Presentation on theme: "Finansiell ekonomi 723g28 Linköpings University"— Presentation transcript:
1Finansiell ekonomi 723g28 Linköpings University Options and FuturesFinansiell ekonomi 723g28Linköpings University
2What is a Derivative?A derivative is an instrument whose value depends on, or is derived from, the value of another asset.Examples: futures, forwards, swaps, options, exotics…Obs: you may jump to slide #21 to start direct with options.
3How Derivatives are Used To hedge risksTo speculate (take a view on the future direction of the market)To lock in an arbitrage profitTo change the nature of a liabilityTo change the nature of an investment without incurring the costs of selling one portfolio and buying another4
4Options vs. Futures/Forwards A futures/forward contract gives the holder the obligation to buy or sell at a certain price at a certain date in the futureAn option gives the holder the right, but not the obligation to buy or sell at a certain price at a certain date in the future
5Foreign Exchange Quotes for GBP, (£) May 24, 2010 The forward price may be different for contracts of different maturities (as shown by the table)BidOfferSpot1.44071.44111-month forward1.44081.44133-month forward1.44101.44156-month forward1.44161.4422
6Long position and short position The party that has agreed to buy has a long positionThe party that has agreed to sell has a short position10
7ExampleOn May 24, 2010 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate ofThis obligates the corporation to pay $1,442,200 for £1 million on November 24, 2010What are the possible outcomes?
8Svenska termerForwards och Terminer • Spotkontrakt: en överenskommelse mellan två parter att utbyta något idag för ett specificerat pris, spotpriset. à vista marknad. • Terminskontrakt: en överenskommelse (skyldighet) mellan två parter att utbyta något för ett specificerat pris, terminspriset, vid en specifik framtida tidpunkt, lösendagen.
9Profit from a Long Forward Position (K= delivery price=forward price at the time contract is entered into)Payoff diagramProfitPrice of Underlying at Maturity, STK14
10Profit from a Short Forward Position (K= delivery price=forward price at the time contract is entered into)ProfitPrice of Underlyingat Maturity, STK15
11Futures ContractsAgreement to buy or sell an asset for a certain price at a certain timeSimilar to forward contracta forward contract is traded over the counter(OTC) (Skräddarsydd)a futures contract is standardized and traded on an exchange.CME GroupNYSE Euronext,BM&F (Sao Paulo, Brazil)TIFFE (Tokyo)
12Key Points About Futures They are settled dailyClosing out a futures position involves entering into an offsetting tradeMost contracts are closed out before maturity
13MarginsA margin is cash or marketable securities deposited by an investor with his or her brokerThe balance in the margin account is adjusted to reflect daily settlementMargins minimize the possibility of a loss through a default on a contract
14Pricing of forward Guld (commodities): F = (1 + rf + s) · S0 Finansiella tillgångar: F = (1 + rf) · S0S0 is the spot price.S is the storage costrf is risk free interest rateF is the forward price
15Examples of Futures Contracts Agreement to:Buy 100 oz. of US$1400/oz. in DecemberSell US$/£ in MarchSell 1,000 bbl. of US$90/bbl. in AprilOz: ounceBbl: barrel9
16Example : An Arbitrage Opportunity? Suppose that:The spot price of gold is US$1,400The 1-year forward price of gold is US$1,500The 1-year US$ interest rate is 5% per annumQ: What should be the 1-year forward price? Is there an arbitrage opportunity?18
17The Forward Price of Gold If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then F = S (1+r )T where r is the 1-year (domestic currency) risk-free rate of interest. In our examples, S = 1400, T = 1, and r =0.05 so that F = 1400(1+0.05) = 147020
18Hedging ExamplesAn investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1. The investor decides to hedge by buying 10 contracts16
19Value of Microsoft Shares with and without Hedging
20Some TerminologyOpen interest: the total number of contracts outstandingequal to number of long positions or number of short positionsSettlement price: the price just before the final bell each dayused for the daily settlement processTrading Volume : the number of trades in one day
21Forward Contracts vs Futures Contracts Private contract between 2 partiesExchange tradedNon-standard contractStandard contractUsually 1 specified delivery dateRange of delivery datesSettled at end of contractSettled dailyDelivery or final cashsettlement usually occursprior to maturityFORWARDSFUTURESSome credit riskVirtually no credit riskContract usually closed out16
22The right but not the obligation… OptionsThe right but not the obligation…Chapter 23 PPT OutlineCalls and PutsOption Values and ProfitReal OptionsBlack-Scholes Pricing Model2
23OptionsA call option is an option to buy a certain asset by a certain date for a certain price (the strike price)A put option is an option to sell a certain asset by a certain date for a certain price (the strike price)
25American vs. European Options An American option can be exercised at any time during its lifeA European option can be exercised only at maturityThe time value will be lost when you exercise prematurely.
