1. Lec 9 Intro to Option contracts1 Lec 1: Intro to Options Contracts (Hull Ch 9) Call Options. If you buy a CALL option on IBM, 1. You have the right, but not the obligation, to buy 100 shares of IBM at a specified price (Exercise Price). 2. The price of the call is known as Call Premium. 3. Call will expire at a specified date (Expiration Date). American vs. European Options Example: Buy a European December 70 call on IBM for $5. Expiration date = 3rd Friday of December Exercise price = K = $70 Call premium (C 0 ) = $5 ( x 100) = $500

2. 2Lec 9 Intro to Option contracts Cash Flow Analysis: At t = 0 (now) you pay $500 to seller of call. at t = Expiration, Possible scenarios: Spot Price (S T )Exercise?Value of { +C T } Gain or Loss ➀ $50 No0-$500 ➁ 60 No0-$500 ➂ 70 Yes/No0-$500 ➃ 80 Yes$1,000+ 500 ➄ 90 Yes$2,000+1,500

3. 3Lec 9 Intro to Option contracts Question: Why buy a call?, Why not buy the stock itself? Assume S 0 = $70. You expect stock price to ↑ to S T = $90. (N.B. This is the buyer's subjective expectation). You have two choices: Buy stock for $70, or buy a call for $5. In December, the possible outcomes are: S T Exercise?Value of { C T }ROR on {+C}ROR on { +S} ➀ $50 NO0-100%-28.6% ➁ 60 NO0-100-14% ➂ 70 No/Yes0-1000 ➃ 80 Yes$10+100%14% ➄ 90 Yes$2028.6%

4. 4Lec 9 Intro to Option contracts So, what do we learn from this exercise? 1. Long Call is appropriate for a VERY bullish investor 2. {+C} requires a (relatively) small investment (equivalent to borrowing 93% of S 0 = $70). 3. Max Loss = $500 (some degree of Downside Protection) 4. BUT {+C} is much more risky than {+S} Q: buyer expects the price to go from $70 to $90. Does the seller share this belief? What about the market? Is the market Bullish or Bearish? What do you think about the following ad?... Another market that has our attention is for Heating Oil. For the past 10 years, between the August low and the seasonal high, the price of heating oil increases by about 20¢ a gallon for potential profit of over $80,000 on just a $10,000 investment. If you follow this ad, you will become rich! Buy low (in summer) and Sell high (in winter).

5. 5Lec 9 Intro to Option contracts Sell a call (write a call, “naked” call writer, short call, -C) If you sell a call, you have the obligation (but not the right) to sell 100 shares of IBM stock for $X, if the "option holder" (the buyer) decides to exercise the call. Example: Sell a December 70 call on IBM stock for $5. Expiration date = 3rd Friday of December Exercise price = $70 Call premium (C 0 ) = $5 ( x 100) Cash Flow Analysis: At t = 0 you (Short, call writer) receive $500 from call buyer

6. 6Lec 9 Intro to Option contracts At T = Expiration. Possible scenarios: Question: Suppose S T = $90 and the call writer already owned the stock, would the loss still be $20? Spot Price (S T )Exercise?Value of { -C T }Gain or Loss ➀ $50 No0+$500 ➁ 60 No0+$500 ➂ 70 Yes/No0+$500 ➃ 80 Yes- $1,000 - 500 ➄ 90 Yes- $2,000 - 1,500

7. 7Lec 9 Intro to Option contracts So, why would you sell a call? 1. Receive Cash immediately! 2. You are Bearish on the stock. (a good “Conservative” Bearish strategy). Notes: Excluding commissions, the options market is a zero-sum game. Including transactions costs, it is a negative-sum game. The call premium reflects the "markets" expectation of the future stock price. Hence, to be successful at this game you must know more than the market (or be lucky!).

8. 8Lec 9 Intro to Option contracts PUT Options. Buy a Put (long a put, +P) If you buy a PUT option on BAC, 1. You have the right, but not the obligation, to sell 100 shares of BAC at a specified price (Exercise Price). 2. The put price is known as the Put Premium. 3. Put will expire at a specified date (Expiration Date). Example: Buy a European December 70 Put on BAC for $3. Expiration date = 3rd Friday of December Exercise price = $70 Put premium (P 0 ) = $3 ( x 100) = $300

9. 9Lec 9 Intro to Option contracts Cash Flow Analysis: At t = 0 (now) you pay $300 to seller of Put option. at t = Expiration, Possible scenarios: So, why Buy a put? 1. You are Very Bearish (“Aggressive Strategy”), and 2. Alternative to a short sale Spot Price (S T )Exercise?Value of {+P T }Gain or Loss ➀ $50 Yes$20$17 ➁ 60 Yes$10$7 ➂ 70 Yes/No0-$3 ➃ 80 No0 - 3 ➄ 90 No0 - 3

