This is a summary for the course Financial Risk Management. The summary is mainly based on slides and notes from the lesson. If the slides were insufficient, I got extra information from the book and put it in the summary.
H9 is not elaborated (1 page). Many other important things I had to get out of class myself because they were skipped in this summary. Some things have also simply been mistaken over.
By: nick1995 • 4 year ago
By: erenturkmenoglu • 5 year ago
By: alexanderhuysmans • 5 year ago
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SUMMARY FINANCIAL RISK MANAGEMENT
INHOUD
chapter 1 : introduction ............................................................................................................................ 4
derivative markets ............................................................................................................................ 4
market size ....................................................................................................................................... 4
terminology ....................................................................................................................................... 5
use of forwards / futures (& pay offs) ............................................................................................... 6
options .............................................................................................................................................. 6
types of traders ................................................................................................................................. 7
chapter 2 : mechanics of futures markets ............................................................................................... 9
futures (specification of the contract) .......................................................................................... 9
convergence of futures price to spot price ....................................................................................... 9
margin accounts ............................................................................................................................. 10
otc markets ................................................................................................................................... 13
delivery ........................................................................................................................................... 14
types of traders and types of orders ............................................................................................... 14
forwards vs. futures ........................................................................................................................ 15
chapter 3: hedging strategies using futures .......................................................................................... 15
hedging strategies .......................................................................................................................... 16
basis risk......................................................................................................................................... 16
rolling over hedges ......................................................................................................................... 19
recap chapters 1-3 ......................................................................................................................... 20
chapter 4: interest rates ......................................................................................................................... 20
general............................................................................................................................................ 20
interest rates ................................................................................................................................... 20
compounding (measuring interest rates) ........................................................................................ 21
other rates ...................................................................................................................................... 22
bootstrapping the zero curve (determing treasury zero rates) ....................................................... 24
forward rates .................................................................................................................................. 27
Discount factor ............................................................................................................................... 28
chapter 5 : determination of forwards and futures prices ...................................................................... 28
investment assets vs. consumption assets .................................................................................... 28
short shelling .................................................................................................................................. 28
assumptions and notations............................................................................................................. 29
Forward price ................................................................................................................................ 29
examples ........................................................................................................................................ 29
forward with known income / known Yield ..................................................................................... 30
1
, forward contract value .................................................................................................................... 31
chapter 7: swaps ................................................................................................................................... 32
mechanics of interest rate swaps ................................................................................................... 32
typical use of swap ......................................................................................................................... 33
valuation of swaps .......................................................................................................................... 37
currency swaps .............................................................................................................................. 38
recap .................................................................................................................................................. 38
chapter 10: mechanics of options markets ............................................................................................ 38
types of options .............................................................................................................................. 39
underlying assets ........................................................................................................................... 40
option positions .............................................................................................................................. 41
terminology ..................................................................................................................................... 42
employee stock options .................................................................................................................. 43
chapter 12: trading strategies involving options .................................................................................... 43
principal protected notes ................................................................................................................ 43
trading an option and the underlying asset .................................................................................... 43
spreads ........................................................................................................................................... 45
