - $1 = $2. The profit is therefore as follows:
Try to graph the profit as the last slide.
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MANG 6020 Financial Risk Management
Other Spreads
• Bear spreads
– Can be created by buying a European put with one strike price and selling a European put with
another strike price. The strike price of the option purchased is greater than the strike price of
the option sold.
– Contrast to bull spread , an investor can enter into a bear spread is hoping that the stock price
will decline
• Box Spreads
– A box spread is a combination of a bull call spread with strike prices K1 and K2 and a bear put
spread with the same two strike prices.
• Butterfly Spreads
– A butterfly spread involves positions in options with three different strike prices.
– It can be created by buying a European call option with a relatively low strike price, K1, buying a
European call option with a relatively high strike price, K3 , and selling two European call options
with a strike price, K2 , halfway between K1 and K3
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MANG 6020 Financial Risk Management
Combinations: Straddle
• A combination is an option trading strategy that involves taking a position in both calls
and puts on the same stock.
• One popular combination is a straddle , which involves buying a European call and put
with the same strike price and expiration date.
• A straddle is appropriate when an investor is expecting a large move in a stock price but
does not know in which direction the move will be.
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MANG 6020 Financial Risk Management
Example
• Consider an investor who feels that the price of a certain stock, currently valued at $69 by
the market, will move significantly in the next three months. The investor could create a
straddle by buying both a put and a call with a strike price of $70 and an expiration date
in three months.
• Suppose that the call costs $4 and the put costs $3. If the stock price stays at $69, it is
easy to see that the strategy costs the investor $6 (an up-front investment of $7 is
required, the call expires worthless, and the put expires worth $1). If the stock price
moves to $70, a loss of $7 is experienced (this is the worst that can happen). However, if
the stock price jumps up to $90, a profit of $13 is made; if the stock moves down to $55,
a profit of $8 is made; and so on.
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Straddle
• A straddle is appropriate when an investor is expecting a large move in a stock price but
does not know in which direction the move will be.
• The graph shown before is sometimes referred to as a bottom straddle or straddle
purchase.
• A top straddle or straddle write is the reverse position.
– It is created by selling a call and a put with the same exercise price and expiration date. It is a
highly risky strategy.
– If the stock price on the expiration date is close to the strike price, a significant profit realizes.
However, the loss arising from a large move is unlimited.
• Other combinations: strips, straps, and strangles which are combined with different
options and positions
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Further Reading
• Hull, J. 2018. Risk Management and Financial Institutions, 5th ed., Wiley, 2018 (Chapter 5)
• Hull, J. 2017, Fundamentals of futures and options markets, Eighth Global ed., Pearson
Education, Inc, Boston ( Chapter 2, chapter 5, chapter 7, chapter 9)
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