Derivatives
Financial Foundations
Objective
This lesson provides a foundation in the derivatives trading business,
covering the main products and their use.
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Introduction
Investing has become more complicated with the creation of derivatives
The idea of derivatives has been around for generations, particularly in the farming industry – e.g., a contract to sell
goods/livestock on a particular date at a particular price
Derivatives have numerous uses, mostly on the hedging and risk management, while incurring various levels of risk.
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Derivatives Securities
Derivative securities are a contract whose value is based on the assets underlying the contract. These are
traditionally the most complex of financial instruments. Generally used for hedging or speculation.
Derivative
Security
Future/ Credit
ABS FX Swap IR Swap
Option Derivatives
Underlying
Assets
Commoditie Interest
Bonds Mortgages Loans FX Rate
s Rate
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Some Key Derivatives Terms
Here are some of the terms you will likely hear when dealing with derivatives:
Counterparty The party taking the other side of the trade
Strike Price The price at which the derivative (option) can be exercised
Expiry The date at which the derivative contract expires
Insuring yourself against a negative event: it does not stop the event from happening,
Hedging
but it does reduce its impact
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Derivative Structure
Here are some of the types of derivatives you will hear about:
Agree to buy or sell something at a specific point of time in the future for a specific
Forward
price
Future A forward that is traded on an exchange
Swap An exchange of two things
The right to buy or sell a security on an agreed future date at a
Options
pre-agreed price
Warrant An option issued by the company itself and traded over the counter
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Forwards I’ll purchase 4 tons of
wheat from you at
$2000 a ton in six Here’s your 4 Thanks,
months. tons of wheat. here’s your
$8000.
6 Months Later
Wheat
Forwards are privately negotiated, sold over the counter, and the terms are negotiable.
The price is established at the inception of the contract.
Higher risk than futures as they do not use a central clearing house and so both sides are
exposed to credit risk.
Mainly used for hedging, i.e., reducing the risk of a negative event
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Futures
Future: a contract that commits to selling or purchasing a specific amount of assets, at a specific price, at a particular
point in the future.
Chicago SRW Wheat Futures Contract
Traded on exchanges
Contract Unit 5000 bushels (~136 metric tons)
Standard sizes Price Quotation Cents per bushel
Standard maturity dates Settlement
Cash
Method
Profits/losses settled each day
Termination Bus. Day preceding 15th of month
Currency USD
Quotes July 2017: 429 cents
Futures are highly standardized and are traded on exchanges such as CME, Euronext, London Metal
Exchange (LME), ICE Futures Europe, Eurex.
Most exchanges clear their own trades and act as central counterparty.
Often bought by speculators betting on the price of the commodity or underlying asset rising or falling.
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Options
I’d like the option to Since the price of
purchase 4 tons of grain Would you like to grain has gone up, I
from you at $2000 a ton in buy this 4 tons of will exercise my call
six months. grain at the agreed option now.
price?
6 Months Later
Wheat
Option: a contract for the option to purchase or sell a specific amount of assets, at a specific price, at a particular point
in the future.
The option price is influenced by the underlying asset’s market price, the length of the contract, the current volatility of
the underlying asset, supply and demand, dividend rate of the underlying asset.
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Option – Risks and Benefits
Let’s look at the underlying risks and profits around the options:
Holder has no obligation to buy the asset (i.e., if the price of the asset on the market is
Buying Call Options
cheaper than the contract price); the risk to the holder is then the loss of the premium.
Otherwise known as writing the contract: maximum profit is the premium value. The loss
Selling Call Options for the seller can be a lot higher if the buyer exercises the option as they will need to sell
the underlying asset at a price worse than market.
The buyer believes the underlying stock market price will fall. They will sell the shares at
the options higher price; if they want to replace the shares, they can then buy them back at
Buying Put options
the lower market price. The risk here is limited to the loss of the premium if the option is
not exercised.
Again writing a contract, the seller believes the underlying asset will increase over time.
Selling Put options Maximum profit again is the premium. The loss will be having to buy shares at a strike price
above the current market value.
