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Unformatted text preview: Option price sensitivities Aureliano Buend a Lecture 8  BlackScholes Greeks BUSI 588, Fall 2011 Diego Garc a KenanFlagler Business School UNC at Chapel Hill September 21st, 2011 c Diego Garc a, BUSI 588, KenanFlagler, Fall 2011 Lecture 8  BlackScholes Greeks 1 / 27 Option price sensitivities Aureliano Buend a Outline 1 Option price sensitivities Replication: and Time decay and options The other Greeks 2 Aureliano Buend a Hedging Gamma and Theta Handouts today: Class slides. Homework 3 solutions. Case 8 solutions. c Diego Garc a, BUSI 588, KenanFlagler, Fall 2011 Lecture 8  BlackScholes Greeks 2 / 27 Option price sensitivities Aureliano Buend a Exotic derivatives Problem 4 in HW3 presented a strange derivative. 1156 2720 6400 170 400 25 It looks cheap, but if we simply buy it, then we risk that the stock goes up twice. Key: buy the replicating portfolio of the derivative (cost 1156). This allows us to be hedged completely and pocket the difference. c Diego Garc a, BUSI 588, KenanFlagler, Fall 2011 Lecture 8  BlackScholes Greeks 3 / 27 Option price sensitivities Aureliano Buend a The main Greeks The BlackScholes option pricing formula (no dividends today) C t = S t N ( x ) K (1 + r f ) T t N ( x T t ) where x = log( St ) log K (1+ r f ) T t T t + 1 2 T t . The Greeks are a bunch of partial derivatives: Delta, = C t / S t . Gamma, = 2 C t / S 2 t . Theta, = C t / t . Recall: partial derivatives measure how something changes with respect to changes in a variable, keeping everything else constant . c Diego Garc a, BUSI 588, KenanFlagler, Fall 2011 Lecture 8  BlackScholes Greeks 4 / 27 Option price sensitivities Aureliano Buend a The main Greeks in English Delta, , change in option price per unit change in the underlying asset price. Gamma, , change in per unit change in the underlying asset price. Theta, , change in option price per unit change in time. Vega, change in option price per unit change in volatility. Rho, , change in option price per unit change in the interest rate. Omega, , percent change in option price per 1% percent change in underlying asset price. Key: partial derivatives means we keep everything else constant. c Diego Garc a, BUSI 588, KenanFlagler, Fall 2011 Lecture 8  BlackScholes Greeks 5 / 27 Option price sensitivities Aureliano Buend a  Delta The change in the option price per unit change in the underlying asset C = C t S t = N ( x ); P = C 1 . It is the number of units of the underlying asset that we need to hold in order to replicate the options payoffs....
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This note was uploaded on 11/25/2011 for the course BUSI 588 taught by Professor Staff during the Fall '10 term at UNC.
 Fall '10
 Staff
 Business, Derivatives

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