combinations .................................................................................................................................. 49
chapter 11: properties of stock options ................................................................................................. 51
factors effecting option prices ........................................................................................................ 51
european vs. american options ...................................................................................................... 52
impact of variables on prices .......................................................................................................... 52
UPPER AND LOWER BOUNDS FOR OPTION PRICES .............................................................. 53
put-call parity .................................................................................................................................. 55
dividend .......................................................................................................................................... 57
recap .................................................................................................................................................. 57
chapter 13: binomial trees ..................................................................................................................... 57
binomial tree ................................................................................................................................... 57
generalization binomial tree ........................................................................................................... 59
chapter 15: the black scholes merton model ......................................................................................... 62
properties ....................................................................................................................................... 63
implied volatility .............................................................................................................................. 63
binomial trees vs black-scholes-merton ......................................................................................... 64
recap chapters 13 and 15 .................................................................................................................. 64
chapter 22: value at risk ........................................................................................................................ 64
measuring risk ................................................................................................................................ 65
ways to measure var and es .......................................................................................................... 66
normal distribution assumption ...................................................................................................... 68
2
, historical simulation approach ........................................................................................................ 69
weighting ........................................................................................................................................ 70
comparison ..................................................................................................................................... 70
comparison ..................................................................................................................................... 71
derivatives to manage risk once we know the risk ......................................................................... 71
recap .................................................................................................................................................. 71
chapter 24 credit risk + chapter 25 credit derivatives ............................................................................ 71
credit risk ........................................................................................................................................ 72
credit risk measurement ................................................................................................................. 72
credit risk ........................................................................................................................................ 74
capital market data ......................................................................................................................... 78
mitigation ........................................................................................................................................ 82
recap + risk management lessons from the global financial crisis ........................................................ 82
risk .................................................................................................................................................. 82
Risk management lessons from the Global Financial Crisis (GFC) .................................................. 88
3
,CHAPTER 1 : INTRODUCTION
DERIVATIVE MARKETS
Two ways to trade derivatives (derivatives = options, futures, forwards, …)
1. Over-the-counter (OTC)
o Banks, large financial institutions, fund managers and corporations are the main
participants in OTC derivative markets
o Bilateral (price, quantity, delivery, etc.)
▪ Ex: watch You and Me have an agreement to trade a watch at a certain
price within 1 month = bilateral
o Participants have contacted each other directly by Phone/ computerized
(communication) OR have used an interdealer broker
o Credit risk (nowadays collateralized, or via CCP)
▪ = the chance of loss due to the other party not meeting contractual obligations
▪ Collateralized you buy the watch and as collateral the other person his
phone to avoid the credit risk
o Central Counter Party
▪ Once an OTC trade has been agreed, the two parties can either present it to
a central counterparty OR trade bilaterally
2. Exchanges
o A derivative exchange is a market where individuals trade standardized contracts that
have been defined by the exchange
o Standardized contracts (price, quantity, delivery, etc.)
▪ Ex: always 10 watches to buy for 250 € / watch
o Exchanges such as the CME, NYSE Euronext, TIFFE, etc.
o Via clearinghouse once two traders have agreed on a trade, it is handled by the
exchange clearinghouse
▪ Clearinghouse is a third person, so we can avoid the credit risk
▪ It stands between the two traders + manages the risk
▪ Traders don’t have to worry about the creditworthiness
▪ The clearing house takes care of credit risk by requiring each of the two
traders to deposit funds (= margin) with the clearing house to ensure that they
will live up to their obligations
MARKET SIZE
OTC forwards
Exchange futures
Both markets are huge, but the number of derivatives transactions per year in OTC markets is smaller
than in exchange traded markets.
The OTC market is much larger than the exchange-traded market.
Bear in mind: the principal underlying an over-the-counter transaction is not the same as its value.
4
,TERMINOLOGY
Forward/futures contract vs. spot contract
❖ Forward / future contract
o = agreement to buy / sell something in the future
o Forward contract traded is traded in the OTC market
o Future contract is traded on the exchange market
❖ Spot contract
o = agreement to buy / sell something on the spot, at this moment. I give now 250 € and
I get the watch now
Long position vs. short position
❖ Long position
o = to buy in the future
❖ Short position
o = to sell in the future
Bid price vs. offer/ask price
❖ Bid:
o = what people are willing to buy at
❖ Offer/ask:
o = what people are willing to sell at
❖ Bid-ask/bid-offer spread
FORW ARD CONTRACTS
It is an agreement to sell or buy an asset at a certain future time for a certain price.