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Option Underliers
Options give you the right but not the obligation to buy or sell the underlying asset at a specified price in the future –
the buyer pays a premium for the rights granted by the contract
Put option: Allows the holder to sell the asset at a stated price within a specific timeframe.
Call option: Allows the holder to buy the asset at a stated price within a specific timeframe.
Example:
Suppose Google shares are trading at $300 a share. You believe they are going to increase in value, so you purchase a
call option.
– The call option has a strike price of $315 for one month in the future for 37 cents per contract (usually sold in 100 lots). Your cash
outlay is $37 for the premium (37c * 100).
– If the stock rises to $320 in that time, you can purchase at $315 and then immediately sell the stock on the open market with a
profile of $5 (and you have purchased 100 shares).
– In this example you paid 37c per share and gained $5 for each share, with a profit of $463 ($5-0.37 * 100).
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Black-Scholes Formula for Option Pricing
𝐶𝐶 = 𝑁𝑁 𝑑𝑑1 𝑆𝑆𝑡𝑡 − 𝑁𝑁 𝑑𝑑2 𝐾𝐾𝑒𝑒 −𝑟𝑟𝑟𝑟 The Black-Scholes model and its many variants
assume that stock prices follow a lognormal
distribution
𝑆𝑆1 𝜎𝜎 2 The formulas allow stock prices to be substituted for
𝑙𝑙𝑙𝑙 + 𝑟𝑟 + 𝑡𝑡 any other asset, e.g., FX, interest rates etc.
𝐾𝐾 2
𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑑𝑑1 =
𝜎𝜎 𝑡𝑡 Option values also depend on an asset’s volatility,
which is essentially the dispersion of its returns
𝑎𝑎𝑎𝑎𝑎𝑎 𝑑𝑑2 = 𝑑𝑑1 − 𝜎𝜎 𝑡𝑡 As such, any product with optionality does not react to
C = call option price market prices in a linear manner in terms of either
value or calculated risk position
N = CDF of the normal distribution
St = spot price of an asset
K = strike price
r = risk-free interest rate
t = time to maturity
σ = volatility of the asset
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Interest Rate Swaps (IRS)
Swap: a contract to exchange a series of cash flows at a specific point in the future based on
a specific principal amount
Assume that LIBOR is 5% and the contract is 1 million GBP.
Bob pays Alice 5.5% = £55K
Bob thinks LIBOR will Alice thinks LIBOR will
decrease
Bond paying Bond paying increase.
LIBOR + 1% Nominal Value: £1,000,000 6% interest
Bob wants a more (Variable) (Fixed) Alice is a speculator and
predictable fixed rate on Alice pays Bob 6% = £60K wants higher returns.
his liabilities to hedge
against market risk.
Rate goes down to 4.5%. Bob pays less and receives more.
Zero-sum game. There is always a winner and a loser.
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Interest Rate Swap Legs
Legs: The cash flows exchanged in an interest rate swap are referred to as legs.
Legs
Bob pays Alice 5.5% = £55K
Bond paying Bond paying 6%
LIBOR + 1% Nominal Value: £1,000,000 interest
(Variable) (Fixed)
Alice pays Bob 6% = £60K
Bob Alice
The two legs may be fixed or floating.
Fixed: Pays a series of payments agreed at the outset of the contract
Floating: Linked to the future level of interest rates
Vanilla swap: where a floating interest rate is exchanged for a fixed rate or vice versa
Mostly traded OTC although some must be traded on a SEF (swap execution facility
trading venue)
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Comparative Advantage Argument
for Interest Rate Swap
Company A: Can borrow fixed at 10% or floating at Libor + 0.35%
Company B: Can borrow fixed at 11.25% or floating at Libor + 1.0%
They both want to borrow $10M from the markets for 5 years. Company A borrows fixed at 10%. Company B
borrows floating at Libor + 1%. Coupons are semi-annual.
Company A and Company B enter into an interest rate swap for 5 years at semi-annual intervals:
Company A pays LIBOR flat to Company B throughout the swap.
Company B pays fixed rate of 9.9% to Company A throughout the swap.
Exercise: Draw the net cash flows and demonstrate that this is more beneficial to both parties than borrowing
floating/fixed on their own.
