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Option Theory

Implications for Corporate Financial Policy. Option Theory. 1. Nature of Options. Contingent Claims: Value depends upon another outcome Can be "written" on virtually any asset Zero Sum game What were the earliest options written on? What effect do options have on the markets today?.

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Option Theory

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  1. Implications for Corporate Financial Policy Option Theory

  2. 1. Nature of Options • Contingent Claims: Value depends upon another outcome • Can be "written" on virtually any asset • Zero Sum game • What were the earliest options written on? • What effect do options have on the markets today?

  3. 2. Option Positions • Long position: You own the option and can exercise it at your discretion. • Short Position: You are liable to have the option exercised against you--you must pay in that event. • The long and short positions sum to zero.

  4. 3. The Basic Call Option • The right to buy an asset at a specified price (the "strike price") at (European) or up to (American) a specified date (the expiration date). • Price is a function of:Strike price, expiration date, market rates, risk of the underlying asset. • What are the relationships between each factor and price?

  5. 4. Call Option Value at Expiration • Value at expiration:S - X, if S>X; 0 otherwise • Net Value(S - X) - P if S>X, 0 - P otherwise

  6. 5. Call Option Positions: Value at Expiration + +C (Long) P 0 X S - C (Short) _

  7. 6. Basic Put Option • The right to sell an asset at a specified price ("Strike price") at (European) or up to (American) a specified date (the expiration date) • Net positions are also a "zero sum" game

  8. 7. Put Option Value at Expiration • Value at expiration:X - S if S<X; 0 otherwise • Net Value:(X - S) - P if S<X; 0 - P otherwise

  9. 8. Put Option Positions: Value at Expiration + -P (short) 0 S X +P (long) _

  10. 9. Put/Call Parity: Synthetic Security Example • Combine the following positions:Long position in a stock (buy at price=P0)Short position in a call option (at exercise price=X)Long position in a put option (at exercise price=X) • +S-C+P=?

  11. 10. Put/Call Parity: Graphical +S + A Net Position 0 X S P0 +P _ -C

  12. 11. Put/Call Parity: Conceptual Formula • Combining the long position in a stock (+S), the short position in the call (-C) and long position in the put (+P) yields a risk free bond (+B) • I.E.: +S-C+P=Brf

  13. 12. Put/Call Parity: Numerical Example • Create a synthetic bond by taking the following positions: • Buy Microsoft stock at at price of $76 per share (+S). • Buy a put option with an exercise price (X) of $80 and term of one year. Price of the put is $6 (+P). • Sell a call option with an exercise price (X) of $80 and a term of one year. Price of the call is $4 (-C). • At the end of one year, you will sell the stock and close out on the option positions. Obviously, depending upon the price of the stock at the time, either you will exercise the put option or the call option will be exercised against you. What will your position look like at the end of one year from now?

  14. 13. Put/Call Parity: End of year cash flow as you close the position • If the price of Microsoft stock exceeds $80 per share (X) at the end of the year (e.g., suppose it is $86): • Sell the stock for $86 • Put option has zero value since S>X • Call option is exercised against you. You lose S-X, or $6. • Your net cash flow is $80 ($86-6) • If the price of the stock is less than $80 per share (X) at the end of the year (e.g., suppose it is $72) • Sell the stock for $72 • You exercise the put option and earn (X-S), or $8. • The call option is not exercised because S<X • Your net cash flow is $80 ($72 +$8) • As you can see, no matter what the outcome for the price of the stock, your cash flow will always be $80 (the exercise price on the options). • By simultaneously holding a long position in the put and short position in the call, with the same exercise price, you lock in your terminal cash flow at X, no matter what you paid for the stock.

  15. 14. Put/Call Parity: Arbitrage • The synthetic security you created was a risk free bond. • Cost of the bond: • Buy the stock at $76 • Buy the put option at $6 • Sell the call option at $4 • Total outlay $76+$6-$4 = $78 • Guaranteed cash return: $80 • Your net cash flow is always +$2 ($80-$78) • Rate of return: $2 / $78 = 2.56% • What do you do if the risk free Treasury rate is 5.5%?

  16. 15. Put/Call Parity: Arbitrage • Compare the two investments: • Synthetic bond earning 2.56% • Treasury bond earning 5.5% • Both provide risk free cash flows • The treasury bond is a superior investment. • I can create a guaranteed arbitrage profit if I do the following: • Short sell the synthetic bond. I can do this by taking the opposite position: i.e. Short sell the stock, sell the put option, buy the call option, or -S-P+C. I will receive $78 by doing this. • Invest the $78 in the t-bill earning 5.5%. • At the end of the year, I collect on the t-bill and close the synthetic position. It will have to pay out $80 to close the synthetic bond, for a net cash flow of -$2 ($78 - $80). • The cash flow from the t-bill is: $78 * 1.055 = $82.29, or a net of +$4.29. • I earn $2.29 without investing any of my own money. The more I do this, the more I make.

  17. Matching Models to the Environment 16. Hybrid Models Volatility Option Models Discounted Cash Flow Models Information

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