underlying assets and reference indices

8/4/2019 Underlying Assets and Reference Indices

1/174

1

Underlying Assets and Reference

Indices

QF 301


2/174

2

Contents

Section 1: Equities Panaroma Ideas about stock prices Stock Exchanges Quotes and Orders Indices

Section 2: Currencies

Section 3: Fixed Income Rates Interest Rate Fundamentals In Practice

Modelling Interest Rates

Section 4: Others

Section 5: Epilogue


3/174

3

To understand derivatives, which are officially first and foremostfinancial instruments to modify risk profiles of certain underlying

assets or reference rates, we need to have an idea what thoseassets or reference rates are and the respective marketmechanisms and factors affecting them

This lecture shows you the tip of the iceberg

It is hoped that the exposure will illuminate to you thesignificance of economic/financial/business news in the papers,

on the internet and in magazines

It is also hoped that the noise that is one component ofderivatives pricing and hedging models compresses into

several equations an huge area that is highly complex andinteresting

Learning Objectives


4/174

4

Section 1: Equities


5/174

5

Panorama


6/174

6

The Concept of Equity

By issuing shares, companies can raise capital topursue business opportunities and meet its operationalneeds

Owning shares is like owning a piece of the company;share owner shares risk with the other owners

Shares can be bought and sold at will in the market


7/174

7

One share of Disney

Source: www.hugovandermolen.nl/scripophily/Disney.php
http://www.hugovandermolen.nl/scripophily/Disney.phphttp://www.hugovandermolen.nl/scripophily/Disney.php


8/174

8

Types of Shares

Common Stock Represent a share in the assets and earnings of a company

Dividends are decided by the directors of the company

Preferred Stock Differ from common stock in regards to voting rights, dividend payout

(higher or guaranteed fixed rate of return), priority to obtaining assetsin case of dissolution

Issued to entice investors (e.g. when company is financially weak)

Share Classes Different classes of common stock with different dividends and voting

rights

E.g. Berkshire Hathaway issues Class B stocks with 1/200 votingright and 1/30 ownership value to small investors (Class A stocks sellfor over $100,000 per piece)


9/174

9

One of the most admiredcompanies in the world


10/174

10

Business Organization and CapitalStructure

Business Organization Sole proprietorship: Entity has no separate existence from owner, debt of

business is debt of owner

Partnership General: Partners manage business and are personally liable for its debt Limited: Certain limited partners give up ability to manage business in exchange

for limited liability on debt Limited Liability: All partners have some form of limited liability

Corporation: Artificial legal entity, shareholders have limited liability

Corporations have two ways to raise capital Issue stocks (equity) Issue bonds (debt)

The combination of equity and debt is called capital structure

In the event of dissolution, payment is carried out in order of hierarchy: Debt: junior/senior, secured/unsecured Equity: common/preferred

Forms of bankruptcy - bankruptcy chapters in the US Chapter 7 Liquidation Chapter 11 - Reorganization


11/174

11

Stock mechanics: IPO

IPO (Initial Public Offering)

Company seeks listing on exchange

Investment bank sought out to be underwriter Underwriter needs to set IPO price; takes responsibility to buy stocks

if price sets too high to sell off into the market over time later

How is the price determined?

IPO stock is often underpriced

Con Less capital raised

Pro Ensures stocks are sold Auction

To minimize underpricing, Dutch auction is sometimes used

Dutch auction high asking price lowered until there is a buyer

Google Dutch-auctioned its shares at IPO; despite that, still rose 17% onfirst day


12/174

12

The worlds largest IPO ever

Fast Facts:

IPO at US$0.39rose to US$0.45

Hang Seng Indexsurged 1.1%


13/174

13

Top Banks - 2006

Source: Wikipedia

Trivia: Which of these banks are not results of mergers?


14/174

Top Banks - 2008

14

Source: http://financialranks.com/?p=69

http://skorcareer.com.my/blog/10-worlds-largest-banks-list-in-2008/2008/06/18/http://jaggerkieth.wordpress.com/2008/07/22/10-world%E2%80%99s-largest-banks-in-2008/
http://financialranks.com/?p=69http://skorcareer.com.my/blog/10-worlds-largest-banks-list-in-2008/2008/06/18/http://skorcareer.com.my/blog/10-worlds-largest-banks-list-in-2008/2008/06/18/http://jaggerkieth.wordpress.com/2008/07/22/10-world%E2%80%99s-largest-banks-in-2008/http://jaggerkieth.wordpress.com/2008/07/22/10-world%E2%80%99s-largest-banks-in-2008/http://jaggerkieth.wordpress.com/2008/07/22/10-world%E2%80%99s-largest-banks-in-2008/http://jaggerkieth.wordpress.com/2008/07/22/10-world%E2%80%99s-largest-banks-in-2008/http://skorcareer.com.my/blog/10-worlds-largest-banks-list-in-2008/2008/06/18/http://skorcareer.com.my/blog/10-worlds-largest-banks-list-in-2008/2008/06/18/http://financialranks.com/?p=69


15/174

15

Stock Mechanics

Follow-on Offering

Issuance of stock subsequent to IPO

Dilutive: New shares are created, more shares therefore valueper share is reduced (why do it?)

Non-dilutive: Sale of shares by directors or insiders

Primary Offering Issuance of stocks by company

Secondary Offering Offer of stock by shareholder


16/174

16

Stock Mechanics: Splits and Options

Stock splits 1:5 split = each share becomes 5 shares, value of each share is divided by 5 To make share accessible to investors, prevent fall in liquidity

Warren Buffetts Berkshire Hathaway is the most expensive stock in the US;BH has policy not to split stock; if GE hadnt split its stock 9 times since IPOin 1892, it would now be about $160,000 per share

Warrants Gives right to purchase company stocks at a strike price on a specified future

date When warrant is exercised, the company issues new shares of stock (call

options differ in this respect) Often added to bond issue for enticement

Employee stock options Call option that is issued to employee, usually executives, so as to align their

motivations with the companys Strike price typically set at the companys stock price on option grant day


17/174

17

Backdating Scandal

Why the concern?

Who are the victims?

