2 Learning ObjectivesUnderstand key terms related to options and options marketsCompute payoffs and profits to option holders and writersCalculate potential profits from various options strategiesDescribe the put-call parity relationship
3 DerivativeA derivative is a security who’s value is dependent on another assetsBase Asset Ex: commodity prices, bond and stock prices, or market index valuesDerivatives are contingent claimsTheir payoffs depend on the value of another securities.Options are a specific type of derivativeThe holder has the right, but not the obligation, to buy or sell a given quantity of an asset on (or before) a given date, at a price agreed upon today.
4 Options: Calls and Puts Call: The owner of a call has the right, but not the obligation, to BUY an asset in the future at the strike or exercise priceValue decreases as the strike price increasesPut: The owner of a put has the right, but not the obligation, to SELL an asset in the future at the strike or exercise priceValue increases with the strike priceValue of both calls and puts increases with time to expiration, WHY?
5 Rights and Obligations Buyer:Gets all the RightsSeller:Gets all the ObligationsCallsRight to Buy the assetIs obliged to Sell the assetPutsRight to Sell the assetIs obliged to Buy the asset
6 Futures ContractsAn agreement made today regarding the delivery of an asset (or in some cases, its cash value) at a specified delivery or maturity date for an agreed-upon price (futures price) to be paid at contract maturityLong position: Take delivery at maturityShort position: Make delivery at maturity
7 Comparison Option Futures Contract Right, but not obligation, to buy or sell; option is exercised only when it is profitableOptions must be purchasedBoth sides have an obligationLong position must buy at the futures priceShort position must sell at futures priceFutures contracts are entered into without cost
8 The Option ContractThe purchase price of the option is called the premium.Stock options cover 100 shares & premium is on a per share basisSellers (or Writers) of options receive premium.If the Holder (or Buyer) exercises the option, the Writer must deliver (call) or take delivery (put) of the underlying asset.
9 Options Terminology Exercising the Option Using the optionStrike Price or Exercise PriceThe price specified by the optionSpot PriceThe market priceExpiration DateThe option’s maturity dateEuropean & American optionsEuropeans can only be exercised at expiration.Americans can be exercised at any time up to expiration. BUT NEVER ARE
10 Options TerminologyIn-the-Money: Exercising the option results in a profitCall: exercise price < market pricePut: exercise price > market priceAt-the-Money: Exercising the option results in 0 profitexercise price = market priceOut-of-the-Money: Exercising the option results in a lossCall: market price < exercise pricePut: market price > exercise price
11 Call Payoff (Intrinsic Value) Call PayoffsHolder of the optionPays the premium at time=0Has the right to exercise the option at time=TNotationStock Price at T = STT is maturity, t is any other timeExercise Price = XDon’t ExerciseExerciseCall Payoff (Intrinsic Value)ST - X
12 Call Holder Payoff and Profit Value of the Call at T: CT = Max [ST – X, 0]What is the value of the Call at t?ST >XST < XCTST – XProfitST - X - Ct-Ct
13 Payoff and Profit to Call Option at Expiration What is the strike price?What is the premium?
14 What is the value of a Call at t? At maturity CT = Max [ST – X, 0]Would you be willing to sell for St-X at t?Hint: What could happened to the stock price?Time value is the premium a rational investor will pay above an options intrinsic valueThis base on the likelihood that the stock price will move making the option more valuableTime Value = Option Price – Intrinsic Value
15 Call Writer Payoff and Profit ST >XST < XExercise Cost-(ST – X)Profit-(ST - X) + CtCt
16 Payoff and Profit to Call Writers at Expiration
17 Calls: A Zero Sum Game Call Option If ST < X If ST > X Decision No exerciseExerciseOption Payoff (holder)ST – XOption Profit (holder)-C(ST – X) – COption Payoff (writer)- (ST – X)Option Profit (writer)+CC - (ST – X)
18 Profit and Loss on a Call A February 2013 call on IBM with an exercise price of $195 was selling on January 18, 2013, for $3.65.The option expires on the third Friday of the month, or February 15, 2013.If the price of IBM on Feb 15, 2013 is $194, what is the call worth?
19 Profit and Loss on a Call (cont.) Suppose IBM sells for $197 at expirationRemember: strike = $195, premium = $3.65What is the value of the option?Call Intrinsic value = stock price-exercise priceWill the option be exercised?What is the Profit/Loss on this investment?Profit = Final value – Original investmentWhat must the price of IBM be for the option to break-even?
20 Call Option ProblemAt time=0 you buy a call option on IBM for $ The option gives you the right to buy 100 shares of IBM stock at time=T at $65What is the payoff to you if ST = $70?What is the payoff for the writer if ST = $70?What is the payoff to you if ST = $60?What is the payoff for the writer if ST = $60?
