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Finding the Price for Options

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Finding the Price for Options

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    1. 1 Finding the Price for Options We can find the price for something easily Determine the price for a close (identical) substitute Price for a red car? Nearly the same as price for a blue car.

    2. 2 “Creating a Stock” with Options The profit/loss diagram for a short put plus a long call

    3. 3 “Creating a Stock” with Options Difference Between Buying Stock and Buying a Call and Selling a Put You need more cash up front to buy the stock. The Stock position never expires. The option position will eventually expire.

    4. 4 Can create a short position in the “artificial stock” long put and a short call

    5. 5 Buy the stock and short the “artificial stock”=Riskless A riskless position results if you combine the stock with a long put and a short call

    6. 6 Covered Call and Long Put Riskless investments should earn the riskless rate of interest If an investor can own a stock, write a call and buy a put and make a profit, arbitrage is present

    7. 7 Variable Definitions C = call premium P = put premium S0 = current stock price S1 = stock price at option expiration X = option striking price R = riskless interest rate t = time until option expiration

    8. 8 The Put/Call Parity Relationship We now know how the call prices, put prices, the stock price, and the riskless interest rate are related:

    9. 9 The Put/Call Parity Relationship The interpretation of this is as follows: Buying a call and shorting a put is the same as: Buying the stock and borrowing X (the exercise price) at the risk free rate

    10. 10 The Put/Call Parity Relationship (cont’d) Equilibrium Stock Price Example You have the following information: Call price = $3.5 Put price = $1 Striking price = $75 Riskless interest rate = 5% Time until option expiration = 32 days If there are no arbitrage opportunities, what is the equilibrium stock price?

    11. 11 The Put/Call Parity Relationship (cont’d) Equilibrium Stock Price Example (cont’d) Using the put/call parity relationship to solve for the stock price:

    12. 12 The Put/Call Parity Relationship A stock trades at $50 with a six month put option (strike price=$50) trading at $4.25. If the interest rate is 3%, what is a six month call option trading at?

    13. 13 The Put/Call Parity Relationship A stock trades at $60 with a put option (strike price=$60) trading at $2.75. If the call option trades at $5.35, what is the interest rate?

    14. 14 Making Arbitrage Profits A stock trades at $25 with a put option (strike price=$25) trading at $3.00. If the call option trades at $3.50 and the interest rate is 5%, how do I make a riskless profit? How much of a profit do I make for each share traded?

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