Source:http://www.wired.com/science/discoveries/news/2006/08/71533


18/174

Pixar options backdating scandal

18Source: http://www.theregister.co.uk/2008/04/29/ann_mather_sec_filing_backdating/Date: 29th April 2008
http://www.theregister.co.uk/2008/04/29/ann_mather_sec_filing_backdating/http://www.theregister.co.uk/2008/04/29/ann_mather_sec_filing_backdating/


19/174

19

Stock Mechanics: Buyback andDividends

When company has too much money and has noplan on investing it, it can Buy back shares

Equal access scheme: company offers to buy back shares pro-rata

Selective buy-back: offers to buy back only from several

shareholders Any other reason for share buy-back?

Issue dividends Frequency: can be regular/announced or irregular/special

Forms of payment: Cash, stock, property Dates: Declaration, Ex-dividend, Record, Payment

Dividend play: someone buys stock to collect dividendsmartmove?


20/174

20

Ex-Dividend Date Price Behaviour

Price falls on ex-dividend date

By how much?

Time

Ex-Dividend Date

Stock price level before

Stock price level after


21/174

21

Taxes

Fast Facts

Capital Gains Tax:Tax levied on profit upon sales of capital assetSingapore: 0%USA: Long-term capital gains tax 15%

France: 27%

Dividends Tax:Singapore 0%

USA: 15% for most individual taxpayers

Arguments against:Double Taxation (this and income tax)

Arguments for:Different tax rates for income through active or inactive work

Source: Wikipedia

For more detailed info:

www.oecd.org


22/174

22

In 1997, the Brazilian government imposed 0.38%tax on all financial transactions to raise revenue

Institutional traders then traded Brazilian stocks asAmerican depository receipts (ADRs) in New York toavoid the tax (owners have right to exchange ADRs

for shares they are issued by banks)

Tax raised less revenue than expected and liquidityin Sao Paulo Bovespa dropped (trading volume from1.2b reais a day in 1997 to 350m reais a day in2001)

In Sept 2001, the Brazilian government announcedthat stock transactions would be tax-exempt

Snippet: Unintended Consequences


23/174

23

Stocks Dynamics: M&A

Mergers and Acquisitions

Combine to add value/Empire

building

Consensual merger/acquisitionor hostile takeover

Poison pill White knight

Cash merger/Stockmerger/Acquire assets

Leveraged Buyout (LBO)

Company X

Hostile acquirer

Friendly acquirer

Source: https://reader009.{domain}/reader009/html5/0512/5af71b2332017/5af71b30d3601.jpg


24/174

Poison Pill and White Knight

Poison Pill

- Target company makes itsown stock less attractive tothe acquirer in order to avoid

takeover bids.

- e.g:

allows the existingshareholders (exceptbidding company) to buymore shares at a discount.

White knight

- A target company is facing ahostile takeover fromanother party.

- The white knight offers thetarget firm a way out with afriendly takeover.

24


25/174

25

Mittal Steel Company

Mittal Steel Company largest steel companyin the world by volume

Source: Wikipedia


26/174

26

Arcelor Mittal

White knight


27/174

27

Arcelor Mittal

Started off hostile

White knight

Poison pill


28/174

28

Arcelor Mittal

Source: Asia Times Online, Jan 27, 2006


29/174

29

Merger (risk) Arbitrage

Cash merger Acquirer announces to purchase stocks of target company

Stock price rises in anticipation of the sale but not to the purchaseprice level due to risk that deal may not go through or may bedelayed

Arbitrageur may buy shares hoping that she may sell the shares atthe higher purchase price after the merger

Stock merger Acquirer announces to exchange stocks of the target for its own

stocks at a certain ratio

Arbitrageur may go long in one and short in the other in the hopethe profit may be reaped upon completion of the M&A

What can affect the deal from going through?


30/174

30

Minority Shareholders Rights

A shareholder who owns asubstantial amount of shareshas a lot of say in the direction

of the company

Shareholder activism usesequity stake to put pressure on

management during AGMs Change financing structure, cut

cost, more environmentallyfriendly

Fund management companies

may adopt activism approach

In Singapore: SecuritiesInvestors Association(Singapore) or SIAS


31/174

31

Carl Icahn - owns 4.98 percent ofYahoo common stock

May 13, 2008 - Icahn launched a proxycontest.

May 15, 2008 Icahn confirmed tocommerce a proxy fight to remove

Yahoo's Board of Directors in responseto their "irrational" actions in rejectingMicrosoft's takeover bid.

July 21, 2008 Icahn agreed to joinYahoo's Board of Directors in a deal thatwould end the proxy fight. According to

Minority Shareholders Rights

the agreement, the Yahoo Board willexpand by two directors to elevenmembers. Eight directors will stand forre-election while the remaining three

seats will include Icahn and twonominees that Icahn will recommend.


32/174

32

Gain control of company through acquiring equity via the use ofdebt

Asset of acquired company used as collateral for debt Also known as bootstrap transactions Debt is obtained by issuing junk bonds Some notable names:

Kohlberg Kravis Roberts & Co (KKR) Creates limited partnerships to acquire corporations Finance some with own funds, the rest through the issuance of

junk bonds Investment banks, such as Drexel Burnham Lambert, led by junk

bond king Michael Milken, helped raised funds for LBO

At one point in 2007, BT reports that many firms in Asia were indanger of being taken over not because they were operatingbadly, but because they were low in debt!

Leveraged Buyout


33/174

33

Credit Ratings

Junk

Investment Grade

For details:http://www2.standardandpoors.com/portal/site/sp/en/ap/page.article/2,1,1,4,1148442391999.html

How does rating affectstock price of company?

What criteria are applied?Who pays for the rating?
http://www2.standardandpoors.com/portal/site/sp/en/aphttp://www2.standardandpoors.com/portal/site/sp/en/ap


34/174

34

Sovereign Ratings

Source: www.fitchratings.com/shared/sovereign_ratings_history.pdf

Guess the ratings of the major financial


35/174

35

Guess the ratings of the major financialinstitutions in Singapore

DBS

UOB

OCBC

Temasek Holdings

GIC


36/174

36

Problems with Ratings companies

Little problem when ratingcompanies for straightforwarddebt issuance

Problematic when ratingcomplex instruments

Raters from the ratingcompanies were not paiddirectly by the debt issuing

companies no conflict ofinterestBut raters of complexinstruments sometimes werepaid conflict of interest

Ratings companies can roil themarketTheir pronouncements areimportantBut they are after all humansand are prone to errors injudgement


37/174

37

Ideas about Stock Prices


38/174

38

Price of stock and value of company

Price of stock is what you read in the papers or off Bloomberg

Value of company is a more subjective concept

What affects ones valuation of a company? Management how it funds itself, the investment the company

makes

The business it is doing and the business environment the riskand opportunities

The economy at large

How do most in the market guess the price of the stock? Work out personal valuation of company Guess prevailing perception of companys value Fundamental analysis Technical Analysis


39/174

39

Views of Stock Prices

Forecasters View

Fundamental Analysis: company fundamentals,macroeconomic factors, politics, etc.

