Corporate Financial Theory

1. Corporate FinancialTheory Lecture 10

2. Derivatives Insurance Risk Management Lloyds Ship Building Jet Fuel Cost Predictability Revenue Certainty

3. Underlying Assets • Stocks (example) • Bonds • Indices • Commodities (examples for metal and ag.) • Currencies • Weather • Carbon emissions • Radio bandwidth

4. Derivative Uses • Arbitrage • Speculation • Hedging

5. Derivatives Definition • Derivatives are financial instruments whose price and value derive from the value of the underlying assets or other variables (ISDA) • Derivatives are a “zero sum game” • Example: Insurance

6. Derivatives & Options Historical Topics (Internal to the Corp) 1 - Capital Budgeting (Investment) 2 - Capital Structure (Financing) Today We are leaving Internal Corporate Finance We are going to Wall St & “Capital Markets” Options - financial and corporate Options are a type of derivative

7. Options

8. Options Terminology • Derivatives - Any financial instrument that is derived from another. (e.g.. options, warrants, futures, swaps, etc.) • Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time. • Call Option - The right to buy a security at a specified price within a specified time. • Put Option - The right to sell a security at a specified price within a specified time. • Option Premium - The price paid for the option, above the price of the underlying security. • Intrinsic Value - Diff between the strike price and the stock price • Time Premium - Value of option above the intrinsic value

9. Options Terminology Exercise Price - (Striking Price) The price at which you buy or sell the security. Expiration Date - The last date on which the option can be exercised. American Option - Can be exercised at any time prior to and including the expiration date. European Option - Can be exercised only on the expiration date. All options “usually” act like European options because you make more money if you sell the option before expiration (vs. exercising it). 3 vs. 70-68=2

10. Option Value The value of an option at expiration is a function of the stock price and the exercise price.

11. Option Value The value of an option at expiration is a function of the stock price and the exercise price. Example - Option values given a exercise price of $85

12. Options CBOE Success 1 - Creation of a central options market place. 2 - Creation of Clearing Corp - the guarantor of all trades. 3 - Standardized expiration dates - 3rd Friday 4 - Created a secondary market

13. Option Value Components of the Option Price 1 - Underlying stock price 2 - Striking 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)

14. Option Value Black-Scholes Option Pricing Model

15. Black-Scholes Option Pricing Model OC- Call Option Price P - Stock Price N(d1) - Cumulative normal density function of (d1) PV(EX) - Present Value of Strike or Exercise price N(d2) - Cumulative normal density function of (d2) r - discount rate (90 day comm paper rate or risk free rate) t - time to maturity of option (as % of year) v - volatility - annualized standard deviation of daily returns

16. Black-Scholes Option Pricing Model

17. Black-Scholes Option Pricing Model N(d1)=

19. Cumulative Normal Density Function

20. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

21. .3070 = .3 = .00 = .007

22. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

23. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

24. Put Price = Call + EX - P - Carrying Cost + Div. Put - Call Parity or Put = Call + EX(e-rt)– Ps - Carrying Cost + Div. Carrying cost = r x EX x t

25. Example ABC is selling at $41 a share. A six month May 40 Call is selling for $4.00. If a May $ .50 dividend is expected and r=10%, what is the put price? Put - Call Parity OP = OC + EX - P - Carrying Cost + Div. OP=4 + 40 - 41 - (.10x 40 x .50) + .50 OP =3 - 2 + .5 Op = $1.50

26. Review Topics (not going over in class) Warrant - a call option with a longer time to expiration. Value a warrant as an option, plus factor in dividends and dilution. Convertible - Bond with the option to exchange it for stock. Value as a regular bond + a call option. Won’t require detailed valuation - general concept on valuation + new option calc and old bond calc. Warrants & Convertibles

27. Option Strategies are viewed via charts. How do you chart an option? Option Strategies Profit Loss Stock Price

28. Option Strategies • Long Stock Bought stock @ Ps = 100

29. Long Call Bought Call @ Oc = 3 S=27 Ps=30 Option Strategies

30. Short Call Sold Call @ Oc = 3 S=27 Ps=30 Option Strategies

31. Long Put = Buy Put @ Op = 2 S=15 Ps=13 Option Strategies

32. Short Put = Sell Put @ Op = 2 S=15 Ps=13 Option Strategies

33. Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 Option Strategies + 1 . 5 0 P / L P s 3 0 2 4 2 7 - 1 . 5 0

34. Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 Option Strategies + 1 . 5 0 P / L P s 3 0 2 4 2 7 - 1 . 5 0

35. Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 Option Strategies

36. Why? 1 - Reduce risk - butterfly spread 2 - Gamble - reverse straddle 3 - Arbitrage - as in synthetics Arbitrage - If the price of a synthetic stock is different than the price of the actual stock, an opportunity for profit exists. Recall discussion on Real Options Option Strategies

37. Dilution

38. Binomial vs. Black Scholes Expanding the binomial model to allow more possible price changes 1 step 2 steps 4 steps (2 outcomes) (3 outcomes) (5 outcomes) etc. etc.