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Finding the Price for Options

This comprehensive guide explores key aspects of options trading, including pricing mechanisms, profit/loss diagrams, and various strategies like covered calls and put/call parity. Learn how to determine the price of options, compare buying stocks versus calls and puts, and create riskless positions through strategic combination of options. The guide provides essential definitions, examples to illustrate the put/call parity relationship, and methods to identify arbitrage opportunities for riskless profit. Ideal for traders seeking to enhance their understanding of options in the stock market.

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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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