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## Mechanics of Options Markets Chapter 8

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**OPTIONS ARE CONTRACTS**Two parties: Seller and buyer A contract: Specifying the rights and obligations of the two parties. An underlying asset: a financial asset, a commodity or a security, that is the basis of the contract.**Assets UnderlyingExchange-Traded Options(p. 190)**• Stocks • Foreign Currency • Stock Indices • Futures • Options • Bonds**OPTIONS BASICS**A contingent claim: The option’s value is contingent upon the value of the underlying asset Two Types of Options: A Call: THE RIGHT TO BUY THE UNDERLYING ASSET A Put: THE RIGHT TO SELL THE UNDERLYING ASSET**CALL Buyer holderlong.**In exchange for making a payment of money, the call premium, the call buyer has the right to BUY a specified quantity of the underlying asset for the exercise (strike) price before the option’s expiration date.**PUT Buyer holderlong.**In exchange for making a payment of money, the put premium, the put buyer has the right to SELL a specified quantity of the underlying asset for the exercise (strike) price before the option’s expiration date.**Call Sellerwritershort.**In exchange for receiving the call’s premium, the Call sellerhas the obligation to SELL the underlying asset for the predetermined exercise (strike) price upon being served with an exercise notice during the life of the option, I.e., before the option expires.**Put Sellerwritershort.**In exchange for receiving the put premium, the Put sellerhas the obligation to BUY the underlying asset for the predetermined exercise (strike) price upon being served with an exercise notice during the life of the option, I.e., before the option expires.**The two main types of Options (PUTS and CALLS)**• American Options • exercisable any time before expiration • European Options • exercisable only on expiration date**OPTIONS NOTATIONS:**S – The underlying asset’s market price K - The exercise (strike) price t – The current date T – The expiration date T -t The time till expiration c, p European call, put premiums C, P American call, put premiums**Options definitions using the above notation:**LONG CALL On date t, the BUYER of a call option pays the call’s market price, ct, Ct, and holds the right to buy the underlying asset at the strike price, K, before the call expires on date T. (or on T, if the call is European). Thus => the call holder expects the price of the underlying asset, St, to increase during the life of the option contract.**SHORT CALL**On date t, the SELLER of a call option receives ct, Ct, and must sell the underlying asset for K, if the option is exercised by its holder before the option expires on date T. Thus => expects the price of the underlying asset, St, to remain below or at the exercise price, K, during the option’s life. This way the writer keeps the premium.**LONG PUT**On date t, the BUYER of a put option pays pt, Pt, and holds the right to sell the underlying asset for K before the put expires on date T. Thus => expects the market price of the underlying asset, St, to decrease during the life of the put.**SHORT PUT**On date t, the SELLER of a put receives pt, Pt, and must buy the underlying asset for K if the put is exercised by its holder before the put expires on date T. Thus => expects the market price of the underlying asset, St, to remain at or above K during the life of the put. This way the put writer keeps the premium.**A numerical example: LONG CALL**C(S= $47.27share;K = $45/share;T-t = .5yrs) Ct= $5.78/share On date t, the BUYER of this call pays the call’s market price, $5.78/share, and holds the right to buy the underlying asset at the strike price, K = $45/share, before the call expires at T, half a year from now (at T, if the call is European). Thus => the call holder expects the price of the underlying asset, St = $47.27/share, to increase during the life of the option contract.**A numerical example: SHORT CALL**C( S=$47.27share;K =$45/share; T-t = .5yrs) Ct= $5.78/share On date t, the SELLER of this call receives $5.78/share and must sell the underlying asset for K = $45/share, if the option is exercised by its holder before the option expires at T, half a year from now. Thus => hopes the price of the underlying asset, currently St = $47.27/share, remains below or at the exercise price, K = $45/share, during the option’s life of half a year and hence, keep the premium ct = $5.78/share**A numerical example: LONG PUT**p(S= $47.27share;K = $45/share;T-t = .5yrs) pt= $2.25/share On date t, the BUYER of this put pays the market price of pt = $2.25/share and holds the right to sell the underlying asset for K = $45/share before the put expires half a year from now, at T. Thus => expects the market price of the underlying asset, St= $47.27/share, to decrease during the half a year life span of the put.**A numerical example: SHROT PUT**p(S =$47.27share;K = $45/share;T-t = .5yrs) pt= $2.25/share On date t, the SELLER of this put receives the market premium pt=$2.25/share and must buy the underlying asset for K = $45 if the put is exercised by its holder before the put expires half a year from now at T. Thus => expects the market price of the underlying asset, St = $47.27/share to remain at or above K = $45 during the life span of the put and to keep the premium, pt = $2.25/share.**$**47.27K = 45 t = nowT = .5yr S**More terminology**• Premium =The option Market Price • Premium = [Intrinsic value + extrinsic value] • Intrinsic value: • Calls Max{0, St - K) ≥ 0 • Puts Max{0, K - St) ≥ 0 • Extrinsic value (time value): • Premium – Intrinsic value**At-the-money**St = K In this case the intrinsic value for both calls and puts is zero: St - K = K - St = 0 and the premium consists of the Extrinsic (time) value only. PREMIUM = 0 + extrinsic value**In-the-money**CallsPuts St > K St < K or: St – K > 0 K – St > 0 The Intrinsic value of an option that is in-the money is positive.**Out-of-the-money**CallsPuts St < K St > K or St - K< 0 K – St < 0 In this case the intrinsic value is zero and the premium consists of the extrinsic (time) value only. PREMIUM = 0 + extrinsic value**The next table shows the market prices (premiums) of calls**and puts on IBM On Friday NOV 30 2007 = t When IBM was trading at St = $105/share. Notice that there where options traded for several expiration dates and for a wide range of strike prices. Blanks mean that the option did not trade on NOV 30 2007 OR did not exist.