Technical Analysis: patterns in price historysuggests future movements

Result: (Strong) Buy/Sell recommendation


40/174

40


Economists View

Efficient Market Hypothesis (EMH): stock prices has

already factored in information*, so no point trying touse that sort of information in trying to beat the market

Information:

Financial data Weak form

All publicly available information Semi-strong form

All information Strong form

Capital Asset Pricing Model (CAPM):

))(()( fmimfi RRERRE +=

Security Market Linebeta

Asset return

Companys stock return

Markets stock return

Risk-free rate

Sensitivity to market returns

Risk premium


41/174

41


QF view Stock prices evolve stochastically

No point trying to guess with precision future pricemoves

Instead, the tools of statistics and probability can

be used to say something definitive/on averageabout prices

Discrete model: prices evolve per unit of time,

each move is either up or down with probability p Continuous model: prices evolve by the

Geometric Brownian Motion


42/174

42

The Binomial Tree Model

1

2

4

1

1/4

1/2

Day 2Day 1

$X

$2X $0.5X

Toss a coin!

Day i

Day i+1


43/174

43

Continuous limit

Let dt -> 0

What do we see?


44/174

44

Random Walk 5 steps

97.5

98

98.5

99

99.5

100

100.5

101

0 2 4 6 8 10 12


45/174

45

Random Walk 100 steps

99.5

100

100.5

101

101.5

102

102.5

103

0 2 4 6 8 10 12


46/174

46

Random Walk 1000 steps

97

98

99

100

101

102

103

0 2 4 6 8 10 12

Th R d W lk M d l


47/174

47

The Random Walk Model

$X

$(X+2)

Day i

Day i+1

$X

2

The normal distribution

Th B i M ti


48/174

48

The Brownian Motion

As dt -> 0, the motionobtained is called theBrownian motion or Wienerprocess

The limit is said to be

continuous

Commonly denoted or

It is the basic building blockfor continuous price modelsin finance

tZ

dt

tW

S


49/174

49

Some basic continuous models

Source: Options, Futures and other Derivative, John C. Hull

G t i B i M ti


50/174

50

Geometric Brownian Motion

Two quantities declared as definitivecharacteristic of stock price

Mean drift (measures company growth) Volatility (measures degree of price

fluctuation/riskiness of company)

Geometric Brownian Motion de facto model ofstock price in finance

tSdlnRoughly, but not quite:

t

t

t dWdtS

dS +=

N t diffi lt thi k


51/174

51

Not as difficult as you think

Step 1: Discretize

Step 2: Excel

ZdtdtWWdtS

SS

idtdtiidt

idtdti

+=+=

+

+

)( )1()1(

Ideas about Models


52/174

52

Ideas about Models

Models have underlying assumptions

Stochastic models such as the Geometric BrownianMotion are not meant for forecasting; they are usedbecause they are mathematically tractable and they

come with parameters that we can empiricallyassociate with intuitive/observable financialquantities (drift = growth, vol = riskiness); they givean average sense of the future evolution of prices

Stochastic models (GBM, Levy models, etc.) areused to price and hedge financial derivatives

Your preference?


53/174

53

Fundamental analysts Look at fundamental reasons/stories things

happening in the world

Technical analysts Look at patterns in price histories

Financial engineers Believe in statistics, use statistical models to

describe price movements

Which style do you prefer?

Your preference?


54/174

54

Stock Exchanges

Stock Markets


55/174

55

Stock markets are concentrated at stockexchanges

Oldest stock exchange: Amsterdam StockExchange Established 1602 by Dutch East India Company

Merged with Brussels Stock Exchange and ParisStock Exchange on Sept 22, 2000 to form

Euronext

Traditional open outcry system

These days electronic exchanges

Stock Markets

Stock Exchanges: Development


56/174

56




57/174

57




58/174

58


Source: http://news.bbc.co.uk/2/hi/business/5039412.stm



59/174

59


How does an exchange make money?

Stock Exchanges: as a business


60/174

60


Source: http://www.marinemoney.com/forums/SIN04/Presentations/Ein.pdf



61/174

61


http://info.sgx.com/SGXWeb_ST.nsf/NEWDOCNAME/REITS_INTRO?OpenDocument

Stock Exchanges: Highly regulated


62/174

62




63/174

63


Excerpt from "Regulating The Capital Markets: Making Market Discipline WorkSpeech by Tharman Shanmugaratnam, Deputy Managing Director, MAS, at the Investment Fund Awards 2001Source: http://www.mas.gov.sg/news_room/statements/2001/Regulating_The_Capital_Markets__Making_Market_Discipline_Work__16_Feb_2001.html

Trading rules


64/174

64

Trading rules

SGX Rulebooks and ManualsSource: http://info.sgx.com/SGXWeb_RMR.nsf/NEWDOCNAME/Rulebooks_and_Manuals

Trading rules


65/174

65

Trading rules

SGX Trading RulesSource: http://info.sgx.com/SGXRuleb.nsf/VwCPForm_SGX_ST_RULES?OpenView

Damping down the activity


66/174

66

a p g do t e act ty

Extreme volatility in the market can be prelude tocrashes

Regulatory responses to extreme volatility Trading halts: trading is stopped when prices have moved

or will imminently move by some specified amount

Price limits: all trade prices are required to be within acertain range on a given day

Transaction taxes: restrict trading by taxing it

Margin requirements and position limits: restrict sizes ofpositions that traders can accumulate

Collars: restrict access to trading systems

Uptick rule: short selling is only permitted following a trade

which is an uptick

Trading Halt


67/174

67

g

Following 1987 market crash, U.S. stock and futures exchanges adopted a setof coordinated trading halt rules

Level 1 halt Condition: DJIA drops by about more than 10% from its closing value on the previous

day Before 2:30pm: halt for an hour Between 2:30pm and 3:30pm: halt for half and hour After 3:30pm: if there is no Level 2 halt, then no halt

Level 2 halt Condition: DJIA drops by more than 20% from its value on the previous day Before 1pm: halt for 2 hours Between 1pm and 2pm: halt for 1 hour After 2pm: if there is no Level 3 halt, then no halt

Level 3 halt Condition: DJIA drops by more than 30% from its value on the previous day Halt for the whole day

Why halt?

