Lect 18 221 web

Lect 18 221 web - Managerial Finance Lecture 18 Options...

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1 Managerial Finance Lecture 18 Options Pricing, Executive Compensation and Option Sensitivities Class 17. Summary The prices of European call and put options are related by put-call parity American calls & puts always have non negative “ time value American calls & puts always have non-negative American calls should not be exercised early unless they pay dividends American puts may be exercised early when interest on strike is high Binomial model: calls, puts and all other derivative securities can be priced by no-arbitrage arguments Steps: 1. Find the cash-flows of the options 2. Find existing assets ( shares and B bonds) that yield the same cash-flows 3. Find the price of those existing assetsand you are done ! Call option : is always between 0 and 1 and T-Bill is between 0 and -K Put option : is always between 0 and -1 and T-Bill is between 0 and K 2
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2 Plan Option pricing models: Binomial option pricing model • Multi-period model • Dynamic trading allow us to replicate payoffs Black-Scholes option pricing • One formula (calculator) for pricing European-style options Option applications: Employee stock options Andrea Korbes and Yahoo! 3 Multi-Period Model What if the Call Option expires in two periods? Call exercise price = 90 Solve for the call price by working backwards We know the final value of the Initial stock price = 74.07 Stock price moves up or down each period We know the final value of the call at each node Solve for the call price in earlier periods using the binomial model S = 100 S = 135 C = 45 4 S = 45 S = 33.33 S = 15 S = 74.07 C = ?
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3 Multi-Period Model We know the value of the option in the second period : - Top branch: 1-period analysis 2. Find a combination of shares and B bonds that yields the same cash-flows: - Bottom branch: zero Solve for the first period 1. What are the cash-flows (value) of the options (from 2 nd period)? “Up”: = 28.57 “Down” = 0 “Up” scenario: 100 x + 1.05 B = 28.57 “Down” scenario: 33.33 x + 1.05 B = 0 Two equations, two unknowns, solve for and B Get: = 0.4285 and B=-13.60 3. Find the price of the replicating portfolio: 74.07 x + B = Price of option 31.74 -13.60 = 18.14 Done 5 Stock price today S 0 74.07 S u 100 S d 33.33 C u 28.57 C d 0 Replicating portfolio is a dynamic strategy Self-financed dynamic strategy: Borrow and buy shares (increase ) as stock price rises Sell shares and pay off debt as stock price falls Value Holdings Buy Stock = 31.74 Bond = -13.60 Total = 18.14 Value Portfolio 42.85 -14.28 28.57 After 50.00 -21.43 28.57 Borrow 7.15 .0715 shares S = 74.07 C= 18 14 S = 100 S = 135 S = 45 C = 45 C = 0 C = 28.57 = 0 . 50 B = -21.43 Final Value 67.50 -22.50 45.00 Final Value 22.50 22 50 6 C = 18.14 = 0 . 4285 B = -13.60 S = 33.33 S = 15 C = 0 C = 0 = 0 B = 0 Final Value 14.28 -14.28 0.00 -22.50 0.00
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4 Making the Model Realistic Binary up or down movements are not realistic Stock prices do not behave that way on an annual/month/daily basis Yt t h dl i l it i f d ti i d Yet the model is more realistic for a one-second time period: • Jump up or down (one-tick or small change in price) Making the model realistic:
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This note was uploaded on 01/08/2012 for the course MS&E 245G taught by Professor Perez-gonzalas during the Fall '11 term at Stanford.

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Lect 18 221 web - Managerial Finance Lecture 18 Options...

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