**Options Markets**• OTC options: • Over the counter (OTC) • Meaning • Not on an organized exchange. • 2. Exchange traded options: • An organized exchange • Options clearing corporation (OCC)**WHEN OPTIONS ARE TRADED ON**THE OTC TRADERS BEAR Credit risk Operational risk Liquidity risk**Credit Risk:**Does the other party have the means to pay? Operational Risk: Will the other party deliver the commodity? Will the other party pay?**Liquidity Risk.**Liquidity = the speed (ease) with which investors can buy or sell securities (commodities) in the market. In case either party wishes to get out of its side of the contract, what are the obstacles? How to find another counterparty? It may not be easy to do that. Even if you find someone who is willing to take your side of the contract, the other party may not agree.**THE Option Clearing Corporation (OCC)(p. 198)**The exchanges understood that there will exist no efficient options markets without contracts standardization and an absolute guarantee to the options’ holders – that the market is default-free, so they have created the: OPTIONS CLEARING CORPORATION (OCC) The OCC is a nonprofit corporation**THE OPTION CLEARING CORPORATION PLACE IN THE MARKET**EXCHANGE CORPORATION OPTIONS CLEARING CORPORATION CLEARING MEMBERS NONCLEARING MEMEBRS OCC MEMBER CLIENTES BROKERS**The OCC’s**absolute guarantee The holders of calls and puts will always be able to exercise their options if they so wish to do!!!**The absolute guarantee**The OCC’s absolute guarantee provides traders with a default-free market. Thus, any investor who wishes to engage in options buying knows that there will be no operational default.**The OCC**Also, clears all options trading. Maintains the list of all long and short positions. Matches all long positions with short positions. Hence, the total sum of all options traders positions must be ZERO at all times.**The OCC**Maintains the accounting books of all trades. Charges fees to cover costs Assigns Exercise notices Given the OCC’s guarantee, the market is anonymous and traders only have to offset their positionsin order to come out of the market. The OCC has no control over the market prices. These are determined by trader’s supply and demand.**The OCC**The OCC’s absolute guarantee together with matching all short and long trading makes the market very liquid. 1 – traders are not afraid to enter the market 2 – traders can quit the market at any point in time by OFFSETTING their original position.**OFFSETTING POSITIONS**• A trader with a LONG position who wishes to get out of the market MAY: • Exercise, or • open a SHORT position with equal number of the same options. • Example:Suppose • LONG 5, SEP, $85, IBM puts; p0 = $4/share • This position must be offset by • SHORT 5, SEP, $85, IBM puts; p1 = $3/share • Cash flows: -$2,000 + $1,500 = -$500.**OFFSETTING POSITIONS**A trader with a SHORT position who wishes to get out of the market MUST open a LONG position with equal number of the same options. Example:Suppose SHORT 25, JAN, $75, BA calls; c = $7/share This position must be offset by LONG 25, JAN, $75, BA calls; c = $5/share Cash flows: $17,500 - $12,500 = $5,000.**THE OCC Standardization:**Contract size: the number of units of the underlying asset covered in one option. Exersice prices: Mostly, increments of $2.5, $5.00 and $10.00. Exercise notice and assignment procedures Delivery sequence.**THE OCC Standardization:**• Expiration dates: Saturday, immediately following the third Friday of the expiration month. • The basic expiration cycles: • [JAN APR JUL OCT] • [FEB MAY AUG NOV] • [MAR JUN SEP DEC]**A Review of Some Financial Economics Principles**Arbitrage: A market situation whereby an investor can make a profit with: no equity and no risk. Efficiency: A market is said to be efficient if prices are such that there exist no arbitrage opportunities. Alternatively, a market is said to be inefficient if prices present arbitrage opportunities for investors in this market.**Valuation: The current market value (price) of any project**or investment is the net present value of all the future expected cash flows from the project. One-Price Law: Any two projects whose cash flows are equal in every possible state of the world have the same market value. Domination: Let two projects have equal cash flows in all possible states of the world but one. The project with the higher cash flow in that particular state of the world has a higher current market value and thus, is said to dominate the other project.**The Holding Period Rate of Return (HPRR):**Buy shares of a stock on date t and sell them later on date T. While holding the shares, the stock has paid a cash dividend in the amount of $D/share. The Holding Period Rate of Return HPRR is:**Example:**St = $50/share ST = $51.5/share DT-t = $1/share T = t + 73days.**Risk-Free Asset: is a security of investment whose return**carries no risk. Thus, the return on this security is known and guaranteed in advance. Risk-Free Borrowing And Landing: By purchasing the risk-free asset, investors lend their capital and by selling the risk-free asset, investors borrow capita at the risk-free rate.**The One-Price Law:**There exists only one risk-free rate in an efficient economy. Proof: By contradiction. Suppose two risk-free rates exist in a market and R > r. Since both are free of risk, ALL investors will try to borrow at r and invest the money borrowed in R, thus assuring themselves the difference. BUT, the excess demand For borrowing at r and excess supply of lending (investing) at R will change them. Supply = demand only when R = r.**Compounded Interest (p. 76)**Any principal amount, P, invested at an annual interest rate, R, compounded annually, for n years would grow to: An = P(1 + R)n. If compounded Quarterly: An = P(1 +R/4)4n.**In general:**Invest P dollars in an account which pays an annual interest rate R with m compounding periods every year. The rate in every period is R/m. The number of compounding periods is nm. Thus, P grows to: An = P(1 +R/m)mn.**An = P(1 +R/m)mn.**Monthly compounding becomes: An = P(1 +R/12)12n and daily compounding yields: An = P(1 +R/365)365n.