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A different kind of Tree

A different kind of Tree . Using trees to help price options. Some of the ideas behind Black- Scholes. Myron Scholes. Fischer Black. http://hilltop.bradley.edu/~arr/bsm/model.html. Option Basics.

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A different kind of Tree

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  1. A different kind of Tree • Using trees to help price options. • Some of the ideas behind Black-Scholes. Myron Scholes Fischer Black http://hilltop.bradley.edu/~arr/bsm/model.html

  2. Option Basics • A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock. • There are two basic option types. • Call options are options to buy the underlying asset. • Put options are options to sell an underlying asset

  3. Example • Suppose Aetna is selling for $30 a share. • Suppose the option price is $1.30. • Consider the following scenarios and whether or not you would exercise your option: • At the expiration date the stock is $28 per share. • At the expiration date the stock is $30 per share. • At the expiration date the stock is $32 per share. • How do you know what a good price is for your option?

  4. Price of stock = $32 Value of option = $2 $30 Price of stock = $28 Value of option = $0 • Suppose you buy x shares and sell one option. • If the price goes up to $32 your portfolio is worth 32x-2. • If the price goes down to $28 your portfolio is worth 28x-0.

  5. Price of stock = $32 Value of option = $2 $30 Price of stock = $28 Value of option = $0 • Suppose you buy x shares and sell one option. • A risk free portfolio will have the same value regardless of what happens: • 32x-2 = 28x-0. Solve for x to get x = ½. If you have ½ a share, then regardless of how the price of the stock changes (up to $32 or down to $28) the portfolio is worth 32(1/2)-2=14. • So a risk free portfolio that contains x shares and sells one option has a value of 1/2x- 1 option = 14. This means an option is worth (1/2)(30) – 1 option = 14. Solve for one option to get 1 option = $1.

  6. $33 $3 $32 $2 $31 $1 $31 $1 $30 $0 $30 $29 $0 $29 $0 $28 $0 $27 $0

  7. The Black and Scholes Model http://hilltop.bradley.edu/~arr/bsm/model.html

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