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

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)
Bid
Offer
Spot
1.4407
1.4411
1-month forward
1.4408
1.4413
3-month forward
1.4410
1.4415
6-month forward
1.4416
1.4422

6. 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 10

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
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 from a Long Forward Position (K= delivery price=forward price at the time contract is entered into)
Payoff diagram
Profit
Price of Underlying at Maturity, ST K 14

10. Profit from a Short Forward Position (K= delivery price=forward price at the time contract is entered into)
Profit
Price of Underlying
at Maturity, ST K 15

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. Pricing of forward Guld (commodities): F = (1 + rf + s) · S0
Finansiella tillgångar: F = (1 + rf) · S0
S0 is the spot price.
S is the storage cost
rf is risk free interest rate
F is the forward price

15. Examples of Futures Contracts
Agreement to:
Buy 100 oz. of US$1400/oz. in December
Sell US$/£ in March
Sell 1,000 bbl. of US$90/bbl. in April
Oz: ounce
Bbl: barrel 9

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? 18

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 20

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 16

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
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
settlement usually occurs
prior to maturity
FORWARDS
FUTURES
Some credit risk
Virtually no credit risk
Contract usually closed out 16

22. The right but not the obligation…
Options
The right but not the obligation…
Chapter 23 PPT Outline
Calls and Puts
Option Values and Profit
Real Options
Black-Scholes Pricing Model 2

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 option5

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
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

27. Call option value (buyer) given a $720 exercise price.
$120
Share Price 8

28. $20 call option (buyer) given a $720 exercise price
Call Option Profit
$20 call option (buyer) given a $720 exercise price
Call option value
$100
Share Price 8

29. Call Option Value
Call option payoff (seller) given a $720 exercise price.
Call option $ payoff
$-120
Share Price 10

30. $20 call option (seller) given a $720 exercise price:
Call Option Profit
$20 call option (seller) given a $720 exercise price:
$-100
Call option $ payoff
$-120
Share Price 10

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 (buyer) given a $720 exercise price:
$120
Share Price 9

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
$90
Share Price 9

34. Put Option Value
Put option payoff (seller) given a $720 exercise price.
Share Price
-$120
Put option $ payoff 11

35. $30 put option (seller) given a $720 exercise price.
Put Option Profit
$30 put option (seller) given a $720 exercise price.
-$90
Share Price
Put option $ payoff 11

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. (Stock price - exercise price) or 0
Options Value
Stock Price
Upper Limit
Lower Limit
(Stock price - exercise price) or 0
which ever is higher 21

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) 22

41. Call Option Value 22

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)
ST > K
ST < K
Portfolio A
Call option
ST − K
Zero-coupon bond K
Total ST
Portfolio B
Put Option
K− ST
Share

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 that c + 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
= *EXP(-0,1*0,25)
= 1,259
c= 3
S0= 31
T = 0.25
r = 10%
K =30

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

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

48. Option Value: profit diagram for a straddle
Straddle - Long call and long put
- Strategy for profiting from high volatility
Long call
Long put
Straddle
Position Value
Share Price 18

49. Option Value Straddle - Long call and long put
- Strategy for profiting from high volatility
Share Price
Position Value
Straddle
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. 19

50. Exotic 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).

51. Long Call
Profit from buying one European call option: option price = $5, strike price = $100, option life = 2 months 30 20 10 -5 70 80 90
100
110
120
130
Profit ($)
Terminal
stock price ($)

52. Short Call
Profit from writing one European call option: option price = $5, strike price = $100
-30
-20
-10 5 70 80 90
100
110
120
130
Profit ($)
Terminal
stock price ($)

53. Long Put
Profit from buying a European put option: option price = $7, strike price = $70 30 20 10 -7 70 60 50 40 80 90
100
Profit ($)
Terminal
stock price ($)

54. Short Put
Profit from writing a European put option: option price = $7, strike price = $70
-30
-20
-10 7 70 60 50 40 80 90
100
Profit ($)
Terminal
stock price ($)

55. Payoffs from Options What is the Option Position in Each Case?
K = Strike price, ST = Price of asset at maturity
Payoff
Payoff ST K
Payoff

56. The Black-Scholes-Merton Formulas

57. Real 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 is
max(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.

58. Options on Real Assets Real Options - Options embedded in real assets
Option to Abandon
Option to Expand 25

59. Options on Financial Assets
Executive Stock Options
Warrants
Convertible Bonds
Callable Bonds
Executive 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