# N Period Binomial Option Pricing Model Kevin Clarke.

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N Period Binomial Option Pricing Model Kevin Clarke

Options Call options A call option gives the holder the right to buy the underlying asset by a certain date for a certain price Put options A put option gives the holder the right to sell the underlying asset by a certain date for a certain price

One Step Binomial Tree A derivative lasts for time T and is dependent on a stock Su ƒ u Sd ƒ d SƒSƒ

Pricing Options From a One Step Tree Consider a portfolio consisting of a long position in  shares and a short position in one option. Assume that no arbitrage opportunities exist.

Two Step Binomial Tree Su ƒ u Sd ƒ d SƒSƒ Su² ƒ uu Sud ƒ ud Sd² ƒ dd

Four Step Binomial Tree S0S0 S0uS0u S0dS0d S0S0 S0S0 S0u 2S0u 2 S0d 2S0d 2 S0u 2S0u 2 S0u 3S0u 3 S0u 4S0u 4 S 0 d 2 S0uS0u S0dS0d S0d 4S0d 4 S0d 3S0d 3

General Case S i+1,j+1 ƒ i+1,j+1 S i+1,j ƒ I+1,j S i,j ƒ i,j (p) (p-1)