21 Puts Gives holder the right (but not the obligation) to sell an asset: At the exercise or strike priceOn or before the expiration dateExercise the option to sell the underlying asset if market value < strike.
22 Put Payoff (Intrinsic Value) Puts PayoffsHolder of the optionPays the premium at time=0Has the right to exercise the option at time=TNotationStock Price at T = STExercise Price = XDon’t ExerciseExercisePut Payoff (Intrinsic Value)X - ST
23 Put Holder Payoff and Profit Value of the Call at T: PT = Max [X - ST , 0]ST <XST > XPayoffX - STProfitX - ST - Pt-Pt
25 Put Writer Payoff and Profit ST <XST > XExercise Cost-(X - ST)Profit-(X - ST) + PtPt
26 Puts: Another Zero Sum Game Put OptionST < XIf ST > XDecisionExerciseNo ExerciseOption Payoff (holder)X – STOption Profit (holder)(X-ST) - P-POption Payoff (writer)- (X-ST)Option Profit (writer)+P - (X-ST)+P
27 Profit and Loss on a PutConsider a February 2013 put on IBM with an exercise price of $195, selling on January 18, for $5.00.Option holder can sell a share of IBM for $195 at any time until February 15.If IBM sells for $196, what is the put worth?
28 Profit and Loss on a Put Suppose IBM’s price at expiration is $188. What is the value of the option?Put value = Exercise price- Stock priceWill the option be exercised?What is the Profit/Loss on this investment?Profit = Final value – Original investmentWhat is the HPR?
29 Put Option ProblemAt time=0 you buy a put option on ITT stock for $ The option gives you the right to sell 100 shares of ITT stock at time=T at $50What is the payoff to you if ST = $55?What is the payoff to the put seller if ST = $55?What is the payoff to you if ST = $45?What is the payoff to the put seller if ST = $45?
30 Option versus Stock Investments Could a call option strategy be preferable to a direct stock purchase?Suppose you think a stock, currently selling for $100, will appreciate.A 6-month call costs $10 (contract size is 100 shares).You have $10,000 to invest.
31 Option versus Stock Investment Investment Strategy InvestmentEquity only Buy $100 (100 shares) $10,000Options only Buy $10 (1,000 options) $10,000Options + Buy $10 (100 options) $1,000T-Bills Buy 3% Yield $9,000
34 Strategy ConclusionsThe all-option portfolio, B, responds more than proportionately to changes in stock value; it is levered.Portfolio C, T-bills plus calls, shows the insurance value of options.C ‘s T-bill position cannot be worth less than $9270.Some return potential is sacrificed to limit downside risk.
35 Combining OptionsPuts and calls can serve as the building blocks for more complex option contractsCan be used to manage riskThis is financial engineeringAllows you to tailor the risk-return profiles to meet your client’s desiresEx: Protective Puts: Underlying asset and put are combined to guarantee a minimum valuationPut is insurance against stock price declines.
37 Covered Calls Purchase stock and write calls against it. Call writer gives up any stock value above X in return for the initial premium.If you planned to sell the stock when the price rises above X anyway, the call imposes “sell discipline.”
39 Straddle The straddle is a bet on volatility. Long straddle: Buy call and put with same exercise price and maturity.To make a profit, the change in stock price must exceed the cost of both options.You make money on a large price shift in either directionThe writer of a straddle is betting the stock price will not change much.
41 SpreadA spread is a combination of two or more calls (or two or more puts) on the same stock with differing exercise prices or times to maturity.Some options are bought, whereas others are sold (written)A bullish spread is a way to profit from moderate stock price increasesEX. Buy a call with a strike of $20 and sell a call with a strike price of $25
43 Put Call Parity P –C = PV (X) - St This is the relation between a put and call with the same exercise price (E) and maturityIt comes from replicating portfolios:The payoffs from buying a call and selling a put is the same as the payoffs from buying the stock and borrowing the PV of the exercise priceP –C = PV (X) - St
45 Portfolios Portfolio 1: Buy a call and Write a put Portfolio 2: Buy the stock but Borrow PV (X)Levered Equity positionsIf the payoffs are the same the price must be the same-C+P = -S0 + Xe-rTC-P = S0 – Xe-rT
46 Proof by Counter Example Assume that:Stock Price = Call Price = 14Put Price = Risk Free = 5%Maturity = 6 months Strike Price = 105Portfolio 1 costs= -9Portfolio 2 costs:e-5 = -7.59Two different costs for the sample payoffs → ABRITRAGE
48 Put Call Parity Example What is the value of a put with an exercise price of $51, if the stock is currently trading at $49. The price of the corresponding call option is $4.65. According to put-call parity, if the effective annual risk-free rate of interest is 4% and there are three months until expiration, what should be the value of the put?FYI: It doesn’t matter if compounding is monthly or quarterly