Company A has a comparative advantage on fixed rate borrowing; Company B has a comparative advantage in
floating rate borrowing. They use these advantages and then they swap via IRS.
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Comparative Advantage Argument for Interest Rate Swap
Company A: Can borrow fixed at 10% or floating at Libor + 0.35%
Company B: Can borrow fixed at 11.25% or floating at Libor + 1.0%
They both want to borrow $10M from the markets for 5 years. Company A borrows fixed at 10%. Company B
borrows floating at Libor + 1%. Coupons are semi-annual.
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Swaptions
Swaption: a contract for the option to enter into a swap agreement at a specific price, at a particular point in the
future. In exchange for an options premium, the buyer gains the right but not an obligation to enter into a specified
swap agreement with the issuer on a specified future date.
I’d like the option to
purchase a CDS on my
Corp PLC Bond in 6
Since default is Would you like
months for a £10 annual
looking likely, I’ll to buy the CDS
premium. NEWS exercise my at the agreed
Sure, it’s just an “Corp PLC is in option. price?
upfront fee. trouble”
6 Months Later
£1000 invested in
3%
Corp PLC Bond
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Swaptions
Swaptions come in two main types:
The purchaser has the right to enter into a swap contract where they become the fixed rate
Payer Swaption
payer and the floating rate receiver
The purchaser has the right to enter into a swap contract where they become the floating
Receiver Swaption
rate payer and receive the fixed rate
These are OTC (Over the Counter) and are not standardized. Everything about these contracts need to be agreed by
the buyer and seller.
Commercial banks are the main market makers in swaptions due to the unstandardized nature; they are the only one
who can monitor a portfolio of swaptions.
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Credit Derivatives
Credit Default Swap (CDS): a contract to insure the
credit risk of an underlying bond for an agreed fee over
an agreed amount of time. Insurer pays
Buyer Buyer
Yes face value +
enters pays Credit
Types: Single name CDS; Basket CDS and Index CDS CDS premium event?
remaining
interest to
contract to insurer
buyer
In a CDS, the buyer of the swap makes payments to
the swap’s seller until the maturity date of the
contract. No No
In return the seller agrees in the event of a credit
event the seller will pay the value of the security as Bond
mature?
well as any interest.
Yes
CDS expires
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In a Credit Default Swap:
Protection seller
earns investment income with no funding cost
gains a customized, synthetic access/exposure to the risky bond
Protection buyer
hedges the default risk on the reference asset (bond etc)
Very often, the bond tenor is longer than the swap tenor. In this way, the protection seller does not have exposure to
the full market risk of the bond throughout its existence.
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CDS Use by a Bank
A bank lends 10mm to a corporate client at L + 65bps. The bank also buys 10mm default protection on the
corporate client for 50bps.
Objective achieved
maintain relationship
reduce credit risk on a new loan
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Credit Events
The CDS is triggered when the following events occur:
Bankruptcy The issuer becomes insolvent or unable to pay debts
Failure to pay The issuer becomes insolvent or unable to pay debts
The configuration of the debt obligations is changed in a way that negatively affects the credit
Debt restructuring
holder
Obligation
Also known as obligation default: the debt payment is scheduled before their maturity date
acceleration
Repudiation /
The issuer refuses to pay the principle and interest amounts
moratorium
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Mortgage-Backed Securities
MBS: Investment similar to a bond made up of a bundle of home loans bought from the banks that issued them.
Investors receive periodic payments similar to bond coupon payments. Investors are purchasing the cash flow from the
underlying mortgages – the monthly mortgage payments.
This leaves the MBS investor open to the risks of repayment defaults, such as falling house prices, job loss,
bankruptcy etc.
MBS-specific risks include:
Prepayment Risk: As interest rates decrease, mortgage-owners are more likely to refinance or prepay their fixed-rate
mortgages, similar to a callable bond.
Correlation Risk: If mortgage default risks are highly correlated due to a geographic area, housing market collapse,
etc., then diversification benefit is significantly reduced.
Illiquidity: Because many MBS investors are institutional, smaller lots are very difficult to sell in the secondary market.