❖ It is traded in the OTC market
❖ Long position = agreement to buy the underlying asset on a certain specified future date for a
certain specified price
❖ Short position = agreement to sell the asset on the same date for the same price
Forward contracts can also be used to hedge foreign currency risk (ex. P. 6-7)
FUTURE CONTRACT
It is an agreement between two parties to buy or sell an asset at a certain time in the future for a
certain price
❖ It is traded on the exchange market
5
, ❖ Standardized features of the contract
USE OF FORW ARDS / FUTURES (& PAY OFFS)
Forwards / futures = Agreement to buy/sell asset at future time for certain price
At maturity (T), payoff are:
Long position: ST – K
o When you buy in the future
Short position: K – ST
o When you sell in the future
K = forward / future price at M
S = spot price (when you own something, you are on the spot) at M
Situation : Situation:
When you are going to buy something (corn) within two When you have an future contract with a future price of
months, but you take future contract with future price (K) 250 euro, but the spot price two months later is 200 euro,
of 250 euro. Two months later you are going to buy the then you will gain 50 euro, because you will be selling for
corn, but spot price is 200 euro, then you will loss, 250 euro.
because you will have to pay 250 euro because of the
future contract. When you have an future contract with a future price of
250 euro, but the spot price two months later is 300 euro,
When the spot price two months later is 300 euro, then then you will lose 50 euro, because you will be selling for
you will gain because you can buy the corn for 250 euro 250 euro instead of 300 euro.
instead of 300 euro due to the future contract
OPTIONS
Options are traded both on exchanges and in the OTC market
❖ Two types:
o Call options
▪ Gives the holder the right to buy the underlying asset by a certain date for a
certain price
o Put options
▪ Gives the holder the right to sell the underlying asset by a certain date for a
certain price
❖ The exercise price / strike price
o The price in the contract
❖ Expiration date or maturity
6
, o The date in the contract
❖ American versus European options
o American can be exercised at any time up to the expiration date
o European can be exercised only on the expiration date itself
Important: the holder does not have to exercise his right! Forwards / Futures, where the holder is
obligated to buy or sell the underlying asset.
But: there is a cost to acquiring an option
There are 4 types of participants in options markets:
1. Buyers of calls
2. Sellers of calls
3. Buyers of puts
4. Sellers of puts
Buyers are referred to as having long position; sellers are referred as to having short positions.
Selling an option is also called writing the option.
TYPES OF TRADERS
Three broad categories of traders can be identified:
1. Hedgers
o Use derivatives to reduce the risk that they face from potential future movements in a
market variable
2. Speculators
o Use them to bet on the future direction of a market variable
3. Arbitrageurs
o Take offsetting positions in two or more instruments to lock in a profit
HEDGERS
Example:
❖ Farmer will have 1,000,000 bushels of corn 2
months from now
❖ Current price is $3.56 per bushel of corn
❖ Hedge against volatile corn prices (uncertainty!)
❖ Example page 11
Instead of waiting what corn price will be 2 months from now, agrees to sell 1,000,000 bushels for
$3.60 per bushel in forward market
❖ Future cashflow: $3.6 million
o If spot price 2 months from now is $2.45: “gain” of $1,150,000
o If spot price 2 months from now is $4.00: “loss” of $400,000
❖ Either way, farmer receives $3.6 million regardless of future spot price
o Position farmer:
▪ Asset at spot price: ST
7
, ▪ Short forward position: K – ST
▪ ST + K – ST = K Payoff at maturity, payoff of your short forward!
• K – ST is what your gain or loss two months later (= at maturity)
• 3.60 – 2.45 = gain
• 3.60 – 4.00 = loss
To avoid volatile prices of corn in the
future for his future corn corps
So the purpose is to reduce the risk. However there is no guarantee that the outcome with hedging will
be better than the outcome without hedging.
We can also hedge using options, example p. 13 (see also the chapter of options)
Comparison between hedging with forwards / futures and hedging with options:
Forward contracts are designed to neutralize risk by fixing the price that the hedger will pay or
receive for the underlying asset
Option contracts, in contrast, provide insurance.
o They offer a way for investors to protect themselves against adverse price movements
in the future while allowing them to benefit from favourable price
o But unlike forwards, options involve the payment of an up-front fee
SPECULATORS & ARBITRAGEURS
❖ Speculation
o They are betting that the price of the asset will go up or they are betting that it will go
down.
o Able to speculate on asset price increase or decrease without large initial investment
(you don’t need the initial investment when you do speculation)
o Read p. 14 – 15
❖ Arbitrage
o ‘Cash and carry’
o In absence of transaction costs
o Locking in a riskless profit by simultaneously entering into transactions in two or more
markets
o Read p. 16 for example
❖ Example:
o Buy S&P500 in spot market for $2,913.98 (you buy all the stocks in the market)
8
, o Sell S&P500 forward 3 months for $2,929.25
o ‘Arbitrage’ profit of $15.27
CHAPTER 2 : MECHANICS OF FUTURES MARKETS
So a future contract is traded on the exchange, and the contract terms are standardized by that
exchange.
