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Unformatted text preview: Lecture 2: Pricing Forwards and Futures This lecture studies the pricing of forward and futures contracts. We first focus on the similarities of the contracts and derive pricing formulas from market equilibrium and the noarbitrage principle. We then analyze the differences between the contracts. I. NoArbitrage Principle II. Forward and Futures Pricing A. Stocks without Dividends B. Stocks with Discrete Fixed Dividends C. Stocks with Continuous Dividend Yield D. Foreign Currencies (FX) E. Commodities F. Treasury Bills III. Summary of Pricing Formulas A. Financial Forwards and Futures B. Costs and Benefits to Holding the Spot C. All Forwards and Futures D. Value of the Forward Contract Pricing Forwards and Futures The Big Picture Lecture is about forwards and futures, but we’re really learning a way of thinking SI Pricing technique we’ll use over and over – Payoff replication – Price the replicating portfolio SI The nature of derivative securities – Risk transfer devices – How to trade risks! ETX They usually payoff in cash ETX But we often think like we’re trading the actual risks Bus 35100 Page 2 Robert NovyMarx Pricing Forwards and Futures I. NoArbitrage Principle An arbitrage opportunity is any trading strategy that does not require a cash input but has some positive probability of making profits without risking a loss. Examples: SI Zero price and strictly positive payoff SI Negative price and nonnegative payoff Arbitrage opportunities are free lunches. They don’t exist in today’s financial markets. We will call this property NA = no arbitrage. Important: arbitrage strategy must be riskless . A zerocost strategy that generates positive returns on average does not violate NA. If such opportunities arise, some investors will trade on them. As a result, the opportunity disappears. How? Bus 35100 Page 3 Robert NovyMarx Pricing Forwards and Futures The Law of OnePrice SI NA implies the “law of one price” – assets with the same payoff have the same price SI We’ll typically be employing the law of one price to get the NA price of the assets that interest us – We’ll look for a portfolio of assets that has exactly the same payoffs as the derivative of interest – We’ll price the derivative by pricing the portfolio and invoking the law of one price SI We’ll call a portfolio of assets that has exactly the same payoffs as the derivative – The replicating portfolio – Or the “synthetic” derivative SI This portfolio is most intuitive with forwards (or futures) – That’s the main reason we start with these Bus 35100 Page 4 Robert NovyMarx Pricing Forwards and Futures Note: To get “tight bounds” ( i.e., exact prices) from NA pricing, the following must hold for someone: SI No transaction costs SI No shortsale costs SI No borrowing or shortsale constraints If the above don’t hold, we only get “NA bounds” SI For example, with transaction costs two assets with the same payoffs can differ in price by as...
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This note was uploaded on 08/14/2009 for the course BUS 35100 taught by Professor Novymarx during the Winter '07 term at CHIC.
 Winter '07
 NovyMarx
 Pricing, Market Equilibrium, Arbitrage

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