Financial Risk Management: everything for the exam
Summary Financial Risk Management: All relevant formulas and step by step calculations
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Erasmus Universiteit Rotterdam (EUR)
Economie en Bedrijfseconomie
Finance 2 (FEB13001)
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Week 1
Introduction to Derivatives Markets
A Derivative is a financial instrument that has a value determined by the price of something else.
These derivatives can be used to speculate or reduce risk. It is not the derivative itself, but how it is
used and who uses it that determines whether or not it is risk-reducing.
Derivatives Markets
Often the introduction of derivatives in a market often coincides with an increase in price risk. This
has been seen in different types of markets, from oil to currencies.
Derivatives have many different uses
- Risk management: Derivatives are a tool for companies and other users to reduce risks.
- Speculation: Derivatives can serve as investment vehicles.
- Reduce transaction costs: Sometimes derivatives provide a lower cost way to undertake
a particular financial transaction.
- Regulatory arbitrage: It is sometimes possible to circumvent regulatory restrictions, taxes
and accounting rules by trading derivatives.
Some examples of derivatives applications are:
- Transnational companies buying FX-derivatives to hedge their currency exposure.
- Airlines enter futures contracts in order to be less vulnerable to oil price changes.
- A goldmine can use derivatives to lock in the current gold price.
- Banks use derivatives to manage interest rate and default risks.
Perspectives on derivatives and the trading process
1
, Exchange-
traded derivatives markets
Much of the trading of financial claims takes place on organized exchanges. In the past this would
have been a physical location, nowadays such places have largely been replaced by electronic
networks and online trading. Most of the trading happens in the US, closely followed by the Asian/
Pacific region and Europe in third place.
After a trade has taken place, a clearinghouse matches buyers and sellers, keeping track of their
obligations and payments. To facilitate these payments and help manage credit risk, a derivatives
clearinghouse typically imposes itself in between the transaction, becoming the buyer to all sellers
and the seller to all buyers. (When trading the ask price is the price a seller is asking for their stock,
a bid price it what a buyer is offering to buy the stock for)
Over-the-counter market (OTC)
It is possible for large traders to trade many financial claims directly with a dealer bypassing
organized exchanges. This is called the over-the-counter (OTC) market. The exchange activity is
public and highly regulated, however activity is not as easy to observe or measure and is less
regulated in the OTC market. In many cases, the OTC market is much larger than the official/public
exchanges.
2
,Introduction to Futures, forwards and options
Forward contracts
A forward contract is a binding agreement (obligation) to buy/sell an underlying asset in the future,
at a price set today. Futures contracts are the same as forwards in principle except for some
institutional and pricing differences. A forward contract specifies:
- The features and quantity of the asset to be delivered
- The delivery logistics, such as time, date, and place
- The price the buyer will pay at the time of delivery
Payoff on a forward contract
Payoff for a contract is its value at expiration. Payoff for:
- Long forward = spot price at expiration - forward price
- Short forward = forward price - spot price at expiration
Example:
Long S&P index forward:
Today: spot: $1000, 6-month forward price = $1020
In 6 months: spot: $1050
Long position payoff = 1050 - 1020 = 30
Short position payoff = 1020 - 1050 = - 30
Additional considerations:
There are different kinds of settlement, either cash (less costly and more practical) or physical
delivery (often avoided due to significant costs). There’s also the problem of counterparty credit
risk: A major problem for OTC contracts, often credit checks, collateral or bank letters of credit are
3
,used to alleviate this problem. It is less severe of a problem for exchange traded contracts because
the exchange guarantees transactions and requires collateral be posted.
Call options
A call option is a non-binding agreement (a right not an obligation) to buy the underlying asset in
the future, at a price set today. This preserves the upside potential while limiting the downside (for
the buyer). The seller of a call option is obligated to deliver if asked.
Definition and terminology
Strike/exercise price: The amount paid by the buyer for the asset if he decides to exercise.
Exercise: The act of paying the strike price to buy the asset.
Expiration: The date by which the option must be exercised or become worthless.
Exercise style: Specifies when the option can be exercised:
- European-style: can be exercised only at expiration date
- American -style: can be exercised at any time before expiration
- Bermudan-style; can be exercised during specified periods
Payoff/profit of a purchased call
Payoff = max[0, spot price at expiration - strike price]
Profit = payoff - future value of option premium
Example:
S&R Index 6-month call option
With: Strike = 1000, premium = 93.81, 6-month RF = 2%
If index value in 6 months = 1100
Payoff = max[0, 1100 - 1000] = 100
Profit = 100 - (93.81 * 1.02) = 4.32
If index value in 6 months = 900
Payoff = max[0, 900 - 1000] = 0
Profit = 0 - (93.81 * 1.02) = -95.68
4
, Payoff/profit of a written (short) call
Payoff = -max[0, spot price at expiration - strike price]
Profit = Future value of option premium + payoff
Put options
A put option gives the owner the right but not the obligation to sell the underlying asset at a
predetermined price during a predetermined time period. The seller of this put option is obligated to
buy if exercised.
Payoff/profit of a purchased (long) put
Payoff = max[0, strike price - spot price at expiration]
Profit = Payoff - future value of option premium
Payoff of a written (short) put
Payoff = -max[0, strike price - spot price at expiration]
Profit = Payoff + future value of option premium
Important items to note
A call option becomes more profitable when the underlying asset appreciates in value, a put option
however becomes more profitable when the underlying asset depreciates in value.
Moneyness:
- In-the-money option: positive payoff if exercised immediately
- At-the-money option: (close to) zero payoff if exercised immediately
- Out-of-the-money option: negative payoff if exercised immediately
Option and forward positions diagrams:
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