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Applications of the PMP. Margin Calculations

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AACIMP 2010 Summer School lecture by Dmitry Krushinsky. "Applied Mathematics" stream. "The p-Median Problem and Its Applications" course. Part 4. …

AACIMP 2010 Summer School lecture by Dmitry Krushinsky. "Applied Mathematics" stream. "The p-Median Problem and Its Applications" course. Part 4.
More info at http://summerschool.ssa.org.ua

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  • 1. Applications of the PMP Margin Calculations
  • 2. Outline • Introduction • Possible models • Possible impacts
  • 3. Background: how the stocks are traded Buy on cash client cash securities full price broker cash full price Stock Market
  • 4. Background: how the stocks are traded Buy on margin client cash securities margin broker cash full price Stock Market
  • 5. Background: definitions Margin – the amount of cash Margin – the money that that must be paid at the are lying without use moment of a buy-sell transaction Margin rate – percentage of the price that must be paid at the moment of a buy-sell transaction Types of Securities Simple: Derivatives: -shares -options -bonds -[futures] -etc.
  • 6. 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 good for buyer right to buy right to sell raising market seller obligation to sell obligation to buy good for falling market
  • 7. Background: options • A profit-loss diagram (acquired call) critical PROFIT point market price of amount paid the underlying LOSS for the option stock exercise price
  • 8. Background: options acquired call sold call acquired put sold put
  • 9. Margining and risk management Simple securities Spreads (combinations) profit profit profit price price price loss loss loss Options profit profit profit underlying underlying underlying loss price loss price loss price
  • 10. 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
  • 11. Motivation: World Crisis World search of economic lack of additional crisis funds sources … possible sources of monetary funds
  • 12. Motivation: World Crisis World search of economic lack of additional crisis funds sources margins … possible sources of monetary funds
  • 13. 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!
  • 14. Optimal pairing and the AP AP = Assignment Problem bullish side bearish side Securities that Securities that bring profit bring profit when the when the (underlying) (underlying) price goes up price goes down
  • 15. Optimal pairing and the AP AP = Assignment Problem bullish side bearish side Securities that Securities that bring profit bring profit when the when the (underlying) (underlying) price goes up price goes down
  • 16. Optimal pairing and the AP bullish side bearish side I J s.t. - dummy stocks
  • 17. N-tuples and the Multidimensional AP structure of the cost objective function matrix pairs 2D AP triples 3D AP N-tuples … MAP (ND AP)
  • 18. MAP and PMP MAP = Multidimensional AP PMP = p-Median Problem MAP clustering PMP bounded number of bounded number of components in a cluster clusters =N =p no dummies !
  • 19. 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
  • 20. 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 This amount exceeds Dutch Government gross If 4-component spreads are considered: external debt in  margin rate is halved 2008  671,308 Euro are set free daily  additional ~200,000,000 Euro are available yearly
  • 21. Conclusions • A possible model based on the PMP – fast – flexible: • no limit on spread size • any margining rules can be “inserted”