Lecture3_PricingForwardsFutures_II - NBA 6730: Derivative...

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1 NBA 6730: Derivative Securities Lecture 3: Pricing Forwards and Futures II 09/02/2010 George Gao NBA6730-Derivative Securities I 2 Agenda This lecture studies how to price Treasury Bill futures, foreign currency futures, and stock index futures. Treasury Bill, index, and currency futures Value of forward and futures contract Case study: MGRM
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2 NBA6730-Derivative Securities I 3 (1) General Principle for Pricing Futures Intuitive principle: the futures price should be the price of “holding the spot security” until maturity If the futures price is higher than the cost of holding the spot security until delivery, no one will buy futures If the futures price is lower, no one will hold the spot The relation between spot and futures is captured by: ࢚, ࢀ ൌ ࢂሺ࢚ሻ ൈ ࢋ ࢘ሺ࢚,ࢀሻൈሺࢀି࢚ሻ ܨሺݐ,ܶሻ = futures price ݎሺݐ, ܶሻ = c.c. risk-free interest rate between ݐ and ܶ ܸሺݐሻ = the amount of money required at ݐ for a strategy that generates one unit of the underlying security at ܶ NBA6730-Derivative Securities I 4 (2) Pricing Treasury Bills Futures The underlying security is a T-bill that matures at ܶ ൅ܶ , where: ܶ = the delivery date in the future when a T-bill is delivered ܶ = the time-to-maturity for the delivered T-bill above Example: you buy a T-bill futures contract today, get a T-bill delivered in ܶ , hold this T-bill until it is matured in ܶ , and get paid for $100 face value (we assume a zero-coupon bond for simplicity). What’s the amount of money required at ݐ to get one unit of T-bill in the end, i.e., to claim $100 in ܶ ? $100 ൈ ݁ ି௥ൈሺ் ା்
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3 NBA6730-Derivative Securities I 5 (2) Pricing Treasury Bills Futures Question: at the end of August, what’s the 4-month (December) futures price for a 3-month T-bill that will pay you $100 face value in March? Assume the 4-month interest rate is 4% Assume the 7-month interest rate is 5% Both rates are annualized and continuously compounded ܨ ݐ,ܶ ൌ $ 100 ൈ݁ ିହ%ൈ భమ ସ%ൈ భమ ൌ$ 97.13 ൈ 1.0134 ൌ $98.42
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This note was uploaded on 10/26/2010 for the course JOHNSON 6730 at Cornell University (Engineering School).

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Lecture3_PricingForwardsFutures_II - NBA 6730: Derivative...

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