Derivatives09-9 -Interest Rates, IR Forwards and Futures

Derivatives09-9 -Interest Rates, IR Forwards and Futures -...

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Derivatives Interest Rates, IR Forwards and Futures
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Where we are Last Session: Continuation of Interest Rates and Forward Rate Agreements (Chapter 5, OFOD) This Session: Conclude FRAs and Interest Rate Futures (Chapters 5-6, OFOD) Next Session: Swaps (Chapter 7, OFOD)
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Plan for This Session Review some items left over from last time Forward and Futures Pricing The Forward Rate Agreement (FRA) Interest Rate Futures Eurodollar (ED) Futures Generating Forward and Spot Rates from ED Bond & Note Futures Hedging using IR futures
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Forward Price F 0 = S 0 e rT Relates the forward price and the spot price for any investment asset that provides no income and has no storage costs S 0 : Spot price today F 0 : Futures or forward price today T : Time until delivery date r : Risk-free interest rate for maturity T
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Forward Price When an Investment Asset Provides a Known Dollar Income F 0 = ( S 0 I )e rT where I is the present value of the income during life of forward contract When an Investment Asset Provides a Known Yield F 0 = S 0 e ( r q ) T where q is the average yield during the life of the contract (expressed with continuous compounding)
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Valuing a Forward Contract Suppose that K: delivery price in a forward contract and F 0 : forward price that would apply to the contract today The value of a long forward contract, ƒ, is ƒ = ( F 0 – K ) e rT – The value of a short forward contract is ( K F 0 ) e rT In terms of the spot price, ƒ = ( F 0 – K ) e rT = ( S 0 e rT – K ) e rT = S 0 – Ke rT
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Forward vs Futures Prices Forward and futures prices are usually assumed to be the same. When interest rates are uncertain they are, in theory, slightly different: A strong positive correlation between interest rates and the asset price implies the futures price is slightly higher than the forward price A strong negative correlation implies the reverse
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Stock Index Can be viewed as an investment asset paying a dividend yield The futures-spot price relationship is therefore F 0 = S 0 e ( r q ) T where q is the average dividend yield on the portfolio represented by the index during life of contract For the formula to be true it is important that the index represent an investment asset In other words, changes in the index must correspond to changes in the value of a tradable portfolio
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Index Arbitrage When F 0 > S 0 e (r-q)T an arbitrageur buys the stocks underlying the index and sells futures When F 0 < S 0 e (r-q)T an arbitrageur buys futures and shorts or sells the stocks underlying the index Index arbitrage involves simultaneous trades in futures and many different stocks Very often a computer is used to generate the trades Occasionally (e.g., on Black Monday) simultaneous trades are not possible and the theoretical no-arbitrage relationship between F 0 and S 0 does not hold
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A foreign currency is analogous to a security providing a dividend yield The continuous dividend yield is the foreign risk-free interest rate
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This note was uploaded on 02/21/2010 for the course FINA 221 taught by Professor Na during the Spring '09 term at HKUST.

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Derivatives09-9 -Interest Rates, IR Forwards and Futures -...

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