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Lecture # 3 Stocktrak Investment Game Dreivatives: Options etc

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

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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)

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Options Long position (Net buy position) Short position (Net sell position) Call option Buyer / Holder Seller / Writer Put option Buyer / Holder Seller / Writer

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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

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Future market for Crude Oil

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Source: NYMEX 13/09/2006

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Future market for Crude Oil Source: NYMEX 13/09/2006 Month OCT 2006 NOV 2006 DEC 2006 JAN 2007 Future price

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Future market for Crude Oil Key Figures 1 Week1 Month 3 Months 6 Months 1 Years Performan ce 23, % %-67.27%-42.82%-5.24% High Low Volatility 4, , , , ,806.46

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

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

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Assumptions behind the Black-Scholes model The stock prices follow a geometric Brownion motion (Wiener process:S = λ*z +ρ*t) with λ and 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

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Stuff to read! Futures an Options Markets – JC Hull – Prentince Hall – ISBN Financial Management – EF Brigham cs – Dryden – ISBN

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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: … r =Risk-free interest rate (continuously compounded)

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