Institutional positions may be too large to easily liquidate, too.
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Principal-Agent Problem in Lending
Historically, commercial banks underwrote loans and were responsible for collecting payments until their maturity. This
incentivized the banks to minimize credit risk as all defaults would impact them.
Because of the strong demand for mortgages from investment banks which securitize them and sell them, the
commercial banks (originators) were able to re-sell their mortgage loans very quickly, and therefore did not hold the
credit risk.
Investment banks purchased mortgage pools based on limited metrics such as credit scores and Loan -To-Value (LTV)
ratio, which were not adequate.
This was a principal-agent problem in the sense that originators acted as the agents of the investment banks, and
eventually of investors, to originate the loans that they did not care too much about credit quality of.
This principal-agent problem encouraged subprime lending.
Additionally, the rating agencies underestimated the risks associated with the MBS lending.
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MBS in the Financial Crisis
How did MBS contribute to the financial crisis in 2008?
Rapid increase in home prices caused banks to lower their lending standards
Quality of all MBS backed securities declined and ratings became meaningless
2006 housing prices peaked
Subprime borrows started to default as housing market started to collapse
More people walked away from their mortgages as they were more expensive than the value of their homes
The large amount of non payments meant many MBSs and collateralized debit obligations (CDOs) based off pools of
mortgages were greatly overvalued
Losses piled up as institutional investors and banks tried and failed to unload bad MBS investments
Credit tightened and banks were at risk of insolvency
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Asset-Backed Securities
Asset-Backed Security (ABS) – A security that is collateralized by a pool of assets.
Examples include loans, leases, credit card debt, royalties or receivables.
An ABS is attractive as an alternative to investing in corporate debt.
Similar to an MBS but the underlying asset is not mortgages.
Usually the underlying assets are illiquid; as such, the ABS are created with lots of different types of underlying assets
to make them tradable. This process is called Securitization.
The creator of ABS can include just about anything that produces cash flow, such as movie revenues.
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Asset-Backed Securities
Securitization
Originate Loan Loan Originators SPV Trust Ready for Sale
• Credit card debt • Loan originators sell • The SPV provides • The trust • Investors receive
to an SPV (special "remoteness" for repackages the cashflows from the
• Home equity loans purpose vehicle) the loan originator. loans as interest- underlying pool of
The SPV will not bearing securities. loans
• Student loans (USA) • SPV: orphan issue the securities.
company created to
• Automotive loans spread risks in • The SPV sells to a • Usually in tranches
underlying assets trust.
by reallocating • Fees are paid to the
across investors. security providers
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CDOs: Collateralized Debt Obligations
CDOs: complex types of asset-backed securities with either mortgage-backed assets, non-mortgage-backed assets or a
combination of both. The assets become the collateral if the loan defaults.
They come in two flavors:
– CLO: Collateralized Loan Obligation – often corporate loans that have a low credit rating
– CBO: Collateralized Bond Obligation – bond backed by a pool of junk bonds
Tranches: pieces of a pooled collection of securities, usually debt instruments
Split up by the risk of other characteristics to make them marketable
The best quality tranches will yield the lowest reward; the low-quality tranches are more risky and therefore
potentially more rewarding
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Collateralised Debt Obligations (CDOs)
Although ABS—and thus CDOs—grew out of MBS,
they are more varied and more complex in
structure.
CDOs consist of a variety of loans and debt
instruments. To create a CDO, investment banks
gather cash flow-generating assets—such as
mortgages, bonds, and other types of debt—and
repackage them into discrete classes, or tranches,
based on their level of credit risk.
Source: Investopedia
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How do Tranches Work?
The tranches making up a security have different credit ratings.
> Contain assets with higher credit ratings than junior tranches
Senior Tranches
> In line to be repaid first in case of default
> Contain assets with a lower credit rating than the senior tranches
Junior Tranches
> May not get repaid in case of default
Tranches exist in MBS also - an MBS is made up of multiple mortgage pools with a wide variety of loan types attached
Tranches in MBS are made to divide up the different mortgage profiles into slices that have financial terms suitable for
investors.
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