10. 10Lec 9 Intro to Option contracts Sell a Put (Write a Put, write a “naked” put, short put, -P) If you Short a put (i.e. sell a put), you have the obligation, but not the right, to buy 100 shares of XYZ stock at a strike price of $X, for a specified period of time. Example: Sell a December 70 PUT on BAC stock for $3. Expiration date = 3rd Friday of December Exercise price = $70 Put premium (P 0 ) = $3 ( x 100) Cash Flow Analysis: At t = 0 you (Writer) receive $300

11. 11Lec 9 Intro to Option contracts At Expiration time (December). Possible scenarios: Why sell a put? 1. Receive cash now, and (if stock price ↑ ) there is no cost later. 2. It is a “Conservative Bullish” Strategy 3. You actually want to buy the stock. For example, Let S 0 = $70; if the stock price falls below $70 put is exercised, you pay $70 and receive the stock. Actual purchase price = 70 - 3 = $67 (< S 0 ). Spot Price (S T )Exercise?Value of {+P T }Gain or Loss ➀ $50 Yes- $20- $17 ➁ 60 Yes- $10- $7 ➂ 70 Yes/No0+ $3 ➃ 80 No0 + 3 ➄ 90 No0 + 3

12. 12Lec 9 Intro to Option contracts In sum: If you expect the stock price to go up: Buy a call (Aggressive Bullish strategy) Sell a put (less aggressive, a “Conservative Bullish” strategy). If you expect price to go down: Buy a put (Aggressive Bearish strategy) Sell a call (less aggressive, “Conservative Bearish” bet). Remember: -C = obligation to sell+C = right to buy -P = obligation to buy+P = right to sell Alternatively: LONG ( + ) SHORT ( - ) CALLright to BUYmay have to SELL PUTright to SELLmay have to BUY

13. 13Lec 9 Intro to Option contracts Put-Call Parity, Law of One-Price (How to Create Synthetic Securities ) Create a Synthetic Long-Stock position. Example: Long Call(X=40), Short Put(X=40), Buy a bond(FV = $40) If S T > $40, Call is in the money. Use $40 from the bond to exercise call. Put is worthless. You own stock, just like if you bought the stock itself. If S T < $40, Call is worthless. Put is in the money, You are obligated to buy the stock for $40. Again, you own stock. Spot Price (S T ) {+C} {-P} {+B}Total CF $300- $10$40 $30 350-5$40 35 400 0$40 40 4550$40 45 50100$40 50

14. 14Lec 9 Intro to Option contracts Alternative intuition: Call captures stock price increases. Put captures stock price decreases. Bond is needed to buy the stock at expiration. {+S} = { +C(X), -P(X), +Bond(FV = $X) }

15. 15Lec 9 Intro to Option contracts Synthetic Long Call: {+S, +P, - Bond(FV=X=$40) }={+C} Example: If S T = $30, Sell the stock thru the put, receive X=$40. Use it to payback $40 bond CF T =0 (same as a call) If S T = $50, Put is worthless. Sell the stock in spot market. Use $40 to payback loan CF T = +50 – 40 = $10 (same as the call) Spot Price (S T ) {+S} {+P} {-B}Total CF $30 $10-$40 $0 35 5-40 0 40 0-40 0 45 0-40 5 50 0-40 10

16. 16Lec 9 Intro to Option contracts Synthetic T-Bill (i.e. bond) Long. (earn risk-free rate) {+B} = { +S, -C, +P} X = $40 = face value of bond. If S T ↑ >40, put is worthless. Call is in the money ∴ exercised. Hand over stock, receive $40. Is S T ↓ <40, call is worthless. Put is in the money ∴ exercise it. Hand over stock to put holder and receive $40. Thus, we end up with $40 just as if we had bought a bond. Spot Price (S T ) {+S} {-C} {+P}Total CF $30 0 $10 $40 35 05 40 00 45 -50 40 50 -100 40

17. 17Lec 9 Intro to Option contracts Points to ponder: 1) The common foundation for these synthetic securities is the Put-Call Parity Relationship: {+S, +P} = {+C, +B} 2. Hence, the following statements are equivalent: +S = + C - P + B +C = + S + P - B +P = - S + C + B +B = + S - C + P 2) By the law of one price the price today of each asset on left hand side must equal price of portfolio on right hand side. 3) To preclude arbitrage, Price of {+B} must = Price of a T-Bill (maturity = life of option). i.e., the ROR on {+B} = {+S, -C, +P} must be the risk-free rate!

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