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Week 5 Lecture

# Week 5 Lecture - CorporateFinanceII Corporate Finance II...

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Corporate Finance II Lecture 5: Corporate Finance II Lecture Week 5 Contingent Claims II:  Valuation

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1 A Model of Stock Prices 2 Static vs. Dynamic Replication 3 Single Period Valuation 4 Multiple Period Valuation 5 Replicating Calls and Puts 6 Early Exercise Decisions 7 Option Price Sensitivities 8 Outline of today’s Lecture: Lecture Summary
A Model of Stock Prices  Discrete time Discrete state. uS C u S C =? dS C d u ” and “ d ” are up and down multiplicative factors. Note: For the tree/lattice to be recombining and symmetric recombining + not symmetric.

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A Model of Stock Prices  Recombining & asymmetric tree: 26.6200 24.2000 22.0000 22.9900 20.0000 20.9000 19.0000 19.8550 18.0500 17.1475 Figure: u = 1.1 and d = 0.95
Recombining & symmetric tree: 26.6200 24.2000 22.0000 22.0000 20.0000 20.0000 18.1800 18.1800 16.5289 15.0263 Figure: u = 1.1 and d = 0.9090 . . . NOTE: for convenience/practical reasons         A Model of Stock Prices

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The previous figures are “binomial trees” or lattices. These are: intuitive + easy to understand; simple to implement; able to accommodate American and exotic options.         A Model of Stock Prices
Assumptions Trading takes place at discrete, evenly spaced times. If S i is the “underlying’s” value at time i , then the only values in the next period are uS i and dS i . Often we will omit the subscript. r f is (1 + R f ) where R f is the risk free rate over each time interval. Markets are frictionless (no transaction costs, no barriers to entry etc). The market is free of arbitrage opportunities: d < r f < u If r f < d < u the “risky” security guarantees a return higher than the risk free rate. If d < u < r f then the risky security never offers a return higher than the risk free rate.         A Model of Stock Prices

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Static vs.  Dynamic Replication  Definition: Static Replication Buy (or sell) and then HOLD a portfolio of securities such that a particular payoff is “replicated”. Example 1 Borrow PV ( X ) 2 Sell a put option on a firm’s assets This Portfolio replicates the payoff of a firm’s debt. There is no need to trade after setting up the portfolio.
Definition: Dynamic Replication Continuously TRADE certain securities in certain amounts so that a desired payoff is “replicated”. For example: Replicating a call option by trading bonds and the underlying security (or stock). This week we focus on dynamic replication. For some simple options static portfolio value = dynamic portfolio value. THIS IS NOT TRUE IN ALL CASES. Static and dynamic valuation approaches are complementary and NOT substitutes for one another. Finding a static replicating portfolio can require some care (e.g replicating American options)         Static vs.  Dynamic Replication

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Single Period Valuation  Once more, recall: 1 p i × CF i where p i is the probability of the i th cashflow CF i occurring.
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Week 5 Lecture - CorporateFinanceII Corporate Finance II...

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