Operational Structure


68/174

68

p

Dealers/BrokersOrder-driven

Clearing Agent

SettlementCustodians/Depositories

Investor

T+3

Brazilian Straddle


69/174

69

Straddle is a trading position in two different types of instruments, one long, oneshort, risk-offsetting

Technically bankrupt traders do not have sufficient wealth to settle their trades;

if prices do not change in their favour, they will soon be forced into actualbankruptcy

When traders are in technical bankruptcy, they lose nothing by massivelyincreasing their positions

If prices change in their favour, their financial woes are over If not, those who guarantee their trades will suffer the losses

This strategy is called Brazilian straddle: large market position vs one-way airticket to Brazil

Clearing members check on these monitor traders who clear through them closely require frequent position report throughout the day, require margin payments to be made when prices move against their customers prohibit customers who cannot settle from trading

contractually allocate profits made by technically bankrupt customers to clearing firm ifproblem not reported


70/174

70

Quotes and Orders

Stock QuotesBid/Ask Whos buying/selling?


71/174

71Source: The Business Times, May 4, 2007

Orders


72/174

72

The specifications of an order Price

Number of shares Order type

Market

Limit Stop

Market-if-touched

Validity/expiration instructions

Quantity instructions

Other instructions Display instructions

Market and Limit Orders


73/174

73

Market order is an instruction to trade at thebest price currently available on the market

Market orders pay the bid-ask spread (price forbeing impatient)

Limit order: Limit price

Instruction to trade at the limit price or a price

better than this If its a limit buy order at $5, youre guaranteed to

buy at that price

Limit buy/sell is usually set lower/higher thanmarket

Limit Order Book


74/174

74

Best prices

Source: Trading & Exchanges Market Microstructure for Practitioners, Larry Harris

Validity/Expiry, Quantity and DisplayInstructions


75/174

75

Examples of validity/expiry instructions Day orders: valid for trading day only

Good-till-cancel: valid till trader expressly cancels

Good-until: valid till a certain date Immediate-or-cancel

Good-after: valid after a certain date

Examples of quantity instructions All-or-none

Minimum-or-none

Display instructions To show no more than some maximum quantity to avoid market

moving away from them

Limit orders are options


76/174

76

When trader issues a limit order, he is in effectwriting an option gives the other traders the optionto trade with him Limit buy order: like put option (because expecting price to

fall)

Limit sell order: like call option (because expecting price to

rise)

Factors affecting value of this option Limit price: too far behind market, little value

How long order will stand: allow other traders to defertrading decision

Price volatility: in volatile market, limit orders are valuable,because probability of execution is increased

Option view explains some phenomena


77/174

77

Bid/ask spreads are wide in volatile market option valuable, traders dont like to give away valuable options,

set the limit price far from the market to reduce value of optionthey give away

Fast traders have advantage over slow traders they quickly take up the valuable options

The nature of liquidity Liquidity is the ability to trade at low cost Traders give away options (limit orders), they offer liquidity, in

return, they are compensated with the potential to realize a better

trading price

Why do markets consolidate (traders like to trade in the sameplace)? They offer lots of options as a whole

Other order types


78/174

78

Stop order Stop price Stop buy/sell order price usually set higher/lower than

market

Market-if-touched order Touch price If market price becomes equal or better than touch price,

the market-if-touched order becomes a market order

Stop orders and Liquidity


79/174

79

Stop orders accelerate price changes

Say a trader has a large stop sell order at $100if best bid falls

below $100its activatedtrader then contributes to thefalling market by trying to sell the stock

Stop orders add momentum to the market

Momentum traders Buy when prices are rising and sell when prices are falling May issue stop orders to brokers Destabilize prices

Contrarian traders Buy when prices are falling and sell when prices are rising May issue limit orders to brokers Stabilize prices

Reflect on this


80/174

80

So is the dynamics/stochastics of stock pricesakin to the toss of a coin?

Hmm..what should I bid next?Twice the current bid or half of it?Lets see what the coin says

The Trader Thinker


81/174

81

Indices

Indices


82/174

82

A market index represents the health of the marketas a whole

An index may be Price-weighted: proportional to the sum of prices of the

index components E.g. DJIA, Nikkei 225

Value (capitalization) -weighted: proportional to the sum ofmarket capitalization (price x number) of index components E.g. S&P 500

What is STI?

Indices are often used as performance benchmarksby mutual funds beat the market

Indices


83/174

83

Some major indices US: S&P 500, Russell 2000, Wilshire 5000 UK: FTSE 100

Brazil: Ibovespa Japan: Nikkei 225, Topix HK: Hang Seng Index Singapore: STI South Korea: KOSPI China: SSE Composite Asia: S&P Asia 50 Latin America: S&P Latin America 40 Europe: S&P Europe 350, FTSE Euro 100

Seehttp://en.wikipedia.org/wiki/List_of_stock_market_indices#Asia

The science of indexing


84/174

84

Ideas about Indices


85/174

85

Index gives an average view of the market but average can havemany dimensions Market capitalization Price Growth

Index represents market return and volatility

Index represents diversification Investing in an index?

Index as an asset?

Option on S&P 500: right to buy 500 stocks?

Many funds use index as a gauge of performance

Hedge funds are also called absolute value funds they dont useindex as gauge of performance

Index instruments:Options on Indices


86/174

86Source: http://www.cboe.com/LearnCenter/workbench/products/sp500.htm

Index strategies: Index Fund


87/174

87 Source: https://flagship.vanguard.com/VGApp/hnw/FundsSnapshot?FundId=0040&FundIntExt=INT

Index Tracking not bad!


88/174

88 Source: https://flagship.vanguard.com/VGApp/hnw/FundsPriceHistory?FundId=0040&FundIntExt=INT

How did they do it?


89/174

89

One possible way


90/174

90

0 or 1

Units oftock i

Total number of stocks

Limit the number of shares of each stock

Upper bound on transaction cost

Value of tracking portfolio

Source: An evolutionary heuristic for the index tracking problem, J.E. Beasley, N. Meade, T.-J. Chang

One possible way


91/174

91

Tracking error

Excess return

Index return

Tracking portfolio return

Objective function

Source: An evolutionary heuristic for the index tracking problem, J.E. Beasley, N. Meade, T.-J. Chang

What assumptions underliethese techniques?

