325017- Derivative Securities and Risk Management . The book, slides and lecture notes combined in one summary which includes the most important topics covered in lecture.
Week 1: Introduction; Futures and forwards; Introduction to options
Chapter 1 & 2 Introduction, Forwards, and Futures
Derivatives A derivative is an instrument whose value depends on the values of other more basic
underlying variables (Options, forwards, futures, interest rate swaps and credit default swaps)
Derivatives markets
- Exchange traded (standard products, trading floor or computer trading, virtually no credit risk)
- Over the counter (non-standard products, telephone market, some credit risk)
Forward contract
- OTC
Long position (buy forward contract) Short position (sell forward contract)
Futures contract
- Agreement to buy/ sell an asset in the future (to lock this price)
- Most contracts are closed out (entering into an offsetting trade) before maturity
- Daily settlement
Margin: cash or marketable securities deposited by investor with broker
Balance in margin account: adjusted to reflect daily settlement
Margins minimize the possibility of loss through default on a contract
Maintenance margin: if it comes below this level, the margin account has to be filled up
to initial margin.
Open interest: total number of contracts outstanding -> equal to number of long positions or number of
short positions
Settlement price: price just before the final bell each day -> used for the daily settlement process
Volume of trading: number of trades in one day
,Collateralization in OTC:
- Require A to post collateral with B equal to the value to B of its outstanding transactions with B
when this value is positive.
A clearing house is a third-party agency or separate entity that acts as a go-between for buyers and
sellers in financial markets. Clearing house takes the risk that the buyer doesn’t pay. To minimize this
risk the clearing house require the exchange members to maintain a minimum account balances.
Bilateraral clearing vs central clearing house
Chapter 5 Pricing of forward and futures contracts
Short selling selling securities you don’t own. Your broker borrows the securities from another client
and sells them in the market in the usual way. At some stage you must buy the securities back so they
can be replaced in the account of the client. You must pay dividend & other benefits the owner receives.
Short selling is motivated by the belief that a security's price will decline, enabling it to be bought back at
a lower price to make a profit. Short selling may be prompted by speculation, or by the desire to hedge
the downside risk of a long position in the same security or a related one. Since the risk of loss on a short
sale is theoretically infinite, short selling should only be used by experienced traders who are familiar
with its risks.
Is there an arbitrage opportunity:
a) The spot price of a non-dividend-paying stock is $40. The 3-month forward price is $43. The 3-
month US$ interest rate is 5% per annum.
S= 40 F=43 r=0,05x(3/12)
Ft= 40e0.0125=40.50
If F> 40.5, sell forward en buy spot
Arbitrage opportunity of 2.5
b) The spot price of nondividend-paying stock is $40. The 3-month forward price is US$39. The 1-
year US$ interest rate is 5% per annum (continuously compounded).
S= 40 F==39 r=0,05x(3/12)
Ft=40e0.0125=40.50
If F<40.5 buy forward and sell spot
Arbitrage opportunity of 1.5
When an investment asset provides a known income
I is the present value of the income during life of forward contract
When an investment aseet provides a known yield
Q is the average yield during the life of the contract
K = Delivery price (financial value of the conveyance of the underlying commodities when a futures
or forward contract expires)
F0= forward price for a contract
,Long forward Buy forward
Short forward Sell forward
Stock index Can be viewed as an investment asset paying a dividend
If an arbitrageur buys the stock underlying the index and sells futures
If buy futures and sell stock See example above
Futures and forwards on currencies a foreign currency is a security providing a yield. The yield is the
foreign risk free interest rate.
Futures prices and expected future spot price (K) with
Systematic risk undiversified risk (risk of market)
Positive systematic risk stock indices
Negative systematic risk gold
Chapter 3 Hedging Strategies Using Futures
Long futures hedge when you know you will purchase an asset in the future & want to lock the price
Short futures hedge when you know you will sell an asset in the future &want to lock the price (so you
are sure you have a fixed income)
Against hedging:
- Shareholders are usually well diversified and can make their own hedging decision
- It may increase risk to hedge when competitors do not
- There can be a loss on the hedge and a gain on the underlying
Basis risk difference between spot and future price. Arises because of the uncertainty about the basis
when the hedge is closed out
Optimal hedge ratio:
Optiomal hedge ratio proportion of the exposure that should optimally be hedged
Chapter 10 Option Markets
Long position in an option you have the right to buy
or sell the stock
Short position in an option you have to buy or sell
the stock if the counterparty who has the option
wants to
Call option to buy
Put option to sell
, Warrants are options that are issued by a corporation or a financial institution (options are an
instrument of the stock exchange). The number of warrants outstanding is determined by the size of the
original issue and changes only when they are exercised or when they expire. Companies include
warrants as a part of a new issue offering to attract investors into buying the new security.
Week 2: Properties of options; Option trading strategies; The binomial model
Chapter 11 Properties of the stock option prices
Effect of variables on option pricing
increase will lead to more
variance of the stock price. Because you
lock the negative side it will be positive
to have higher variane because this will
lead to a higher probability on the
positive side
A higher stock price will lead to a higher
profit for call options
D PV of dividends paid during life of
option
D+C negative because a dividend will decrease the stock price
R+C If interest rate inreases the stock price will increase
American options are worth more/ at least as much as a European option because they have a longer
period to call the options. European option are only possible to call op the day of maturity, so not during
the period.
Lower bound for European call
Lower bound for European put
Put- Call parity Portfolio
A: European call on a stock + PV of the strike price in
cash. Portfolio
B: European put on the stock + the stock
American Option can early exercise expect from a call on a non-dividend paying stock, this cannot be
excised early.
C=c For call options it’s not interesting to exercise early
P>p For put option it might be interesting to exercise early
Why not exercise a call option early? Option value is created by intrinsic value and time value. If a
stock price goes up it gets more intrinsic value and less time value. However but as long as the option is
not deep in the money its still going to have some time value but if you exercise the option it will lose
the time value. So a better move is just sell a call option for more than you paid for it. If you exercise your
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