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Options and Futures: Risk Management

Options and Futures: Risk Management. 730g81 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…. Size of OTC and Exchange-Traded Markets.

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Options and Futures: Risk Management

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  1. Options and Futures:Risk Management 730g81 Linköpings University

  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…

  3. Size of OTC and Exchange-Traded Markets Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market

  4. The Lehman Bankruptcy Lehman’s filed for bankruptcy on September 15, 2008. one of the biggest bankruptcy in US history • Lehman was an active participant in the OTC derivatives markets and got into financial difficulties because it took high risks and found it was unable to roll over its short term funding • It had hundreds of thousands of transactions outstanding with about 8,000 counterparties • Unwinding these transactions has been challenging for both the Lehman liquidators and their counterparties

  5. How Derivatives are Used • To hedge risks • To speculate (take a bet on the future direction of the market) • To lock in an arbitrage profit (forwards) • 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

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

  7. Long position and short position • The party that has agreed to buy has a long position • The party that has agreed to sell has a short position

  8. 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 $1442200 for £1 million on November 24, 2010 • What are the possible outcomes?

  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) K

  10. Profit Price of Underlying at Maturity, ST Profit from a Short Forward 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 • Whereas a forward contract is traded over the counter, a futures contract is traded on an exchange. CME Group NYSE Euronext, BM&F (Sao Paulo, Brazil) TIFFE (Tokyo) …

  12. 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

  13. Forward price • If the spot price of a commodity is S and the forward price for a contract deliverable in T years is F, then F= S (1+r )T • Essentially a forward is a implicit loan.

  14. Gold price: An Arbitrage Opportunity? Suppose you observe: the spot price of gold is US$1400 The 1-year forward price of gold is US$1500 The 1-year US$ interest rate is 5% per annum, Is there an arbitrage opportunity?

  15. 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. S = 1400, T = 1, and r=0.05 so that F = 1400(1+0.05) = 1470$ Yes, there is an arbitrage opportunity. Borrow at 5%, buy gold now and cover it with the forward contract. You net 1500-1470=30 $ per contract!

  16. Options • A call option is the right but not the obligationto buy a certain asset by a certain date for a certain price (the strike price) • A put option is the right but not the obligation to sell a certain asset by a certain date for a certain price (the strike price)

  17. The writer of the option has obligations to buy and sell

  18. 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

  19. Google Call Option Prices(June 15, 2010; Stock Price is bid 497.07, offer 497.25) Source: CBOE

  20. Google Put Option Prices (June 15, 2010; Stock Price is bid 497.07, offer 497.25); Source: CBOE

  21. Options vs. Futures/Forwards • A futures/forward contract gives the holder the obligation to buy or sell at a certain price • An option gives the holder the right but not the obligation to buy or sell at a certain price

  22. Hedging Examples • A German company will pay £10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract • 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

  23. Value of Microsoft Shares with and without Hedging The investor will do better when the price goes below 26,5$.

  24. Example: Speculation vs. hedging An investor with $2,000 to invest feels that a stock price will increase over the next 2 months. The current stock price is $20 and the price of a 2-month call option with a strike of 22.50 is $1 • What are the alternative strategies?

  25. Speculation • He buys 100 shares of the stock. 100*20$=2000 • He buys 2000 call option 2000*1=2000$. If the market price increases to more than 22,5 during the 2 months, the call option will have a higher payoff than the plain stocks. • Suppose the stock price is 25 at the expiration date: the call option has gained (25-22,5)*2000=5000$ or a 150% profit, while the first case gives 500/2000=25% • Suppose the market price is lower than 22,5$, the investor loses all, that is, -100%.

  26. Hedge Funds • Hedge funds are not subject to the same rules as mutual funds and cannot offer their securities publicly. • Mutual funds must • disclose investment policies, • makes shares redeemable at any time, • limit use of leverage Hedge funds are not subject to these constraints. • Hedge funds use complex trading strategies are big users of derivatives for hedging, speculation and arbitrage

  27. 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 • Margin call: when the margin is below the required minimum, it is subject to margin call. The client is obliged to increase the margin to the minimun.

  28. Example of a Futures Trade • An investor takes a long position in 2 December gold futures contracts on June 5 • contract size is 100 oz. • futures price is US$1250 • initial margin requirement is US$6,000/contract (US$12,000 in total) • maintenance margin is US$4,500/contract (US$9,000 in total)

  29. Options 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

  30. Key Points About Futures • They are settled daily. (marked to the market) • Closing out a futures position involves entering into an offsetting trade • Most contracts are closed out before maturity

  31. Delivery • If a futures contract is not closed out before maturity, it is usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses. • A few contracts (for example, those on stock indices and Eurodollars) are settled in cash. • When there is cash settlement, contracts are traded until a predetermined time. All are then declared to be closed out.

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

  33. Option Value • The value of an option at expiration is a function of the stock price and the exercise price (S-X for call and X-S for put). Example Option values (exercise price = $720)

  34. Option Value Call option value (graphic) on Google Stock on option expiration date, exercise price=$720. $120 Call optionvalue 720 840 SharePrice

  35. Option Value Put option value (graphic) on Google stock on option expiration date. ( exercise price=$720 ) Put option value $120 600 720 Share Price

  36. Option Value Call option payoff (to the writer) on Google stock ($720 exercise price) Call option $ payoff 720 Share Price

  37. Option Value Put option payoff (to the writer ) on Google Stock exercise price=$720 . Putoption$ payoff 720 Share Price

  38. Option Value Protective Put - Long stock and long put LongStock Protective Put Position Value Long Put Share Price

  39. Option Value Protective Put - Long stock and long put Protective Put PositionValue Share Price

  40. 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

  41. 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.

  42. Combinations of Options (cont'd) Strangle A portfolio that is long a call option and a put option on the same stock with the same exercise date but the strike price on the call exceeds the strike price on the put

  43. Textbook Example 20.5

  44. Textbook Example 20.5

  45. Combinations of Options Butterfly Spread A portfolio that is long two call options with differing strike prices, and short two call options with a strike price equal to the average strike price of the first two calls While a straddle strategy makes money when the stock and strike prices are far apart, a butterfly spread makes money when the stock and strike prices are close.

  46. Figure 20.6 Butterfly Spread

  47. 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).

  48. Figure 20.7 Portfolio Insurance The plots show two different ways to insure against the possibility of the price of Amazon stock falling below $45. The orange line in (a) indicates the value on the expiration date of a position that is long one share of Amazon stock and one European put option with a strike of $45 (the blue dashed line is the payoff of the stock itself). The orange line in (b) shows the value on the expiration date of a position that is long a zero-coupon riskfree bond with a face value of $45 and a European call option on Amazon with a strike price of $45 (the green dashed line is the bond payoff).

  49. Option Value Call buyer profit diagram on Google stock– strike price = $720 and option price= $80.50 Long call Break even Position Value -80.50 720 800.50 Share Price

  50. Option Value Put seller profit diagramwith strike price=$720 and option price of $71.20 Break even Short put Position Value +71.20 648.80 720 Share Price

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