26Option Value: Example Option values given an exercise price of $720 Exercise Price – The price at which the underlying security can be purchased (call option) or sold (put option). The exercise price is determined at the time the option contract is formed. Also known as the strike price.What are the payoff limits for call option buyers? Sellers?What are the payoff limits for put option buyers? Sellers?7
27Call option value (buyer) given a $720 exercise price. $120Share Price8
28$20 call option (buyer) given a $720 exercise price Call Option Profit$20 call option (buyer) given a $720 exercise priceCall option value$100Share Price8
29Call Option ValueCall option payoff (seller) given a $720 exercise price.Call option $ payoff$-120Share Price10
30$20 call option (seller) given a $720 exercise price: Call Option Profit$20 call option (seller) given a $720 exercise price:$-100Call option $ payoff$-120Share Price10
31Call Option: ExampleHow much must the stock be worth at expiration in order for a call holder to break even if the exercise price is $50 and the call premium was $4?
32Put option value (buyer) given a $720 exercise price: $120Share Price9
33$30 put option (buyer) given a $720 exercise price: Put Option Profit$30 put option (buyer) given a $720 exercise price:Put option value$90Share Price9
34Put Option ValuePut option payoff (seller) given a $720 exercise price.Share Price-$120Put option $ payoff11
35$30 put option (seller) given a $720 exercise price. Put Option Profit$30 put option (seller) given a $720 exercise price.-$90Share PricePut option $ payoff11
36Put Options: ExampleWhat is your return on exercising a put option which was purchased for $10 with an exercise price of $85? The stock price at expiration is $81.
37(Stock price - exercise price) or 0 Options ValueStock PriceUpper LimitLower Limit(Stock price - exercise price) or 0which ever is higher21
39Option ValuePoint A -When the stock is worthless, the option is worthless.Point B -When the stock price becomes very high, the option price approaches the stock price less the present value of the exercise price.Point C -The option price always exceeds its minimum value (except at maturity or when stock price is zero).The value of an option increases with both the variability of the share price and the time to expiration.
40Option Value Components of the Option Price 1 - Underlying stock price 2 - Strike or Exercise price3 - Volatility of the stock returns (standard deviation of annual returns)4 - Time to option expiration5 - Time value of money (discount rate)22
42Put-Call Parity: No Dividends Consider the following 2 portfolios:Portfolio A: call option on a stock + zero-coupon bond (or a deposit) that pays K at time TPortfolio B: Put option on the stock + the stock
43Values of Portfolios are the same at expiration (förfalldag) ST > KST < KPortfolio ACall optionST − KZero-coupon bondKTotalSTPortfolio BPut OptionK− STShare
44The Put-Call Parity Result Both are worth max(ST , K ) at the maturity of the optionsThey must therefore be worth the same today. This means that c + Ke -rT = p + S0
45Ex: put-call parity Suppose that What are the put option price? c + Ke -rT = p + S0p = c-S0 +Ke -rT= *EXP(-0,1*0,25)= 1,259c= 3S0= 31T = 0.25r = 10%K =30
46Bounds for European and American Put Options (No Dividends)
47Synthetic optionsTwo or more options combines together creates exotic options
48Option Value: profit diagram for a straddle Straddle - Long call and long put- Strategy for profiting from high volatilityLong callLong putStraddlePosition ValueShare Price18
49Option Value Straddle - Long call and long put - Strategy for profiting from high volatilityShare PricePosition ValueStraddleAn investor may take a long straddle position if he thinks the market is highly volatile, but does not know in which direction it is going to move.19
50Exotic options: a butterfly option A long butterfly position will make profit if the future volatility is lower than the implied volatility.The spread is created by buying a call with a relatively low strike (x1), buying a call with a relatively high strike (x3), and shorting two calls with a strike in between (x2).
51Long CallProfit from buying one European call option: option price = $5, strike price = $100, option life = 2 months302010-5708090100110120130Profit ($)Terminalstock price ($)
52Short CallProfit from writing one European call option: option price = $5, strike price = $100-30-20-105708090100110120130Profit ($)Terminalstock price ($)
53Long PutProfit from buying a European put option: option price = $7, strike price = $70302010-7706050408090100Profit ($)Terminalstock price ($)
54Short PutProfit from writing a European put option: option price = $7, strike price = $70-30-20-107706050408090100Profit ($)Terminalstock price ($)
55Payoffs from Options What is the Option Position in Each Case? K = Strike price, ST = Price of asset at maturityPayoffPayoffSTKPayoff
57Real options max(VT −D, 0) With the limited liability of the modern corporations, the shareholders´ equity can be regarded as a real option on the assets of the firm.The shareholder value of equity value ismax(VT −D, 0)where VT is the value of the firm and D is the debt repayment required.Thus the company can be considered as a call option on the firm value V at the strike price of D.
58Options on Real Assets Real Options - Options embedded in real assets Option to AbandonOption to Expand25
59Options on Financial Assets Executive Stock OptionsWarrantsConvertible BondsCallable BondsExecutive Stock Options – Long term call options given to executives as part of their compensation package.Warrants - Right to buy shares from a company at a stipulated price before a set date.Convertible Bond - Bond that the holder may exchange for a specific number of shares.Callable Bond - Bond that may be repurchased by the issuer before maturity at specified call price.26