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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

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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

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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

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Option Obligations

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

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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

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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

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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)

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Black-Scholes Option Pricing Model O C = P s [N(d 1 )] - S[N(d 2 )]e -rt

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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

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(d 1 )= ln + ( r + ) t PsSPsS v22v22 v t 32 34 36 38 40 Cumulative Normal Density Function N(d 1 )=

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Cumulative Normal Density Function

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

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

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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 ) = -.3070N(d 1 ) = 1 -.6206 =.3794

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

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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 ) = -.5056 N(d 2 ) = 1 -.6935 =.3065 (d 2 ) = d 1 -v t

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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

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

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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

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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 = 4 + 40 - 41 - (.10x 40 x.50) +.50 Op = 3 - 2 +.5 Op = $1.50

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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.

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

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Option Strategies Long Stock Bought stock @ Ps = 100

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

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

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

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

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Option Strategies Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27 P/LPs 27 30 24 -1.50 +1.50

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Option Strategies P/LPs 27 30 24 -1.50 +1.50 Synthetic Stock = Short Put & Long Call @ Oc = 1.50 Op=1.50 S=27 Ps=27

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

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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.

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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

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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

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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 2 120 (.6) 100 (.6) 90 (.4) NPV = 145 70 (.6) 50 (.4) 40 (.4)

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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 2 120 (.6) 100 (.6) 90 (.4) NPV = 162 150 (.4) Option Value = 162 - 145 = $17 mil

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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

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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

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How estimated call price changes as number of binomial steps increases No. of stepsEstimated value 148.1 241.0 342.1 541.8 1041.4 5040.3 10040.6 Black-Scholes40.5 Binomial vs. Black Scholes

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