Basic thoughts about options. Stein W. Wallace Centre for Advanced Study Norwegian Academy of Science and Letters

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1 Basic thoughts about options Stein W. Wallace Centre for Advanced Study Norwegian Academy of Science and Letters

2 What is an option? The possibility to observe the outcome of a random event, and then do something (if you so wish). An option provides flexibility, and flexibility has value. An option usually comes at a cost

3 The right to buy a share (a call) Random event: The value of the share at some point in time Cost: The price of the option Flexibility: You can secure an upper bound on the cost of the share

4 The right to sell a share (a put) Random event: The value of the share at some point in time. Cost: The price of the option Flexibility: You can secure a lower bound on the value of your share

5 The size of the platform deck Random event: The properties of the oil field at some point in the future. Cost: The cost of the extra deck space Flexibility: The possibility to adopt to new information about field properties (size, sand, water)

6 The size of a lot Random event: Future demand Cost: The extra price of the larger lot Flexibility: The ability to expand production at the same site

7 New technology Random event: The success of a certain technology in the future Cost: Buying / developing / deploying the technology Flexibility: The ability to use the technology if it is a success

8 Training more personnel than you need for a special task Random event: People are sick Cost: Extra cost of training Flexibility: Your trouble if a trained person is ill is less serious

9 Evaluation of an option = ? 0 Share Bond Option to buy Strike price =

10 Buy 1 share and sell m options (to buy) for price c 20-mc 25-3m 16 The portfolio is risk free if 25-3m = 16 Hence, sell m=3 options A risk free portfolio must have the same value as a bond 20-3c=16=25-3*3 making c=4/3 So the option is worth 4/

11 Evaluation of an option = /3? 0 Share Bond Option to buy Strike price =

12 Exchange rate risk In one year, your are to sell a product for 2 USD, but in NOK this is either 16 or 25. How can you secure this transaction measured in NOK? Forward value of two dollars 1 1 Bond 25-22=3 1.15? 0 Option to buy two dollars

13 Example 1 - insurance of exchange risk You are to sell a product for 2 USD (=16 or 25 NOK) next year Two possibilities: Sell one forward contract on 2 USD to receive 18. Next year, use your income in USD to fulfil the contract Sell 3 options now to receive Next period you get 25-3*3=16 if the world is up and 16 if it is down. Net effect (1/1.1)16=

14 Speculation Assume you have 20. Show the effect of investing in a share (worth 16 or 25) options to buy the share at 22 no discounting

15 Example 2 - speculation 25 1 share options

16 Speculation 2 You need 20 now. Explain the difference between Obtaining the money by selling a share short (and buying it back later) Selling options to buy the share at

17 Example 3 - you need money Sell a share (you do not have) Pay to buy back share 45 Sell 15 options to buy 20 Pay to buyer of options

18 To be learned Deterministic models will not work Always a question after the realization of the random event Consistency in data No arbitrage

19 Determinism To find the value of an option (= to find out if you should buy it) you must include future decisions (= will it be exercised?) Generally: Problems with deterministic models

20 Deterministic approach If the price goes up: Do not sell the options (before the price goes up). If the price goes down: Sell options (before it happens). We need decisions following the realization of the random event

21 Consistency If the option has any other value than the one we found, we have arbitrage (the possibility to make something out of nothing). Generally: Consistency in data

22 Consistency What if the price of the option is 2 > 4/3? Buy one share:20 Sell 3 options: 6 Net cost: 14 Sell share: 25 Pay for options: 9 Net income: 16 Sell share: 16 Net income: 16 You get a certain profit of 2 (without any risk) - arbitrage

23 Real and financial options Financial: The right to perform a financial transaction. Buy a share Sell a bond Real: The right to make a real investment Build a building Buy a new car

24 What do we mean by option theory? The proper evaluation of flexibility The mathematical theory of options (Black- Sholes) Be careful about which one you mean!

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