Closing out positions
The vast majority of futures contracts do not lead to delivery.
Reason: most traders choose to close out their positions prior to the delivery period specified
in the contract
Closing out a position means entering into the opposite trade to the original one
Example:
❖ New York trader who bought September corn futures contract on June 5 close out the
position by selling (= shorting) one September corn futures contract on July 20
❖ Kansas trader who sold (= shorted) a September contract on June 5 can close out the
position by buying one September contract on 25 august
❖ Each case, the trader’s total gain or loss is determined by the change in the futures price
between June 5 and the day when the contract is closed out
FUTURES (SPECIFICATION OF TH E CONTRACT)
Since forwards are OTC and futures are exchange traded, focus mainly on futures! The difference
between futures & forwards is the contract!
Futures are standardized contracts, which specify:
❖ The asset to be delivered (quantity, quality)
o Ex: only possible to have futures for 5000l gasoline
o Asset is commodity?
▪ There may be a variation in the quality of what is available in the marketplace
o Financial assets
▪ Are generally well defined and unambiguous
❖ Contract size
o The amount of the asset that has to be delivered under one contract
o Important because when the contract size is too small, trading may be expensive
because there is a cost associated with each contract traded
❖ Delivery arrangements (method, date)
o Where and when the delivery can be made
❖ Price
General rule: it is the party with the short position (so the party that has agreed to sell the asset) that
chooses what will happen when alternatives are specified by the exchange.
CONVERGENCE OF FUTURES PRICE TO SPOT PRI CE
As delivery period for a futures contract is approached, the futures price converges to the spot price of
the underlying asset.
If delivery period is reached, the futures price equals – or is very close to – the spot price
9
, Reason:
❖ Futures price > Spot price
o Clear arbitrage opportunity :
▪ Sell (= short) a futures contract
▪ Buy the asset
▪ Make delivery
o These steps will lead to a profit equal to the amount by which the futures price
exceeds the profit price
o When traders exploit this arbitrage opportunity, the futures price will fall
❖ Futures price < Spot price
o Companies interested in acquiring the asset will find it attractive to enter into a long
futures contract and then wait for delivery to be made
o Futures price will tend to rise
❖ Result: futures price is very close to the spot price during the delivery period
MARGIN ACCOUNTS
One of the key roles of the exchange is to organize trading so that contract defaults are avoided. This
is where margin accounts come in
Futures contracts are settled daily you can have a daily loss or gain on your future. It can be in your
favour or not!
Daily settlement
Situation: investor contacts his broker to buy two December gold futures contracts on the COMEX.
Current futures price is $1.450 per ounce
o Contract size is 100 ounces
o Investor has contracted to buy a total of 200 ounces at this price
Broker will require the investor to deposit funds in margin account
o The amount that has to be deposited at the time the contract is entered into is known
as the initial margin
At the end of each day, the margin account is adjusted to reflect the investor’s gain or loss
o = daily settlement or marking to market
Margin account
❖ What?
o Deposit cash or t-bills in margin account
o Losses/gains reflected in the margin account (marking-to-market: your price of the
future asset will be adjusted everyday)
o To protect against credit risk
❖ Post initial margin (~5-15% of contract value)
o The initial margin = is the initial amount of money that a trader must place in an
account to open a futures position.
o The amount is established by the exchange and is a percentage of the value of the
futures contract.
❖ Price changes lead to changes in margin account
❖ If it drops below the maintenance margin, receive a margin call! Then you will have to put
extra money in your margin account to level up to the initial level of your margin account
10
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