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 Obligations

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

Options 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 O C = P s [N(d 1 )] - S[N(d 2 )]e -rt

Black-Scholes Option Pricing Model O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C - Call Option Price P s - Stock Price N(d 1 ) - Cumulative normal density function of (d 1 ) S - 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

(d 1 )= ln + ( r + ) t PsSPsS v22v22 v t Cumulative Normal Density Function N(d 1 )=

Cumulative Normal Density Function

(d 1 )= ln + ( r + ) t PsSPsS v22v22 v t Cumulative Normal Density Function (d 2 ) = d 1 -v t

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

Call Option Example What is the price of a call option given the following?. P = 36r = 10%v =.40 S = 40t = 90 days / 365 (d 1 ) = ln + ( r + ) t PsSPsS v22v22 v t (d 1 ) = N(d 1 ) = =.3794

Call Option.3070=.3 =.00 =.007

Call Option Example What is the price of a call option given the following?. P = 36r = 10%v =.40 S = 40t = 90 days / 365 (d 2 ) = N(d 2 ) = =.3065 (d 2 ) = d 1 -v t

Call Option Example What is the price of a call option given the following?. P = 36r = 10%v =.40 S = 40t = 90 days / 365 O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C = 36[.3794] - 40[.3065]e - (.10)(.2466) O C = $ 1.70

Put - Call Parity Put Price = Oc + S - P - Carrying Cost + Div. Carrying cost = r x S x t

Example IBM 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

Example IBM 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 + S - P - Carrying Cost + Div. Op = (.10x 40 x.50) +.50 Op = Op = $1.50

Warrants & Convertibles Review Ch 22 (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

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

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.

Corporate Options Ch 21 3 types of “Real Options” 1 - The opportunity to make follow-up investments. 2 - The opportunity to abandon a project 3 - The opportunity to “wait” and invest later. Value “Real Option” = NPV with option - NPV w/o option

Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Use a discount rate of 10% Corporate Options

Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Corporate Options Year 0Year 1Year (.6) 100 (.6) 90 (.4) NPV = (.6) 50 (.4) 40 (.4)

Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Corporate Options Year 0Year 1Year (.6) 100 (.6) 90 (.4) NPV = (.4) Option Value = = $17 mil

Reality Decision trees for valuing “real options” in a corporate setting can not be practically done by hand. We must introduce binomial theory & B-S models Corporate Options

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

How estimated call price changes as number of binomial steps increases No. of stepsEstimated value Black-Scholes40.5 Binomial vs. Black Scholes