Applications of the PMP. Margin Calculations
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Transcript of Applications of the PMP. Margin Calculations
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Applications of the PMP
Margin Calculations
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Outline
• Introduction
• Possible models
• Possible impacts
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Background: how the stocks are traded
cash securities
cash
client
broker
Buy on cash
Stock Market
full price
full price
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Background: how the stocks are traded
cash securities
cash
client
broker
Buy on margin
Stock Market
full price
margin
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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
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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
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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
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Background: options
acquired call sold call
acquired put sold put
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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
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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
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Motivation: World Crisis
World
economic
crisis
lack of
funds
search of
additional
sources
possible sources of monetary funds
…
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Motivation: World Crisis
World
economic
crisis
lack of
funds
search of
additional
sources
possible sources of monetary funds
margins …
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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!
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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
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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
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Optimal pairing and the AP
bullish side
I
bearish side
J
s.t.
- dummy stocks
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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)
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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 !
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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
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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
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Conclusions
• A possible model based on the PMP
– fast
– flexible:
• no limit on spread size
• any margining rules can be “inserted”