Investments19-LargeSlides

Investments19-LargeSlides - Binomial Option Pricing...

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1 Professor Pierre-Olivier Weill Binomial Option Pricing
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2 Last time s Two exotic option strategies Straddle and collar s Put-call parity
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3 Binomial Option Pricing s Pricing of call options on non-dividend paying stocks s Methodology works for all derivatives! s Two-state option pricing s Replication s Hedge ratio s Option pricing in a “tree” s Dynamic hedging
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4 Binomial Option Pricing: Two-state option pricing 1. Assume that the stock price at expiration can have 2 possible values (2 scenarios) 2. Compute the option payoff in each scenario 3. Replicate the option payoff with a portfolio of stocks and risk-free securities 4. Compute the price of the replicating portfolio 5. This is the option price (because of no arbitrage) !
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5 Binomial Option Pricing: example
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6 Binomial Option Pricing: the one period ahead case
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7 Hedge Ratio or “Delta” s The number of stocks in the replicating portfolio (or hedge portfolio) is called the hedge ratio or delta, Δ s The hedge ratio tells you how much the option price changes per unit of change in the stock price: - + - + - - = Δ S S C C
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Investments19-LargeSlides - Binomial Option Pricing...

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