Buy an index?


92/174

Questions:

Why does UBS want to buyAIGs commodity index?

What determines the success

of an index?


93/174

93

Section 2: Currencies

Trading Money


94/174

94

Money is traded due to demand and supply forces

Whats the worth of money? Whats its function?

What demand forces? What supply forces?

A medium of exchange

Buying a good for S$100 (on the flip side: selling S$100!) How to buy a foreign good?

One of the earliest currencies: Greek coins

Basic human innovation: better than barter!

What have been used as money?

Sheep, shells, whale teeth, tobacco, nails, oxen, fish-hooks,jewels, elephant tails, wampum

Greek silver coin, face of Athena, c.480B.C.(Source: Economic History of the World)

Trading Money


95/174

95

A unit of account

Measure value of goods relative to a currency: price tags

A finance jargon meaning the same: numeraire

A store of value

Companies hold ready cash for daily transactions What affects currencies worth as store of value?

Banana money zero worth now

Germany is known for conservative monetary policy and

aversion to inflation historical root? (fear of hyperinflation)

Hyperinflation


96/174

96

German hyperinflation (c. 1923)

1923-issue 50 million mark banknote. Worth approximately $1 US when printed,this sum would have been worth approximately $12 million nine years earlier.The note was practically worthless a few weeks later due to continued inflation

Inflation 192324: a woman feeds her tiled stove with money.At the time, burning money was less expensive than buying firewood.Source: Wikipedia

In a hyperinflation, the value of money relative to goods reduce rapidly

Currencies


97/174

97

Governments print paper money, mint coins Careful about it as it can cause inflation

Money is commonly accepted by fiat

An avenue of national pride

How many currencies are there around the world? There are slightly more than 200 currencies around the world

Some countries do not have their own currencies, e.g. Ecuador, Panama, East Timor

Useful link: https://www.cia.gov/cia/publications/factbook/

Trivia: What is the currency of Luxembourg, South Africa, Botswana

First President of SingaporeYusof bin Ishak

Singpaores National Coat of Arms

Major Currencies
https://www.cia.gov/cia/publications/factbook/https://www.cia.gov/cia/publications/factbook/


98/174

98

The United States Dollar (USD)

The Euro (EUR)

The Japanese Yen (JPY) The Great Britain Pound (GBP) (aka Sterling)

The Swiss Franc (CHF)

ISO 4217 Currency Code Usually first 2 letters refer to country, third letter refers to

currency name

What is CHF? Whats the ISO code for Canadian Dollar?

What about Mexican Peso?

Foreign Exchange turnover


99/174

99Source: BIS Triennial Central Bank Survey

The Foreign Exchange Market

H d il f b USD


100/174

100

Has an average daily turnover of about USD2 trillion (daily turnover at NYSE before

merger with Euronext was about USD 40-50billion)

Worlds largest financial market Some participants relatively larger than others

But all small in the grand scale of things

Largely unregulated OTC market Central banks monitor currencies together with

interest rates (monetary policies)


K i


101/174

101

Key instruments

Spot

Forwards Swaps

Derivatives: futures, options, exotic options

FX k t i l t 24 7



102/174

102

FX market is close to 24-7

Opens in Wellington, New Zealand, on their Monday at 7am

Closes on Friday evening in the US

Used to be traded via telephone or telex; now e-trades, online

Quotes and information readily available(www.forexnews.com, www.dailyfx.com,www.fxstreet.com ), market very liquid

Spot Quotes
http://www.forexnews.com/http://www.dailyfx.com/http://www.fxstreet.com/http://www.fxstreet.com/http://www.dailyfx.com/http://www.forexnews.com/


103/174

103 Source: Bloomberg.com

USDCAD

EUR|USD

Currency pair: USDEUR or USD|EUR

Spot Quotes


104/174

104

Currency pair: USDEUR or USD|EUR Read Dollar Euro

USD is base currency, EUR is quote currency

First currency thought of as asset, e.g. EURUSD 1.3583means that 1 Euro is worth USD 1.3582

Its a price: price of 1 USD in terms of EUR

European/indirect terms: USD|EUR

American/direct terms: EUR|USD

Nicknames: GBP|USD = Cable; AUD|USD = Aussie; NZD|USD = Kiwi

Spot Quotes

USD|CHF 1 2162


105/174

105

USD|CHF 1.2162

Market lingo

I buy dollar yen! A five-pip decline in EUR|USD

Euro-Dollar is trading at one-twenty-eight the

figure USD|JPY rises one big figure from 111.00

2 pips: smallest quoted unit100 pips make 1 big figure

Triangular arbitrage

USD|EUR 1 3583


106/174

106

USD|EUR 1.3583

EUR|Yen 162.894

Yen|USD 0.0083

Do you smell anything fishy?

USD|EUR 0 7362

Triangular arbitrage


107/174

107

USD|EUR 0.7362

EUR|Yen 162.894

Yen|USD 0.0083

Still fishy?

Tim Weithers, author of Foreign Exchange APractical Guide to the FX Markets, mentioned

someone in class asking UBSs FX spot dealers ifthey had ever done traingular arbitrageyes, I did,once, back in 1977

Marketmakers

Whos quoting?


108/174

108

Marketmakers stand ready to buy if client wishes to sell and vice

versa Found in banks, brokerages (e.g. www.forex.com)

Earn through bid-ask spread (buy low sellhigh) Measure of how liquid the market is (how easy it

is to buy and sell) Measure of profit marketmaker makes

Quote with bid/ask: EUR|AUD 1.7686|90

The handle

What drives exchange rates?

Who determines exchange


109/174

109

grates? Nobody Floating exchange

rate era (read history of foreign

exchange)

Equilibrium considerations Purchasing Power Parity

exchange rates are determinedby relative prices of similarbaskets of goods, e.g. Big Maccosts S$3 in Singapore andUS$2 in the US, so theexchange rate by PPP ought to

be USD|SIN 1.50 The Economists Big Mac

Index is a widely cited indicatorof PPP

Theoretical conception: Equilibrium considerations

What drives exchange rates?


110/174

110

p q Interest rate parity: because one can exchange currencies and

deposit at the corresponding interest rate, exchange rates andinterest rates satisfy a no-arbitrage relationship

Macroeconomic factors

US current account deficits

About US$800b, 7% US GDP spends more than earns Daily international funding is on the order of US$8b

Looming fear that it will trigger a large and rapid decline in USD

Japans almost zero interest rate encouraged the yen-carrytrade

Monetary policies, country economics, political stability,

happenings in other asset classes, etc.

