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Lecture # 3

Stocktrak Investment Game Dreivatives: Options etc. Lecture # 3. Relationship Spot Market & Option Market. Option Market Call / Put option. Spot Share Market t = 0. Spot Share Market t = n. Option market links spot market now with

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Lecture # 3

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  1. Stocktrak Investment Game Dreivatives: Options etc Lecture # 3

  2. Relationship Spot Market & Option Market Option Market Call / Put option Spot Share Market t = 0 Spot Share Market t = n Option market links spot market now with the spot market future of the underlying value ( = share)

  3. Forward contracts, futures and options • Forward contracts: • An agreement to exchange currencies (or stocks etc) at specified future date and at a specified price (forward rate) • Futures: • An agreement to exchange currencies (or stocks etc) at specified future date and at a specified price (forward rate). Future contracts are normally traded on an exchange. • Options: • Gives the holder the right (but not the obligation) to buy (call option) or to sell (put option) the underlying asset (e.g. currencies, stocks etc) by a certain date (expiration or exercise date or maturity) for a certain price (exercise or strike price)

  4. Options

  5. Pricing of options, the idea C = S– X C = Price or value of an (european) call (stock) option S = Price of asset underlying derivate (stock) X = Strike or exercise price of an option

  6. Future market for Crude Oil

  7. Future market for Crude Oil Source: NYMEX 13/09/2006

  8. Future market for Crude Oil Source: NYMEX 13/09/2006

  9. Future market for Crude Oil

  10. European Call Option (Buyer) Π C = S -X S

  11. European Put Option (Buyer) Π P = X - S S

  12. Assumptions behind the Black-Scholes model • The stock prices follow a geometric Brownion motion (Wiener process: S = λ*z +ρ*t) with λand ρ being constants (lognormal distribution) • The short selling of securities with full use of proceeds is permitted • There are no transactions costs or taxes; all securities are perfectly divisble • There are no dividends during the life of the derivate • There aer no riskless arbitrage opportunities • Security trading is continuous • The risk-free interest is constant and the same for all maturities

  13. Stuff to read! • Futures an Options Markets • JC Hull • Prentince Hall • ISBN 0137833172 • Financial Management • EF Brigham cs • Dryden • ISBN9780030210297

  14. Derivatives & Volatility Option pricing Black-Scholes (stock) option pricing formula (Call option) C = S*N(d1) – X*e-r*(T-t)*N(d2) C = Price European call (stock) option S = Price of asset underlying derivate (stock) X = Strike or exercise price of an option N(d1) =Standardised normal distribution N(d2) =Standardised normal distribution  = Standard deviation of the stock prices (volatility)  = Mean of the stock prices e = Base natural logarithmes: 2.718281828… r = Risk-free interest rate (continuously compounded)

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