Applications of the PMP

Margin Calculations

Outline

• Introduction

• Possible models

• Possible impacts

Background: how the stocks are traded

cash securities

cash

client

broker

Buy on cash

Stock Market

full price

full price

Background: how the stocks are traded

cash securities

cash

client

broker

Buy on margin

Stock Market

full price

margin

Background: definitions

Margin – the amount of cash

that must be paid at the

moment of a buy-sell

transaction

Types of Securities

Simple:

-shares

-bonds

-etc.

Derivatives:

-options

-[futures]

Margin – the money that

are lying without use

Margin rate – percentage of the price that must be paid

at the moment of a buy-sell transaction

Background: options

Option – a contract that gives its owner a right to buy/sell a

specified amount of specified stock within a specified time

period for a specified price (exercise price)

call option put option

buyer

seller

right to buy

obligation to sell

right to sell

obligation to buy

good for

raising market

good for falling

market

Background: options

• A profit-loss diagram (acquired call)

market price of

the underlying

stock

exercise price

amount paid

for the option

PROFIT

LOSS

critical

point

Background: options

acquired call sold call

acquired put sold put

Margining and risk management

price

profit

lossprice

profit

lossprice

profit

loss

Simple securities

underlying

price

profit

loss

profit

loss

profit

loss

Options

Spreads (combinations)

underlying

priceunderlying

price

Motivation: Euronext Amsterdam stock

market

average daily turnover of options in January 2009

was 3,356,541 Euro

average margin rate is 40%

1,342,616 Euro were kept as margin daily

more that 1 million Euro are kept away from

investments every day

Motivation: World Crisis

World

economic

crisis

lack of

funds

search of

additional

sources

possible sources of monetary funds

…

Motivation: World Crisis

World

economic

crisis

lack of

funds

search of

additional

sources

possible sources of monetary funds

margins …

Zero Margin Rate: Cure or Disaster?

For clients:

• unlimited investments

For brokers:

• attractive for clients

• more money is lent −−> higher income

But:

Margining is the only mechanism that protects

brokers from clients’ default!

Optimal pairing and the AP

Securities that

bring profit

when the

(underlying)

price goes up

Securities that

bring profit

when the

(underlying)

price goes down

AP = Assignment Problem

bullish side bearish side

Optimal pairing and the AP

Securities that

bring profit

when the

(underlying)

price goes up

Securities that

bring profit

when the

(underlying)

price goes down

AP = Assignment Problem

bullish side bearish side

Optimal pairing and the AP

bullish side

I

bearish side

J

s.t.

- dummy stocks

N-tuples and the Multidimensional APp

airs

3D AP

structure of the cost

matrixobjective function

2D AP

…

trip

les

N-t

up

les

MAP

(ND AP)

MAP and PMPMAP = Multidimensional AP PMP = p-Median Problem

clusteringMAP PMP

bounded number of

components in a cluster

= N

bounded number of

clusters

= pno dummies !

Conclusions: a note on importance

• Existing tools use heuristic procedures and AP model

• Tools approved by stock exchanges can catch only two-

component spreads

• Tools capable of catching spreads with more than four

components do not exist

• If the number of components in a spread is doubled, the

margin is halved

Conclusions: impact

Euronext Amsterdam:

average daily turnover of options in

January 2009 was 3,356,541 Euro

average margin rate is 40%

1,342,616 Euro were kept as margin daily

If 4-component spreads are considered:

margin rate is halved

671,308 Euro are set free daily

additional ~200,000,000 Euro are available yearly

This amount

exceeds Dutch

Government gross

external debt in

2008

Conclusions

• A possible model based on the PMP

– fast

– flexible:

• no limit on spread size

• any margining rules can be “inserted”