Snapshot: Thai baht


111/174

111

Snapshot: Argentine peso


112/174

112

Section 3: Fixed Income Rates


113/174

113

Section 3: Fixed Income Rates

Fixed Income - Overview

Investment that gives regular return


114/174

114

Institution raises funds with it, incurring debt

2 main market Money market (< 1yr) Capital market (longer term)

Instruments Notes and Bonds

Corporate Government, municipal

Floating rate note (FRN)

Swaps Credit-linked products Asset-backed securities (ABS) Collateralized Debt Obligations (CDO)

Money market instruments: Commercial Paper (CP), Certificate ofDeposit (CD), Bankers Acceptance (BA), T-Bills, Fed Funds,Eurodollar deposits, Repo, money market mutual funds

Interest Rate Fundamentals


115/174

115

Interest Rate Fundamentals

Basic Concepts in Fixed Income

Discounting and Compounding


116/174

116

Discounting and Compounding

Present Value (PV)

Discounting Factor (f)

Rate (r)

N days

Whats the Present Value?

Today

$K

Discounting: PV = K x fCompounding: K = PV / ff = 1/(1+r x DAYCOUNTFRAC)Compounding Number

Basic Concept in Fixed Income

Rates are stated annualized


117/174

117

Day count convention

Simple vs continuous

Interest rates are usually stated annualized

Annualized rates


118/174

118

y

In other words, it describes the amount ofinterest earned in 1 year

If $100 is deposited at 5% for 6 months, whatsthe interest at maturity?

Interest = x 5% x $100 = $25


Slightly more generally, what is the interest earned on


119/174

11

9

$100 at 5% if the term is from Jan 10, 2007 till 3 Mar,2007?

The interest earned is $100 x FRAC x 5%, where

FRAC is a fraction that depends on the particular day-count convention that is adopted

Some common day count conventions: Actual/Actual,Actual/365, Actual/360


Actual/Actual:


120/174

12

0

2007 has 365 days (not leap year)

Between Jan 10 and Mar 3, there are 52 days

FRAC = 52/365 Interest = $100 x 52/365 x 5% = $0.7123

Actual/365

Between Jan 10 and Mar 3, there are 52 days FRAC = 52/365

Interest = $0.7123

Actual/360 Between Jan 10 and Mar 3, there are 52 days

FRAC = 52/360

Interest = $0.7222


Most common is Actual/360 and is used by USD and


121/174

12

1

EUR

What is FRAC for Actual/360 when the term is 1 year?

Other conventions abound: 30/360: each month is treated as having 30 days

ACT/252: common is South American instruments; 252 is thenumber of business days in a year


$100 is deposited from Jan 4, 2007 to Jun 8, 2007


122/174

12

2

Day count convention: Actual/360

Quoted interest rate: 7%

What do you get on Jun 8, 2007?

Compounding

What is the interest earned on $100 at 5% if the termi f J 1 2007 till J l 1 2009?


123/174

12

3

is from Jan 1, 2007 till Jul 1, 2009?

For such a long period, the deposits interest is earnedby compounding

Suppose the compounding frequency is semi-annual

If day count convention is not taken into account:

Jan 1, 2007 Jul 1, 2009

6m 6m 6m 6m

100 100x1.025 100x1.0252 100x1.0253 100x1.0253

=107.6891

Compounding

If day count convention, say Actual/360, is taken intot th t l di i d t b


124/174

12

4

account, the actual compounding periods must bedetermined: e.g. Jul 1, 2007; Jan 1, 2008; Jul 1, 2008;Jan 1, 2009 in addition to the start and maturity

Jan 1, 2007 Jul 1, 2007: 181 days

Jul 1, 2007 Jan 1, 2008: 184 days

Jan 1, 2008 Jul 1, 2008: 182 days

Jul 1, 2008 Jan 1, 2009: 184 days

Jan 1, 2009 Jul 1, 2009: 181 days

Payoff at maturity =100(1+181/360x5%)(1+184/360x5%)(1+182/360x5%)

x (1+184/360x5%)(1+181/360x5%) = 113.3249

Interest rate: r

General form:Disregarding day count convention


125/174

12

5

Principal: N

Compounding frequency: n times a year

Term: m years

The payoff at maturity is: Nx(1+r/n)m/n

General form:With day count convention

If d i i k i h


126/174

12

6

If day count convention is taken into account, the

actual dates in the compounding periods must benoted

Say: t0, t1, , tk

The payoff at maturity is:

N(1+FRAC(t0, t1)r) (1+FRAC(t1, t2)r)(1+FRAC(tk-1, tk )r)

If rate = 5%, compounding frequency is quarterly, whatis the equivalent annual rate?

Equivalent annual rate


127/174

12

7

is the equivalent annual rate?

The interest earned in 1 year (on $1 principal)= (1+1/4 * 5%)4 1 = 0.050945

The equivalent annual rate is 5.0945%

If compounding frequency is n times a year, what doyou think is the equivalent annual rate when n is verylarge?

The exponential function

Observe:

(1 1/10 * 5%)10 1 051140


128/174

12

8

(1+1/10 * 5%)10 = 1.051140

(1+1/100 * 5%)100 = 1.051258

(1+1/1000 * 5%)1000 = 1.051270

(1+1/10000 * 5%)10000 = 1.051271

In fact, exp(0.05) = 1.051271

Generally,

Leonhard Euler (1707-1783) on CHF 10

If rate = 5% is continuous, what is the interest on $100deposit after 1 year?

Interest with continuous rate


129/174

12

9

deposit after 1 year?

Payoff after 1 year = 100e0.05 = 105.1271

Interest = 5.1271

What is the payoff after 2.55 years?

Payoff after 2.55 years = 100e2.55x0.05 = 113.5985

Generally, rate = r, term = T years, principal = N

=> Payoff = NerT

Principal = 1

Term = 1 year

Difference between rates


130/174

13

0

Term = 1 year

Rate = r

Payoff if rate is continuous: er

Payoff if rate is simple: 1+r

Payoff if compounding frequency is quarterly: (1+r/4)4

Binomial expansion: (1+r/4)4 = 1+r+6(r/4)2+

Taylor series expansion: er = 1+r+r2/2+r3/6+

The payoffs are roughly equal provided r is small

Equivalent rates

You own Bank Smiley and you want to pay an interestof $5 for a 1-year deposit on $100


131/174

13

1

of $5 for a 1 year deposit on $100

What is the simple rate (equivalent annual rate)?

