CORPORATE FINANCIAL THEORY Lecture 10

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

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

 Arbitrage  Speculation  Hedging Derivative Uses

 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 Definition

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

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

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 =2

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

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

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

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)

Black-Scholes Option Pricing Model Option Value

O C - Call Option Price P - Stock Price N(d 1 ) - Cumulative normal density function of (d 1 ) PV(EX) - Present Value of Strike or Exercise price N(d 2 ) - Cumulative normal density function of (d 2 ) 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 Black-Scholes Option Pricing Model

N(d 1 )= Black-Scholes Option Pricing Model

Cumulative Normal Density Function

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

.3070=.3 =.00 =.007

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

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

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

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? O P = O C + EX - P - Carrying Cost + Div. O P = (.10x 40 x.50) +.50 O P = O p = $1.50

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.

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

Long Stock Bought Ps = 100 Option Strategies

 Long Call Bought Oc = 3 S=27 Ps=30

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

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

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

Option Strategies Synthetic Stock = Short Put & Long Oc = 1.50 Op=1.50 S=27 Ps=27 P/LPs

Option Strategies Synthetic Stock = Short Put & Long Oc = 1.50 Op=1.50 S=27 Ps=27 P/LPs

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

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

Dilution

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