Dynamic Trading Lecture - Debt Instruments and Markets...

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Debt Instruments and Markets Professor Carpenter Dynamic Trading Strategies 1 Dynamic Trading Strategies Multi-Period Bond Model Replication and Pricing Using Dynamic Trading Strategies Pricing Using Risk- Neutral Probabilities One-factor model, no-arbitrage restrictions Concepts and Buzzwords Veronesi, Chapter 10 Tuckman, Chapter 9 Reading

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Debt Instruments and Markets Professor Carpenter Dynamic Trading Strategies 2 No Arbitrage Pricing in a Multi-period Setting In the last two lectures we priced a derivative in a one-period setting: –Finance: if payoff can be replicated, price equals replication cost –Math: replication cost can be represented as expected discounted payoff using “risk-neutral probabilities” that make the expected return on the underlying match the riskless return This lecture enriches the setting with multiple trading dates, and shows how dynamic trading strategies with just a few basic assets can create, and thus price, more complex payoff patterns. For now we will continue to treat future possible payoffs of the basic assets as given, and focus on how to use them to price derivatives . Later, after we understand how the model will be used, we can think about how best to build the model itself. Motivation: Pricing a One-Year Call Suppose we want to price a call on \$1000 par of a zero that matures at time 1.5. –The call expires at time 1. –The strike price is \$975. –The call is European--it cannot be exercised prior to expiration. Suppose there are two trading dates prior to expiration, time 0 and time 0.5. Then we need to model the bond market at three points in time, time 0, time 0.5, and time 1. New problem: Now there are two bonds with a risky time 0.5 value, the zero maturing at time 1 and the zero maturing at time 1.5. Should we let them move separately or should we make them move up or down together?
Debt Instruments and Markets Professor Carpenter Dynamic Trading Strategies 3 How many factors?

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