100x(1+rsimple) = 105 => rsimple = 105/100 1 = 5%

What is the continuous rate?100exp(rcont) = 105 => rcont = ln(105/100) = 4.879016%

What is the rate if compounding frequency is quarterly?

100(1+r4/4)4=105=>r4= ((105/100)1/4-1)x4 = 4.908894%

Snap!

1) What rate of interest with continuous compoundingis equivalent to 15% per annum with monthly


132/174

13

2

is equivalent to 15% per annum with monthlycompounding?

2) A deposit account pays 12% per annum withcontinuous compounding, but interest is actually paidquarterly. How much interest will be paid each quarteron a $10,000 deposit?

In Practice


133/174

13

3

Notional Notional/Face Value

C F

Bonds terminology


134/174

13

4

Coupon Frequency

Maturity Accrued interest Cash/dirty price // Quoted/clean price

Dirty Price = Clean Price + Accrued Interest

Discount (Coupon) Rate

(Reference) Floating, Fixed Payment in fine (reset date and coupon date coincide)/in arrear

(reset at beginning of coupon period)

Day-count convention Yield: a single number that describes the quality of the instrument Currency Issuer/Credit rating

10-yr US Treasury Note

Settlement date:

1/18/2005


135/174

13

5

Current (trade) date:

1/17/2005 Maturity:

11/15/2014

Coupon rate: 4.25%

Coupon frequency: S/A Face value: 1,000,000

Quoted price:

100+10/32+1/64 =100.328125 per 100 face

Day count convention:act/act

11/15/2004-1/18/2005:

64 days

UST convention: -10 means 10/32; + means 1/64Bloomberg convention: M = 1,000

Cashflows in a Bond (fixed rate)

F l

Day count conventionAccrued interest belongs to seller


136/174

13

6

Face value+ coupon

Coupon= 4.25% x N/365 x Face

Interest accruesat 4.25% for this period;

Payment at end of period: in-arrear

MaturityIssue date

Coupon frequency: SA

Settlementdate

Tradedate

Accrued interest belongs to seller

Clean price: discount these cashflows to settlement date; nearest coupon only remaining fraction taken

Cash/Dirty vs Quoted/Clean Prices

A


137/174

13

7

Dirty price = Clean price (buyer receives full coupon A, no accruedInterest for seller)

6m 6m

tdy

Dirty price = Clean price + accrued interest (part of A belongs toseller as he has been holding on to the bond for the first 3m of the

coupon period)

3m 6m

tdy A

3m

T-bill

Bid > Ask ?! Free-lunch!?


138/174

13

8

Bid price

=100 2.57= 97.43per hundred face

Ask price= 100-2.56= 97.44per hundred face

Length of investment bills, notes, bonds

Want to invest in fixed income? Thinkabout it


139/174

13

9

Fixed or floating coupon Bonds: coupon rate is fixed, matures in a (moderately) long

time FRNs: floating rate version of bonds

Interest rate environment (the spot curve) changesover time serves as prices of fixed incomeinstruments and as expectations of future ratemovements

Which strategy do you choose buy-and-hold-till-maturity or opportunistic trading

Many rates

LIBOR

EURIBOR Spot rate

Forward rate


140/174

14

0

SIBOR

Fed Funds rate

Prime rate

Overnight rate

Swap rate

Constant maturity swaprate (CMS)

Overnight indexed swaprate (OIS)

Par rate

The above areequivalent to each other

Short rate,instantaneous forwardrates, market rates

One of the most widely watched/referenced rates CMEs Eurodollar futures (most heavily traded short-term interest rate

futures contract) are based on USD LIBOR3m

LIBOR and LIBOR Fixing


141/174

14

1

London Interbank Offered Rate

Interest rate at which a bank is willing to lend funds to another bank(inter-bank market)

Terms: overnight, 1w, 2w, 1-12m

How is it produced? BBA maintains a panel of 8 contributor banks Top and bottom quartile are disregarded Middle two quartiles are averaged Announced shortly after 11am each day

Usage of LIBOR rates is via simple compounding with ACT/360

convention: e.g. x (1 + L x ACT/360)

Spot rate

A spot rate of N years is the rate at which interestaccrues if cash were deposited for N years from today


142/174

14

2

The graph of the function t |-> r(t), where t is time tomaturity and r(t) is the corresponding spot rate, iscalled the spot (rate) curve

Curve under normal conditions looks like this:

t

r

Whats your mood, Mr Banker?

r


143/174

14

3

t

t

r

Source: http://www.ces.ncsu.edu/AboutCES/smp/19/smhap.gif

Fundamentals of Finance - 1

The Fundamental Strategy of Finance:


144/174

14

4

Buy Low, Sell High

t

r

Low High

How to capture the discrepancy and realize it as profit?

Borrow short (term), lend long (term)

The Business of Commercial Banking


145/174

14

5

Short term rate r 1 + 1 year Long term rate R 2 years

Liability: [(1+r)-1] = r in first year, r + r(1+r) =r2 + 2r in the second year

Revenue: (1+R)2 1 = 2R + R2 in the secondyear

The interest rate environment extended view

Very low now: Bernanke at the helm in new financial territory


146/174

14

6

Greenspan Put

(lower rates to stimulate economy afterDot Com bust

Volker stepping on the brakes

to stop inflation, which begansince 1973 oil price shocks

Ideas about the spot curve (termstructure)

Expectations Theory Long-term interest rates reflect expectation of future short-

term interest rates


147/174

14

7

Market Segmentation Theory Rate of a term indicate demand and supply for borrowing

and lending for that term

Liquidity Preference Theory Investors like to deposit short-term for liquidity reasons Borrowers like to borrow long-term to lock in rates

Banks will need to finance long-term loans with short-termdeposits; any change in short-term environment willadversely affect the financing => excessive interest rate risk

Banks therefore raise long-term rates to reduce demand forlong-term borrowings relative to short-term depositions

What affects rates?

Government monetary policies


148/174

14

8

US FOMC announcement of rate hike/rise Holds 8 regularly scheduled meetings each year

Date of each meeting is confirmed at the meeting

preceding it

Happenings in other markets

Stock/commodity market red-hot indicative ofinflation pressure

Federal Reserve and Monetary Policy


149/174

14

9 Source: http://www.federalreserve.gov/fomc/fundsrate.htm

Take a look!

