Corporate Financial Theory Lecture 10

Derivatives Insurance Risk Management Lloyds Ship Building Jet Fuel Cost Predictability Revenue Certainty 1

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

Derivative Uses Arbitrage Speculation Hedging

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

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 1

Options 5

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 2

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 3

Option Value The value of an option at expiration is a function of the stock price and the exercise price. 6

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 7

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 4

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) 22

Black-Scholes Option Pricing Model Option Value Black-Scholes Option Pricing Model 23

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 7

Black-Scholes Option Pricing Model 7

Black-Scholes Option Pricing Model N(d1)= 8

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Cumulative Normal Density Function 9

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 11

.3070 = .3 = .00 = .007 11

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 12

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 13

Put Price = Call + EX - P - Carrying Cost + Div. Put - Call Parity Put Price = Call + EX - P - Carrying Cost + Div. or Put = Call + EX(e-rt)– Ps - Carrying Cost + Div. Carrying cost = r x EX x t 14

Put - Call Parity 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? OP = OC + EX - P - Carrying Cost + Div. OP = 4 + 40 - 41 - (.10x 40 x .50) + .50 OP = 3 - 2 + .5 Op = $1.50 15

Warrants & Convertibles 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. 17

Option Strategies Option Strategies are viewed via charts. How do you chart an option? Profit Loss Stock Price 18

Option Strategies Long Stock Bought stock @ Ps = 100 19

Option Strategies Long Call Bought Call @ Oc = 3 S=27 Ps=30 20

Option Strategies Short Call Sold Call @ Oc = 3 S=27 Ps=30 21

Option Strategies Long Put = Buy Put @ Op = 2 S=15 Ps=13 22

Option Strategies Short Put = Sell Put @ Op = 2 S=15 Ps=13 23

Option Strategies Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 + 1 . 5 P / L P s 2 4 2 7 3 - 1 . 5 28

Option Strategies Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 + 1 . 5 P / L P s 2 4 2 7 3 - 1 . 5 29

Option Strategies Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 30

Option Strategies 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 36

Dilution Exercise of a warrant increases the number of shares outstanding. The dilution factor reflects that fact.

Expanding the binomial model to allow more possible price changes 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.