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Options and Futures

Options and Futures. Finansiell ekonomi 723g28 Linköpings University. What 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…

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Options and Futures

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  1. Options and Futures Finansiellekonomi 723g28 LinköpingsUniversity

  2. What 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.

  3. How Derivatives are Used • To hedge risks • To speculate (take a view on the future direction of the market) • To lock in an arbitrage profit • To change the nature of a liability • To change the nature of an investment without incurring the costs of selling one portfolio and buying another

  4. Options 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 future • An 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

  5. Foreign Exchange Quotes for GBP, (£) May 24, 2010 The forward price may be different for contracts of different maturities (as shown by the table)

  6. Long position and short position • The party that has agreed to buyhas a long position • The party that has agreed to sell has a short position

  7. Example • On 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 of 1.4422 • This obligates the corporation to pay $1,442,200 for £1 million on November 24, 2010 • What are the possible outcomes?

  8. Svenska termer Forwards 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.

  9. Profit Price of Underlying at Maturity, ST Profit from a Long Forward Position (K= delivery price=forward price at the time contract is entered into) Payoff diagram K

  10. Profit Price of Underlying at Maturity, ST Profit from a ShortForward Position (K= delivery price=forward price at the time contract is entered into) K

  11. Futures Contracts • Agreement to buy or sell an asset for a certain price at a certain time • Similar to forward contract • a forward contract is traded over the counter (OTC) (Skräddarsydd) • a futures contract is standardized and traded on an exchange. CME Group NYSE Euronext, BM&F (Sao Paulo, Brazil) TIFFE (Tokyo)

  12. Key Points About Futures • They are settled daily • Closing out a futures position involves entering into an offsetting trade • Most contracts are closed out before maturity

  13. Margins • A margin is cash or marketable securities deposited by an investor with his or her broker • The balance in the margin account is adjusted to reflect daily settlement • Margins minimize the possibility of a loss through a default on a contract

  14. Pricingof forward • Guld (commodities): F = (1 + rf + s) · S0 • Finansiella tillgångar: F = (1 + rf) · S0 S0 is the spot price. S is the storagecost rf is risk freeinterestrate F is the forward price

  15. Examples of Futures Contracts Agreement to: • Buy 100 oz. of gold @ US$1400/oz. in December • Sell £62,500 @ 1.4500 US$/£ in March • Sell 1,000 bbl. of oil @ US$90/bbl. in April Oz: ounce Bbl: barrel

  16. Example : An Arbitrage Opportunity? Suppose that: The spot price of gold is US$1,400 The 1-year forward price of gold is US$1,500 The 1-year US$ interest rate is 5% per annum Q: What should be the 1-year forward price? Is there an arbitrage opportunity?

  17. The 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) = 1470

  18. Hedging Examples • An 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 contracts

  19. Value of Microsoft Shares with and without Hedging

  20. Some Terminology • Open interest: the total number of contracts outstanding • equal to number of long positions or number of short positions • Settlement price: the price just before the final bell each day • used for the daily settlement process • Trading Volume : the number of trades in one day

  21. Forward Contracts vs Futures Contracts FORWARDS FUTURES Private contract between 2 parties Exchange traded Non-standard contract Standard contract Usually 1 specified delivery date Range of delivery dates Settled at end of contract Settled daily Delivery or final cash Contract usually closed out settlement usually occurs prior to maturity Some credit risk Virtually no credit risk

  22. Options The right but not the obligation…

  23. Options • A 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)

  24. Option Obligations: the writer of the option

  25. American vs. European Options • An American option can be exercised at any time during its life • A European option can be exercised only at maturity • The time value will be lost when you exercise prematurely.

  26. Option Value: Example Option values given an exercise price of $720 What are the payoff limits for call option buyers? Sellers? What are the payoff limits for put option buyers? Sellers?

  27. Call Option Value Call option value (buyer) given a $720 exercise price. Call option value $120 720 840 Share Price

  28. Call Option Profit $20 call option (buyer) given a $720 exercise price Call option value $100 720 840 Share Price

  29. Call Option Value Call option payoff (seller) given a $720 exercise price. 720 840 Call option $ payoff $-120 Share Price

  30. Call Option Profit $20 call option (seller) given a $720 exercise price: 720 840 $-100 Call option $ payoff $-120 Share Price

  31. Call Option: Example How 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?

  32. Put Option Value Put option value (buyer) given a $720 exercise price: Put option value $120 600 720 Share Price

  33. Put Option Profit $30 put option (buyer) given a $720 exercise price: Put option value $90 Share Price 600 720

  34. Put Option Value Put option payoff (seller) given a $720 exercise price. Share Price -$120 Put option $ payoff 600 720

  35. Put Option Profit $30 put option (seller) given a $720 exercise price. -$90 Share Price Put option $ payoff 600 720

  36. Put Options: Example What 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. Upper Limit Lower Limit (Stock price - exercise price) or 0 which ever is higher Options Value Stock Price

  38. Option Value

  39. Option Value • Point 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.

  40. Option Value Components of the Option Price 1 - Underlying stock price 2 - Strike or Exercise price 3 - Volatility of the stock returns (standard deviation of annual returns) 4 - Time to option expiration 5 - Time value of money (discount rate)

  41. Call Option Value

  42. Put-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 T • Portfolio B: Put option on the stock + the stock

  43. Values of Portfolios are the same at expiration (förfalldag)

  44. The Put-Call Parity Result • Both are worth max(ST, K ) at the maturity of the options • They must therefore be worth the same today. This means thatc + Ke -rT= p + S0

  45. Ex: put-call parity Suppose that • What are the put option price? c + Ke -rT= p + S0 p = c-S0 +Ke -rT =3-31+30*EXP(-0,1*0,25) = 1,259

  46. Bounds for European and American Put Options (No Dividends)

  47. Synthetic options Two or more options combines together creates exotic options

  48. Long put Long call Straddle Option Value: profit diagram for a straddle Straddle - Long call and long put - Strategy for profiting from high volatility Position Value Share Price

  49. Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Straddle Position Value Share Price An 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.

  50. Exotic options: a butterfly option • A butterfly x3 x2 x1 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).

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