Federal Reserve and Monetary Policy


150/174

15

0

Fed Dec 16, 2008 Monetary PolicyPress Release


151/174

15

1

This is

unconventional

Fed Funds Rate Target vs Effective


152/174

15

2Source: http://www.schwab.com/public/schwab/research_strategies/market_insight/todays_market/recent_commentary/unconventional_0_to_25_range.html

What now?

Nominal interest rate near zero economists call this (near) liquiditytrap

That means: people would rather hold on to money than to spend it (or


153/174

15

3

p p y p (make short term investments rather than long term investments)

Major central banks use interest rates as tool to stimulate economy (orcool it down)

With rates near 0, and economy needs lots of stimulation HOW?

Various views Helicopter Money - give money directly to businesses, which is what the

2008 $700B US Govt Bailout Plan is supposed to do

Deficit Spending spend on infrastructural projects in recession and underdeficit conditions to stimulate economy (the view is that short-term policiesshould weigh over long-term policies to get out of the present crisisinKeynes words In the long run, were all dead)

Snap!

1) LIBID vs LIBOR

Guess what is LIBID


154/174

15

4

Which is higher?

2) Why are US Treasury rates significantly

lower than other rates that are close to risk-free?

Modelling Interest Rates


155/174

15

5

What do you think?

In the long run, whats the differencebetween the price of a stock (assuming the


156/174

15

6

company thrives and does not go bankrupt)and an interest rate, such as the USDLIBOR3m rate?

Mean Reversion


157/174

15

7Source: Options, Futures and other Derivatives, John C. Hull

The Vasicek Model

Vasiceks model is

dzdtrbadr += )(mean reversion speed


158/174

15

8

dzdtrbadr +)(

r = r(t) short rate Wiener process

volatility

reversion level

Vasicek Model is tractable


159/174

15


Term Structure according to theVasicek Model


160/174

16


What is short rate?

Suppose short rate is r(t) (0


161/174

16

1

Then discount factor is

Roughly, the interest earned between the

period (t, t+dt) is r(t)dt on $1

If short rate is stochastic, and if the (stochastic)

payoff of an instrument (that pays at time T) isfT , then the instrument is worth today at

e 0

T

dttr

feE

T

0)( (taken wrt risk neutral measure)

Theres only 1 stock price

Interest rate modelling is more difficultthan stock price modelling


162/174

16

2

Theres a whole term structure of interestrates!

Correlation exists between rates: e.g. 1-yearspot rate is correlated with 2-year spot rate

Why is the Vasicek Model simplistic from thisperspective?

Section 4: Others


163/174

16

3

UNDERLYING assets/REFERENCEindices, relative to?

Financial derivatives are financial instruments that stipulatecashflows in the future whose sizes depend on the prices ofcertain underlying assets or the magnitudes of certain referenceindices


164/174

16

4

Vanilla European option

Call option : Payoff Max(ST K, 0) at maturity T

Put option : Payoff Max(K - ST, 0) at maturity T

Inverse Floater

A note that pays coupons periodically (e.g. semi-annually) of acertain percentage of a notional amount

What certain percentage? Max(0, 8% - LIBOR3m) xDayCountFraction

Inflation index

Index used is Consumer Price Index

Inflation derivatives


165/174

16

5

Inflation cap

Inflation swap

Inflation swaption

Inflation bond

Inflation cap payoff:

Temperature

HDD: Heating degree days CDD: Cooling degree days

A = average of highest and lowest temperature during


166/174

16

6

the day at a specified weather station A days HDD := max(0,65-A)

A days CDD := max(0,A-65)

Example of a weather derivative: Call option on cumulative HDD during February 2005

Strike price 700 Rate of $10,000 per degree day

If cumulative HDD = 820, payoff = (820-700) x 10,000 =1,200,000

Temperature


167/174

16

7 Source: http://www.fenews.com/fen51/one_time_articles/weather-derivatives/weather-derivatives.html

Temperature


168/174

16

8 Source: http://www.fenews.com/fen51/one_time_articles/weather-derivatives/weather-derivatives.html

Volatility


169/174

16

9

Source: CBOEs website

Volatility


170/174

17

0

Source: CBOEs website

Hmm

Property derivatives are making inroads intothe mainstream finance world they arebased on property indices


171/174

17

1

Interesting thoughthow do writers of exotic

derivatives on indices hedge their risks?

Section 5: Epilogue


172/174

17

2

Financial derivatives are contracts that refer to anunderlying asset or a reference index or rate

S f h j l hi h h

The Points


173/174

17

3

Some of the major asset classes which havecommonly served as underlying assets for derivativesare the equities, currencies and commodities. From

the fixed income world, interest rates are often used inderivative contracts as reference rates.

The significance of being an underlying of a derivativeis that the derivative attempts to alter the risk profile ofthe underlying asset.

Prices from different asset classes and different rates are drivenby a complicated web of factors. This results in qualitativelydifferent price and return histories. This is important as onefundamental piece of the theory of derivatives pricing is the

th ti ll d d l f th d l i i / t / t

The Points


174/174

17

4

mathematically assumed model of the underlying price/rate/returnstochastics.

The Geometric Brownian Model is the de facto model of returns

stochastics in finance, even though it is far from being accurate.Financial engineers have improved the modelling by adoptingmore complicated models of price/rate/return stochastics.

This lecture describes the complexities that make up each assetclass to highlight the simple-minded nature of the mathematicalmodels.

underlying assets and reference indices

Documents

ecs2601 -...

s&p shariah indices methodology -...

group group – income statement - aga … assets held for...

ubs financial services inc. rbc capital markets, llc ·...

existing legal framework for distressed assets in · pdf...

working paper series - ecineq · the de vergottini indices,...

limiting risk exposure with s&p risk control...

underlying operating profit basic underlying...

2019 prospectus - blackrock · determined by s&p dow jones...

ipd indice fondi immobiliari italiani ipd italian...

indices - cdn.ihs.com · the indices are composed of...

monthly economic indicators...12 price indices 5 13 average...

high yield indices - the ice · high yield indices phil...

regulatory analysis of contracts for...

option pricing where the underlying assets follow a … ·...

corporate presentation - mvis indices...corporate...

the fcocockpit –global bubble status report peter cauwels...

mattereum protocol: turning code into law...furthermore, the...

mts indices - european...

mechanics of options markets chapter 8 1. 2 assets...